Shane Michael Eaton. Copyright by Shane Michael Eaton, 2008

Transcription

1 CONTRASTS IN THERMAL DIFFUSION AND HEAT ACCUMULATION EFFECTS IN THE FABRICATION OF WAVEGUIDES IN GLASSES USING VARIABLE REPETITION RATE FEMTOSECOND LASER by Shane Michael Eaton A thesis submitted in conformity with the requirements for the degree of Doctorate of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto Copyright by Shane Michael Eaton, 2008

2 Abstract Contrasts in thermal diusion and heat accumulation eects in the fabrication of waveguides in glasses using variable repetition rate femtosecond laser Shane Michael Eaton Doctorate of Philosophy Graduate Department of Electrical and Computer Engineering University of Toronto 2008 A variable (0.2 to 5 MHz) repetition rate femtosecond laser was applied to delineate the role of thermal diusion and heat accumulation eects in forming low-loss optical waveguides in borosilicate glass across a broad range of laser exposure conditions. For the rst time, a transition from thermal diusion-dominated transport at 200-kHz repetition rate to strong heat accumulation at 0.5 to 2 MHz was observed to drive signicant variations in waveguide morphology, with rapidly increasing waveguide diameter that accurately followed a simple thermal diusion model over all exposure variables tested. Amongst these strong thermal trends, a common exposure window of 200-mW average power and 15-mm/s scan speed was discovered across the range of 200-kHz to 2-MHz repetition rates for minimizing insertion loss despite a 10-fold drop in laser pulse energy. Waveguide morphology and thermal modeling indicate that strong thermal diusion eects at 200 khz give way to a weak heat accumulation eect at 1-µJ pulse energy for generating low loss waveguides, while stronger heat accumulation eects above 1-MHz repetition rate oered overall superior guiding. The waveguides were shown to be thermally stable up to 800 C, showing promise for high temperature applications. Using a low numerical aperture (0.4) lens, the eect of spherical aberration was reduced, enabling similar low-loss waveguides over an unprecedented 520- µm ii

3 depth range, opening the door for multi-level, three-dimensional, optical integrated circuits. In contrast to borosilicate glass, waveguides written in pure fused silica under similar conditions showed only little evidence of heat accumulation, yielding morphology similar to waveguides fabricated with low repetition rate (1 khz) Ti-Sapphire lasers. Despite the absence of heat accumulation in fused silica owing to its large bandgap and high melting point, optimization of the laser wavelength, power, repetition rate, polarization, pulse duration and writing speed resulted in uniform, high-index contrast waveguide structures with low insertion loss. Optimum laser exposure recipes for waveguide formation in borosilicate and fused silica glass were applied to fabricate optical devices such as wavelength-sensitive and insensitive directional couplers for passive optical networks, buried and surface microuidic and waveguide networks for lab-on-a-chip functionality, and narrowband grating waveguides for sensing. iii

4 Contents Acknowledgements Published Work List of Acronyms xxii xxiv xxix 1 Introduction 1 2 Background Fabrication of waveguides in glass Planar lightwave circuit technology Femtosecond laser writing of waveguides Interaction of femtosecond laser pulses with transparent materials Free electron plasma formation Relaxation and modication Propagation eects Linear propagation Nonlinear propagation Glass composition Waveguide theory Solution to Maxwell's equations for optical bers Evanescent coupling iv

5 3 Experimental Femtosecond laser system IMRA femtosecond ber laser Beam delivery system Micromachining station Second harmonic generation Autocorrelation Sample preparation Waveguide characterization Microscope observation Fiber-based waveguide characterization Insertion loss Mode prole measurement Coupling loss Propagation loss Refracted near eld prolometer Waveguide fabrication in borosilicate glass Heat accumulation versus thermal diusion eects Heat diusion and accumulation model Waveguide diameters Cross sectional refractive index proles Waveguide processing window Repetition rate, scan speed and average power v

6 4.2.2 Pulse duration and polarization Spectral response of insertion loss Spherical aberration Thermal stability of waveguides Summary Waveguide fabrication in fused silica glass Static laser exposures Waveguide processing window Optimization of wavelength Optimization of polarization Optimization of pulse duration Spectral response of insertion loss Summary Device fabrication Directional coupler Wavelength demultiplexer Broadband power splitter Fused silica devices Summary Discussion Comparison of waveguides in fused silica and borosilicate glasses Comparison with other literature results Signicance of work vi

7 8 Conclusion 153 A 158 vii

8 List of Tables 2.1 Thermal, structural and optical properties of glasses studied. All properties recorded at room temperature (25 C) [84] Commercial lasers available for waveguide fabrication. Italicized systems were unavailable at the time time of laser purchase for this thesis work (2003) Second harmonic conversion eciency and focal length at dierent repetition rates Deconvolution factor for determining pulse width from autocorrelation width APE PulseCheck settings for IMRA laser Cameras for mode proling at telecom wavelengths [9294] Exposure conditions, MFD and IL of lowest loss waveguides written in fused silica at repetition rates of 0.25, 0.5, 1 and 2-MHz repetition rate (522-nm wavelength). Sample length 2.5 cm. Laser polarization was parallel to the scan direction Insertion loss and mode eld diameter (1550-nm wavelength) as a function of writing polarization for 1-MHz repetition rate, 175-nJ pulse energy and 0.75-mm/s scan speed viii

9 5.3 Insertion loss and mode eld diameter as a function of pulse duration for 1-MHz repetition rate, 0.75-mm/s scan speed and parallel polarization Coupling coecient and bending phase at 1300-nm and 1550-nm wavelengths for d = 10 µm A list of the broadband couplers, their geometries and bandwidths (±5%) Properties and exposure conditions for lowest loss waveguides fabricated in fused silica and borosilicate glass Properties of waveguides fabricated by PLC [30] and femtosecond laser technology ix

10 List of Figures 2.1 Fabrication steps in ame hydrolysis method for producing planar lightwave circuits in glass [30] Longitudinal and transverse writing geometries for femtosecond laser waveguide fabrication in the bulk of transparent materials. In transverse (longitudinal) writing, the sample is scanned transverse (parallel) with respect to the incident femtosecond laser [49] Schematic of tunneling (γ < 1.5) and multiphoton (γ > 1.5) and intermediate regimes (γ 1.5) of high-intensity photoionization in an atom [34] Illustration of multiphoton ionization (a) for seeding electrons for free-carrier absorption (b) followed by impact ionization (c) once the conduction band electron's energy has exceeded the bandgap energy [56] x

11 2.5 Illustration of the interaction physics of focused femtosecond pulses in bulk transparent materials. (a) The laser is focused below the sample surface resulting in a high intensity in the focal volume. (b) The energy is nonlinearly absorbed and a free electron plasma is created by multiphoton/tunneling and avalanche photoionization. (c) The plasma transfers its energy to the lattice on a 10 ps time scale resulting in one of three types of permanent modication (d): isotropic refractive index change at low pulse energy due to rapid quenching, birefringent nanogratings at moderate energy due to laser-plasma interference, and empty voids at high pulse energy due to microexplosion and shockwave propagation [7] Scanning electron microscope image of nanogratings formed at 65-µm depth (sample cleaved and polished at writing depth) with polarization parallel (a) and perpendicular (b) to the scan direction. Overhead view (c) of etched microchannels demonstrating polarization selective etching with parallel (top), linear 45 (middle) and perpendicular (bottom) polarizations [67] Binary bits (voids) recorded in fused silica with 100-fs laser [69] Optical microscope image of static laser exposures formed in borosilicate glass with 5-nJ, 25-MHz, 30-fs pulses focused with 1.4-NA objective. The number of pulses increases, by factors of 10, from 10 2 on the left to 10 5 on the right [7] Intensity distribution of 800-nm wavelength laser focused 1 mm below the surface of glass with NA = 0.1, 0.2 and 0.6 [77] Self-phase modulation and self-focusing of ultrashort pulses in a dielectric material [56] xi

12 2.11 Enthalpy (or volume, inverse of density) versus temperature plot for glass under fast and slow cooling rates showing liquid, glass transition and crystalline states [82] Viscosity as a function of temperature for common optical glasses showing important glass temperatures [83] Comparison of the shape of the fundamental mode eld (open circles) with the optimally matched Gaussian distribution (solid dots) with V = 2.4. [86] Chirped-pulse amplication in IMRA µjewel laser [88] Beam delivery optics showing normal beam path (solid red line) and optional beam paths (dotted red lines) for autocorrelation and transmission through AOM. TM = turning mirror, FM = ip mirror, HM = hot mirror, A = aperture for alignment purposes Laser micromachining station on granite arch: output from femtosecond ber laser was directed towards the objective, which focused light below the surface of fused silica and borosilicate glass samples. WP = waveplate Setup for second harmonic generation of 522-nm light from incident 1045-nm radiation. The LBO crystal is placed at the focus of a telescope to maximize conversion eciency xii

13 3.5 Intensity autocorrelation in non-collinear geometry: Pulses are split and passed through two arms with variable path length dierence before interfering at SHG crystal. When the pulses did not overlap temporally (left frame), no autocorrelation signal was detected. When pulse overlap temporally (right frame), an SHG autocorrelation signal was detected [90] APE PulseCheck software showing Lorentzian prole of intensity autocorrelation function Cross sectional (left) and overhead (right) view of good waveguide written in borosilicate glass. In the cross sectional view, the incident laser was incident from the top as shown by the red arrow Far-eld intensity distribution of 633-nm wavelength light output from femtosecond laser-written waveguide Sample characterization setup: input and output bers are aligned with sample using manual positioners. An overhead vision system linked to a computer monitor is used for visual alignment Screen-capture of Spiricon software for capturing intensity distribution of waveguide mode Refracted near eld technique for measuring the cross sectional refractive index proles of femtosecond laser-written waveguides [99] xiii

14 4.1 (Electronic attachment: Fig4-1.mov, 3.3 MB). Simulated temperature prole evolution (0 to 25 µs) for static laser exposures (200-nJ absorbed energy/pulse) in Corning EAGLE2000 borosilicate glass for repetition rates of 200 khz (left) and 1.5 MHz (right). The horizontal red line at T s = 985 C is the softening point for EAGLE2000 used to dene the threshold radius for melting Finite-dierence model of glass temperature versus exposure at repetition rates of 100 khz, 500 khz and 1 MHz, at a radial position of 3 µm from the center of the laser beam. The absorbed pulse energy of 200 nj was the same at each repetition rate. The temperature driven at 100-kHz repetition rate saturates beyond 20 pulses, never exceeding the softening point Absorption (a) versus repetition rate for pulse energies of 100, 200 and 250 nj, and transverse waveguide diameter (b) versus scan speed for pulse energies of 100, 200 and 250 nj at 1.5-MHz repetition rate. Colored lines show calculated diameter. The black line at 2-µm diameter shows the approximate spot diameter (2w 0 ) of the laser Overhead microscope images (a) of waveguides fabricated with 250-nJ pulse energy, 15-mm/s scan speed at repetition rates of 1.5 MHz (top), 0.5 MHz (middle) and 0.2 MHz (bottom) and (b) waveguide diameters plotted against scan speed for 250-nJ pulse energy and repetition rates of 0.2 MHz (blue triangles), 0.5 MHz (green circles) and 1.5 MHz (red squares). The circled data points show melt diameters at the same net uence of 2 kj/cm 2. Calculated thermal model values of the melt diameter are shown by the solid lines xiv

15 4.5 Transverse waveguide diameter (a) as a function of scan speed for repetition rates of 0.2, 0.5 and 1.5 MHz at a constant average power of 200 mw. Data points are experimental diameters and solid lines are diameters predicted by thermal model; corresponding values of absorption and absorbed energy (b) versus repetition rate at 200-mW average power Overhead microscope image (a) at 100Ö magnication showing thermal diffusion from single-pulse modication zones irradiated with 1-µJ pulse energy at 100-mm/s scan speed and 40-kHz repetition rate. Pulses were focused 150-µm below the surface with a 0.55-NA lens. Comparison of experimental (blue diamond) and calculated (red square) modication diameters (b) from single-pulse diusion eects as a function of incident laser pulse energy Experimental values of threshold pulse energy for onset of heat accumulation as a function of laser repetition rate for scan speeds of 2, 10 and 40 mm/s and NA = 0.55 focusing Cross-sectional refractive index proles from RNF measurements of waveguides written with 0.55-NA focusing, 200-mW power, 150-µm depth, 25-mm/s scan speed and repetition rates of 0.2, 0.5, 1, 1.5, and 2 MHz. The writing laser was incident from the top Cross sectional microscope image of waveguide written in EAGLE2000 with 1-kHz repetition rate Ti:Sapphire laser (pulse duration 100 fs, energy 3 µj, scan speed 0.5 mm/s, NA = 0.55) [104] xv

16 4.10 Classication of waveguide properties as a function of average power and scan speed for 1.5-MHz repetition rate and NA = 0.55 focusing at 150-µm depth: red, blue and black squares indicate low (< 3 db), medium (3 6 db) and high (>6 db) insertion loss, respectively, and black diamonds indicate waveguides that support multiple transverse modes Measured insertion loss and mode eld diameter (a) and coupling and propagation loss (b) versus repetition rate for waveguides written with 200-mW average power and 15-mm/s scan speed. Waveguides were formed 150 µm below the surface with a 0.55-NA lens. The waveguide lengths were 2.5 cm Refractive-near eld measurements of cross-sectional refractive index proles for waveguides written with 0.55-NA lens, 200-mW power, 150-µm depth, 1.5- MHz repetition rate and scan speeds of 5, 15 and 30 mm/s. The writing laser was incident from the top Waveguide fabricated with 1.5-MHz repetition rate, 200-mW power, NA lens, 150-µm depth and 15-mm/s scan speed: Cross sectional refractive index prole (left), simulated mode prole (middle) and measured mode prole (right). Red arrow indicates position of mode relative to waveguide cross section Insertion loss versus wavelength for 5-cm long waveguides fabricated in EA- GLE2000 with (a) 300-fs ber laser and 8 to 20-mm/s scan speed (1.5-MHz repetition rate, 200-mW power) and (b) 100-fs, 1-kHz Ti:Sapphire laser [107]. 95 xvi

17 4.15 Mode eld diameter versus focusing depth for waveguides formed with 1.5- MHz repetition rate, 15-mm/s scan speed with 0.55 NA (230 mw) and 0.4 NA (200 mw) exposure condition in EAGLE2000 borosilicate glass Coordinates used to calculate the intensity distribution at a point P inside glass: ρ is the radial distance from the propagation axis, z is the depth below the focus in the absence of the second medium, and d is the distance from the surface to the diraction-limited focus Normalized intensity along axial direction for various focusing depths for (a) NA = 0.55, (b) NA = 0.4, (c) NA = 0.34 and (d) NA = nm mode prole (top) and overhead microscope (bottom) image at different annealing temperatures for waveguide fabricated in EAGLE2000 with 230-mW power, 1.5-MHz repetition rate, 0.4-NA, 150-µm depth and 15-mm/s scan speed Mode eld diameter (a) and insertion loss (b) versus baking temperature for waveguides fabricated with 230-mW power, 1.5-MHz repetition rate, 0.4 NA, 150-µm depth and scan speeds of 8 to 20 mm/s. The EAGLE2000 borosilicate glass sample was baked for 1 hour at each temperature Optical microscope images showing laser-modied zones formed in Corning 7980 fused silica with 450-nJ energy, 1045-nm wavelength pulses focused with 0.65-NA lens. Total pulse (top) and uence accumulation (bottom) is shown for each column and the laser repetition rate (100 khz to 1 MHz) is indicated for each row. Laser direction is normal to page xvii

18 5.2 Overhead microscope images of laser modication tracks in fused silica written at 1045-nm wavelength with 1-MHz repetition rate, 175-mW average power, and 0.2 to 50-mm/s scan speed Overhead microscope images of laser modication tracks in fused silica written at 522-nm wavelength with 1-MHz repetition rate, 175-mW average power, and 0.5 to 10-mm/s scan speed Cross sectional phase contrast microscopy images of waveguides written at circular, parallel and perpendicular polarizations at 1-MHz repetition rate, 175-nJ pulse energy, 0.75-mm/s scan speed Intensity autocorrelation function (ACF) for pulse durations of (i) 200 fs, (ii) 280 fs and (iii) 400 fs measured at 522-nm wavelength and FWHM of Lorentzian. Incident fundamental (1045 nm) ACF shown in red and second harmonic (522 nm) ACF shown in green Insertion loss versus pulse duration for waveguides fabricated in fused silica with 1-MHz repetition rate, 0.75-mm/s scan speed and parallel polarization. Mode proles at 1550-nm wavelength are shown at each data point Cross sectional microscope images of waveguides written at pulse durations of 220 fs, 280 fs and 400 fs as specied in Table 5.3. The laser was incident from the top and the dashed red line shows the approximate location of the focal plane, 75 µm below the surface Insertion loss versus wavelength for 2.5-cm long waveguides fabricated in fused silica with 1-MHz, 220-fs ber laser (0.55 NA, 522-nm wavelength, 0.7-mm/s scan speed, 150-mW average power) xviii

19 6.1 Bend loss (dierential insertion loss between coupler arm and straight waveguide) versus radius of curvature for waveguides written with 20-mm/s scan speed, 200-nJ pulse energy and 1-MHz repetition rate in EAGLE2000 borosilicate glass. Inset shows one arm of the directional coupler under test with four bends of radius R Schematic of 3-dB directional coupler and optical microscope image of waveguides in coupling region (top) together with mode proles of 1550-nm laser light from launch ber at port 1 and from output facets at ports 2 and 3. 50/50 coupling was demonstrated at d = 17.5 µm and L = 20.6 mm, using writing conditions of 200-nJ pulse energy, 20-mm/s scan speed, 150-µm focal depth and 1-MHz repetition rate. In the waveguide mode proles shown at the output, the writing laser was incident from the top Through port coupling ratio dependence on interaction length for separations d = 7.5, 12.5 and 17.5 µm at 1310 and 1550-nm wavelengths. Sinusoidal curve ts shown are shown as solid lines Beat length as a function of separation distance for 1.31 and 1.55-µm wavelengths. Experimental data points are shown along with analytic representations (solid and dashed lines) Directional coupler geometry with center-to-center separation d, interaction length L and S-bend radius R = 50 mm xix

20 6.6 Measured (solid square) coupling ratio versus interaction length at (a) 1300 nm and (b) 1550 nm wavelengths, and sinusoidal curve ts (solid lines) for d = 10 µm. The beat length is 3.83 mm and 2.57 mm at 1300-nm and 1550-nm wavelength, respectively. Coupling coecient and bending phase (c) versus wavelength for directional coupler with 10-µm center-to-center separation Measured coupling ratio versus wavelength for interaction lengths of (a) L = 0, 0.8, 1.6 mm and (b) 3.2, 5.2, 6.8 mm for d = 10 µm Directional coupler implementation for wavelength-attened power splitter. The rst arm was written at 12 mm/s and the second arm was written at 8 mm/s (asymmetric), 12 mm/s (symmetric) or 20 mm/s (asymmetric) Coupling coecient (solid lines) and bending phase (dashed lines) versus wavelength for symmetric coupler with separation distances of 6, 6.5, 7.5 and 10 µm Coupling ratio versus wavelength for symmetric coupler with separation distances of 6 µm and interaction lengths of 0, 0.5, 1, 1.5, 2, and 2.5 mm The spectral responses of couplers with the largest bandwidths for coupling ratios of 0, 10, 20, 35, 50, 60, 70, 90 and 100%. Coupler geometries and exposure conditions are summarized in Table Fused silica waveguide for intercepting surface microchannel fabricated at 15 µm below the surface with the corresponding mode prole at 1550-nm wavelength Integrated optouidic sensor: buried microchannel between input and output reservoirs intercepted by buried waveguide [137] xx

21 6.14 Coupling ratio versus wavelength for directional couplers in fused silica with interaction lengths of 1.5, 1.8 and 2.7 mm xxi

22 Acknowledgments A friend once described the PhD as the darkest moment in life. Although there were dicult times throughout my years at the University of Toronto, the support from my friends and colleagues made the process less of a struggle than I anticipated. I would like to start by thanking my colleagues at U of T, several of whom I formed strong friendships with that I hope will continue in the next stage of our lives. I would like to thank Dragan for his excellent mentorship during the initial stages of my Master's degree. I thank Chris for sharing his excellent experimental sense during the F 2 experiments we performed together, especially during the experiment that coincided with Blackout '03. I thank Andrew for showing me the discipline needed to nish a graduate degree in Toronto and for his help with the MATLAB animation. I thank Lao Li, the most important person in our lab, for his continued inspiration, mentorship and sense of humour. In addition to cheap optical spectrum analyzers, another fortunate result of the bubble burst was the arrival of Rajiv and Clark from JDS Uniphase. I am grateful for Rajiv's words of wisdom - both in optics and in life. I am thankful to Clark for pushing me to write waveguides in KGW, which led to our rst postdeadline talk at CLEO. With the arrival of two femtosecond lasers, Haibin and I built up the ultrafast laser lab. This teamwork extended to research with an excellent cooperative eort on several papers. In particular, I thank Haibin for improving my simple cumulative heating model, allowing us to accurately compare theory with experiment. I thank Stephen for his kindness and for pushing me to try new things. I thank Mi Li for her excellent advice and insight, which has made me a better researcher and person. I thank William for carrying on my research and challenging me to prove its worth. I thank Tariq for performing the surface waveguides experiment with me and for taking over as the group's IT administrator. I thank Sergey, who was a crucial part of my PhD project, for helping build up the laser lab and for polishing dozens of my glass waveguide samples. Although Debashis, Eddy, James, Abbas, Ladan and Dr. Lin were not involved in my research area, it was a pleasure having them as work colleagues. My collaboration with IMRA America was very important to the early successes in my PhD career and I am grateful to the groups in Ann Arbor and Fremont for their support. I thank Stephan Rinck for performing refracted near eld measurements and Joern Bonse for phase contrast microscopy characterization of BK7 and fused silica waveguides. I thank my committee members Stewart Aitchison and Amr Helmy, who have given excellent advice throughout my PhD which has led to several papers. Most importantly, I thank my supervisor Peter Herman, for his excellent guidance and physical insight. Peter always pushed me to strive harder in my research and to focus on making an impact with my journal publications. I am grateful that Peter supported me to attend international conferences, which gave me the opportunity to meet other experts in optics, allowing me to further my career in academia. I would like thank my loyal non-photonics friends and most importantly my Mom and Dad and brother Daniel for their encouragement during my PhD. I thank Sharon who bravely followed me to Ontario and endured the harsh winters of Kingston to complete her Law degree. Although perhaps regretting her decision at times, Sharon inspired me to attend graduate school and I thank her for her patience and support. xxii

23 I am grateful for support from the SPIE Scholarship, Ontario Graduate Scholarship, Natural Sciences and Engineering Research Council of Canada (NSERC) Postgraduate Scholarship and Walter C. Sumner memorial fellowship. Research support from the Canadian Institute for Photonics Innovation (CIPI) and NSERC is acknowledged. xxiii

24 Published Work Patent applications 1. L. Shah, S. Eaton, P. R. Herman, "Pulsed Laser Source with Adjustable Grating Compressor," US Patent Application US2006/ A1. 2. H. Zhang, P. R. Herman, S. M. Eaton, application submitted Journal publications 1. S. M. Eaton, H. Zhang, M. L. Ng, J. Li, W. Chen, S. Ho, P. R. Herman, Contrasts in thermal diusion and heat accumulation eects in femtosecond laser writing of buried optical waveguides in borosilicate glass, submitted to Opt. Express. 2. S. M. Eaton, M. L. Ng, J. Bonse, A. Mermillod-Blondin, H. Zhang, A. Rosenfeld, P. R. Herman, Low-loss waveguides fabricated in BK7 glass by high repetition rate femtosecond ber laser, Appl. Opt. 47, (2008). 3. S. M. Eaton, C. A. Merchant, R. Iyer, A. J. Zilkie, A. S. Helmy, J. S. Aitchison, P. R. Herman, D. Kraemer, R. J. D. Miller, C. Hnatovsky, R. S. Taylor, Raman gain from waveguides inscribed in KGd(WO 4 ) 2 by high repetition rate femtosecond laser, Appl. Phys. Lett. 92, (2008). 4. H. Zhang, S. M. Eaton, and P. R. Herman, Single-step writing of Bragg grating waveguides in fused silica with an externally modulated femtosecond ber laser, Opt. Lett. 32, (2007). 2 citations 5. H. Zhang, S. M. Eaton, J. Li, A. H. Nejadmalayeri, P. R. Herman, Type II highstrength Bragg grating waveguides photowritten with ultrashort laser pulses," Opt. Express 15, (2007). 4 citations 6. H. Zhang, S. Ho, M. L. Ng, S. M. Eaton, J. Li, P. R. Herman, 3-D laser writing of Bragg grating waveguides in bulk glasses, CIPI PHOTONS Technical Review 5, (2007). 7. H. Zhang, S. M. Eaton, J. Li, P. R. Herman, Heat accumulation during high repetition rate ultrafast laser interaction: Waveguide writing in borosilicate glass, Journal of Physics: Conference Series 59, (2007). 8. S. Nakamura, S. Ho, J. Li, S. M. Eaton, H. Zhang, P. R. Herman, Femtosecond Laser Direct Writing of Optical Waveguides in Silicone Film, JLMN 2, (2007). xxiv

25 9. H. Zhang, S. M. Eaton, J. Li, P. R. Herman, Femtosecond laser direct writing of multiwavelength Bragg grating waveguides in glass, Opt. Lett. 31, (2006). 3 citations 10. H. Zhang, S. M. Eaton, P. R. Herman, Low-loss Type II waveguide writing in fused silica with single picosecond laser pulses, Opt. Express 14, (2006). 9 citations 11. S. M. Eaton, W. Chen, L. Zhang, H. Zhang, R. Iyer, J. S. Aitchison, P. R. Herman, Telecom-band Directional Coupler Written with Femtosecond Fiber Laser, IEEE Photonics Technol. Lett. 18, (2006). 2 citations 12. H. Zhang, S. M. Eaton, J. Li, P. R. Herman, Type II femtosecond laser writing of Bragg grating waveguides in bulk glass, Electron. Lett. 42, (2006). 13. W. J. Reichman, D. M. Krol, L. Shah, F. Yoshino, A. Arai, S. M. Eaton, P. R. Herman, A spectroscopic comparison of femtosecond-laser-modied fused silica using kilohertz and megahertz laser systems, J. Appl. Phys. 99, (2006). 1 citation 14. S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, J. Bovatsek, A. Y. Arai, Heat accumulation eects in femtosecond laser-written waveguides with variable repetition rate, Opt. Express 13, (2005). 38 citations 15. L. Shah, A. Y. Arai, S. M. Eaton, P. R. Herman, Waveguide writing in fused silica with a femtosecond ber laser at 522 nm and 1 MHz repetition rate, Opt. Express 13, (2005). 24 citations Conference proceedings and invited talks 1. W. Chen, S. M. Eaton, H. Zhang, P. R. Herman, Wavelength-Flattened Asymmetric Directional Couplers Written by Focused Femtosecond Lasers, Talk CTuG3, CLEO 2008, San Jose, CA. 2. J. Li, H. Zhang, S. M. Eaton, P. R. Herman, 5-D Spectroscopic Microscopy for Intelligent Femtosecond Laser Writing of Optical Waveguides, Talk JWE3, CLEO 2008, San Jose, CA. 3. H. Zhang, S. Ho, S. M. Eaton, M. L. Ng, J. Li, P. R. Herman, Single-step burst writing of high-strength Bragg grating waveguides in bulk fused silica glass for high temperature optical sensing, in Photonics West 2008, Proc. SPIE (2008). 4. W. Chen, S. M. Eaton, S. Yang, P. R. Herman, Polarization control in femtosecond laser writing of waveguide directional couplers, in Photonics West 2008, Proc. SPIE 6897A-30 (2008). 5. M. L. Ng, S. M. Eaton, D. Chanda, P. R. Herman, Femtosecond laser direct writing of buried diractive optical elements in fused silica, in Photonics West 2008, Proc. SPIE 6897A-20 (2008). xxv

26 6. S. Ho, M. L. Ng, S. M. Eaton, H. Zhang, C. C. Qu, P. R. Herman, J. S. Aitchison, Femtosecond laser writing for selective chemical etching and optical device integration in 3D optouidic systems, in Photonics West 2008, Proc. SPIE (2008). 7. J. Li, H. Zhang, S. M. Eaton, P. R. Herman, Ultrafast laser 5-D microscopy for controlling 3-D laser nanoprocessing, in Photonics West 2008, Proc. SPIE (2008). 8. S. M. Eaton, J. Bonse, H. Zhang, M. L. Ng, S. Ho, W. Chen, J. Li, T. Raque, A. Rosenfeld, P. R. Herman, "Direct writing of waveguide devices in fused silica glass using high repetition rate ber laser, in Photonics West 2008, Proc. SPIE 6897A-29 (2008). 9. J. Li, H. Zhang, S. M. Eaton, T. Navedi, A. Hosseini, P. R. Herman, Integration of femtosecond laser 5D microscopy and 3D, Poster PMO-2, Conference on Laser Ablation 2007, Tenerife, Spain. 10. H. Zhang, S. Ho, S. M. Eaton, J. Li, P. R. Herman, Contrasts in single-pulse and burst ultrafast laser writing of Bragg grating waveguides in bulk glasses, Poster PMO- 1, Conference on Laser Ablation 2007, Tenerife, Spain. 11. H. Zhang, S. M. Eaton, P. R. Herman, Type II and Burst Methods for Ultrashort Laser Direct Fabrication of High-Strength Bragg Grating Waveguides inside Bulk Glasses: A Comparison, Talk BTuD2, Bragg Gratings Poling and Photosensitivity 2007, Quebec City, Canada. 12. S. M. Eaton, H. Zhang. M. L. Ng, S. Ho, P. R. Herman, Optimization of repetition rate, pulse duration, and polarization for femtosecond-laser-writing of waveguides in borosilicate and fused silica glasses, Talk CE5-5-WED, CLEO Europe 2007, Munich, Germany. 13. M. L. Ng, S. M. Eaton, D. Chanda, P. R. Herman, Femtosecond direct laser writing of buried diractive optical elements in glasses, Talk CE4-6-TUE, CLEO Europe 2007, Munich, Germany. 14. H. Zhang. S. M. Eaton, S. Ho, J. Li, P. R. Herman, Fabricating high-strength Bragg-grating-waveguide devices in glass with ultrashort laser pulses, Talk CF8-6- THU, CLEO Europe 2007, Munich, Germany. 15. H. Zhang, S. M. Eaton, P. R. Herman, Direct Writing of High Strength Bragg Grating Waveguides in Fused Silica by an Externally Modulated Ultrafast Fiber Laser, Talk CPDB7 (Postdeadline), CLEO 2007, Baltimore, MD. 16. C. A. Merchant, S. M. Eaton, R. Iyer, A. S. Helmy, J. S. Aitchson, C. Hnatovksy, R. S. Taylor, Low-loss Waveguides Fabricated in KGd(WO 4 ) 2 by High Repetition Rate Femtosecond Laser, Talk CPDB8 (Postdeadline), CLEO 2007, Baltimore, MD. xxvi

27 17. S. M. Eaton, W. Chen, H. Zhang, M. L. Ng, P. R. Herman, Depth-Independent, Low-Loss Waveguides Formed by High-Repetition Rate Femtosecond Fiber Laser, Talk CThS7, CLEO 2007, Baltimore, MD. 18. S. Ho, M. L. Ng, S. M. Eaton, P. R. Herman, J. S. Aitchison, Single and Multi-Scan Femtosecond Laser Writing for Selective Chemical Etching of Glass Micro-Channels, Talk CThJ4, CLEO 2007, Baltimore, MD. 19. L. E. Abolghasemi, S. M. Eaton, A. Hosseini, P. R. Herman, Three-Dimensional Laser Nano-structuring: Contrast in Three-Photon and Two-Photon Polymerization of SU-8, Talk CThN6, CLEO 2007, Baltimore, MD. 20. H. Zhang, S. M. Eaton, J. Li, A. H. Nejadmalayeri, P. R. Herman, Writing High- Strength Bragg Grating Waveguides in Bulk Glasses with Picosecond Laser Pulses, Talk CThS1, CLEO 2007, Baltimore, MD. 21. M. Y. Xu, S. A. Hosseini, S. M. Eaton, L. D. Lilge, P. R. Herman, Heat Accumulation Eects in Femtosecond Laser Ablation of ITO Thin Films for DEP Trapping Devices, Talk CFR3, CLEO 2007, Baltimore, MD. 22. J. Li, P. R. Herman, S. M. Eaton, H. Zhang, A. H. Nejadmalayeri, S. A. Hosseini, Combining 5-D Microscopy with 3-D Femtosecond Laser Nanoprocessing, Talk CFR4, CLEO 2007, Baltimore, MD. 23. S. M. Eaton, M. L. Ng Micromachining of glass using ultrafast and ultraviolet lasers, Max Born Institut, 27-April-2007, invited talk hosted by Dr. J. Bonse. 24. S. M. Eaton, Depth-indepedent waveguides formed by high repetition rate femtosecond laser, Oral Talk, 26-April-07, Laser Laboratorium Goettingen 20th year anniversary workshop. 25. S. M. Eaton, Waveguide writing in glass using a high repetition rate femtosecond ber laser, Politecnico di Milano, 16-April-2007, invited talk hosted by Prof. R. Osellame. 26. S. Nakamura, S. Ho, J. Li, S. M. Eaton, H. Zhang, P. R. Herman, Femtosecond Laser Direct Writing of Optical Waveguides in Silicone Film, Oral Talk, LPM 2007, Vienna, Austria. 27. S. M. Eaton, W. Chen, H. Zhang, P. R. Herman, Telecom band directional couplers written with a high repetition rate femtosecond ber laser, Poster JTuD8, CLEO 2006, Long Beach, CA. 28. W. J. Reichman, D. M. Krol, L. Shah, F. Yoshino, A. Arai, S. M. Eaton, Peter R. Herman, Fluorescence and Raman microscopy of waveguides fabricated using khz and MHz repetition rate femtosecond lasers, Talk CME2, CLEO 2006, Long Beach, CA. xxvii

28 29. H. Zhang, S. M. Eaton, A. Hosseini, P. R. Herman, Low-damage Type-II waveguide writing in fused silica with femtosecond and picosecond lasers, Talk CMX6, CLEO 2006, Long Beach, CA. 30. P. R. Herman, S. M. Eaton, H. Zhang, J. Li, Femtosecond laser waveguide writing: contrasting interactions at MHz and khz repetition rates, Talk ThT3 (Invited), LEOS Annual Meeting 2006, Montreal, QC, Canada. 31. S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, J. Bovatsek, A. Arai, Optical Waveguides Written with a Variable Repetition Rate Femtosecond Fiber Laser, Talk Tu-O18, Conference on Laser Ablation (COLA) 2005, Ban, AB, Canada. 32. S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, J. Bovatsek, A. Arai, Heat accumulation eects in femtosecond laser-written waveguides with variable repetition rate, Young Scientists in Photonics Forum (YSPF), co-located with LASER 2005, Munich, Germany, June S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, A. Y. Arai, Writing optical waveguides with a MHz repetition rate femtosecond ber laser, Talk CFG4, CLEO 2005, Baltimore, MD. 34. S. M. Eaton, F. Yoshino, L. Shah, A. Arai, H. Zhang, S. Ho, P. Herman, Thermal heating eects in writing optical waveguides with a MHz rate ultrafast ber laser, in Photonics West 2005, Proc. SPIE 5713A L. Shah, F. Yoshino, A. Arai, S. M. Eaton, H. Zhang, S. Ho, P. Herman, MHz-rate ultrafast ber laser for writing of optical waveguides in silica glasses, in Photonics West 2005, Proc. SPIE S. Ho, J. S. Aitchison, S. M. Eaton, P. R. Herman, J. Li, "F2-laser microfabrication for integrating optical circuits with microuidic biochips, in Optics East 2004, Proc. SPIE xxviii

29 List of Acronyms 3D: three dimensional AOM: acousto-optic modulator ACF: autocorrelation function AWG: arrayed waveguide grating BBO: beta barium borate BGW: Bragg grating waveguide CCD: charge coupled device CL: coupling loss CW: continuous wave EAGLE2000: Corning EAGLE2000 borosilicate glass FHD: ame hydrolysis deposition FTTH: ber-to-the-home FWHM: full width at half maximum IL: insertion loss IR: infrared LCD: liquid crystal display LBO: lithium triborate MFD: mode eld diameter MZI: Mach-Zehnder interferometer NA: numerical aperture NCPM: non-critical phase matching OSA: optical spectrum analyzer PD: photodiode PLC: planar lightwave circuit PMT: photomultiplier tube PON: passive optical network PSO: position-synchronized output RIE: reactive ion etching RNF: refracted near eld RF: radio frequency SMF: single mode ber SNR: single to noise ratio TTL: transistor-transistor logic xxix

30 UV: ultraviolet WDM: wavelength division multiplexing WG: waveguide WP: waveplate xxx

31 Chapter 1 Introduction The invention of the laser in 1960 [1, 2] enabled much higher light intensities than previously possible. Since then, laser development has progressed rapidly, with high intensities demonstrating that optical materials may exhibit nonlinear behavior, such as the optical Kerr eect [3] and frequency generation [4]. The development of subpicosecond laser sources in the past 30 years has enabled peak intensities greater than 10 TW/cm 2 [5], capable of driving nonlinear multiphoton absorption in dielectric materials that would otherwise be transparent [6]. At the surface of materials, focused subpicosecond pulses enable precise micromachining of sub-wavelength features because multiphoton absorption is a nonlinear function of laser intensity, but also because the pulse duration is short relative to any relaxation processes [7]. In 1996, Hirao's group showed that by focusing subpicosecond pulses in the bulk of transparent glass, the modication induced beneath the sample surface could be tailored to produce a permanent refractive index increase localized to the focal volume [8]. By scanning the sample relative to the laser focus, a region of increased refractive index could be formed along an arbitrary three-dimensional path, unlike traditional photolithography, which is limited to fabricating devices in-plane. Femtosecond laser writing oers further advantages 1

32 over photolithography such as maskless fabrication and a simple, exible and enviromentally insensitive setup. Since the rst discovery of femtosecond laser writing of waveguides, over ve hundred papers have been published on the topic, with waveguides demonstrated in a variety of materials including glasses [811], crystals [1215] and polymers [16]. Femtosecond laser waveguide fabrication has enabled novel optical circuits including 3D y-branch power splitters [17], 3 3 directional couplers [18], ring resonators [19] and arrays of waveguides for applications in nonlinear optics [20, 21]. The advent of high-repetition rate femtosecond lasers has enabled a unique thermal regime for laser micromachining of glasses. At low to moderate repetition rates (1-200 khz), an increase in laser pulse energy leads to formation of larger modication structures as thermal diusion extends the laser-heated region far outside the focal volume. In this way, isotropic thermal diusion can compensate for an asymmetric focal heating volume to produce a cylindrically symmetric waveguide cross section [22]. As repetition rate increases, the time between laser pulses becomes shorter than the time for the absorbed laser radiation to diuse out of the focal volume, resulting in a buildup of heat. This eect was rst exploited in the surface micromachining of glass to form smooth, crack-free holes due to laser interaction with a thin sheath of ductile pre-heated glass [23]. Schaer et al. reported a dramatic increase in the size of laser-modied structures formed in the bulk of glass under strong heat accumulation eects with a 25-MHz laser oscillator compared to structures formed by thermal diusion-only processes [24]. At high repetition rates, isotropic thermal diusion and heat accumulation act together to produce nearly cylindrical waveguide zones with the added benet of 1000-fold higher writing speeds [24, 25] compared to commonly employed 1-kHz repetition rate Ti:Sapphire amplied lasers [17, 2628]. 2

33 Despite the advances in the eld of femtosecond laser waveguide writing, there still remains the open question of what roles heat accumulation and thermal diusion play in dening similar modied zones at moderate 200-kHz to high >1-MHz repetition rates. In this thesis, a novel variable-repetition rate femtosecond ber laser is used to explore the interplay of these two processes as a function of repetition rate (200 khz to 5 MHz) and other laser exposure parameters in fused silica and borosilicate glasses. Fused silica is an excellent candidate for integrated optical circuits due to its excellent transparency at ultraviolet (UV) to infrared (IR) wavelengths, low thermal expansion and high thermal diusivity. Borosilicate glass has a smaller bandgap, higher thermal expansion coecient and lower thermal diusivity, but is very popular due to its lower cost, nding common use in at-panel displays, lenses and as mirror substrates. Waveguides formed in fused silica do not show evidence of heat accumulation, which is attributed to the higher bandgap which inhibits nonlinear absorption coupled with a higher melting point. Borosilicate glass, which shows strong evidence of heat accumulation and thermal diusion eects, is therefore the primary glass studied. The main objective of this thesis is to understand the eect of thermal diusion and heat accumulation on the resulting morphology and guiding properties of waveguides formed in borosilicate glass to gain further knowledge of the modication physics. Such insight will be shown to lead to better control in producing low-loss waveguides in glass for optical integrated circuits. In previous work, a xed threshold repetition rate of 1 MHz for heat accumulation was identied for borosilicate glass [29]. In this thesis, the threshold for heat accumulation to expand diameters beyond single-pulse diusion zones is shown to be best represented in terms of a pulse energy, dening the minimum strength of the heating source 3

34 so that heat accumulation proceeds at a given repetition rate. This threshold pulse energy for heat accumulation will be demonstrated to depend on the repetition rate and scan speed. A nite-dierence thermal diusion model will be applied to model the temperature prole as a function of time to gain a greater understanding of the laser-material interaction. The model will be shown to accurately predict the size of waveguide structures formed primarily by thermal diusion at low repetition rates (200 khz) and by a combination of diusion and heat accumulation at high repetition rates (> 200 khz). A further objective is to thermally anneal waveguides written in the heat accumulation regime for the rst time and test the high temperature stability as it relates to the underlying heat modication physics. To date, waveguides written with femtosecond lasers have demonstrated substantially higher propagation losses (typically 1 db/cm) compared to those achieved by planar fabrication circuit (PLC) fabrication ( 0.01 db/cm [30]). Nasu et al. recently demonstrated waveguides written in fused silica with 0.1-dB/cm propagation loss over the telecommunications band using a 1-kHz Ti:Sapphire laser [31]. However, their technique relied on a multi-scan approach resulting in a long processing time. For waveguides written in borosilicate glass within the heat accumulation regime, Tong et al. demonstrated propagation losses of 0.5 db/cm at a substantially faster scan speed of 20 mm/s enabled by a 25-MHz repetition rate oscillator [32]. In this thesis, repetition rate is used as an experimental variable for the rst time, to further reduce waveguide loss and demonstrate femtosecond laser writing as an attractive alternative to PLC technology for producing integrated optical circuits in glasses. In borosilicate glass, a common optimum processing zone of 200-mW average power and 15-mm/s scan speed is identied for writing low-loss ( 0.3 db/cm) waveguides at all repetition rates (200 4

35 khz to 2 MHz). Strong thermal diusion from high pulse energy at low repetition rate balances the decreased pulse energy and increased heat accumulation at high repetition rates to produce waveguides with similar dimensions, refractive index prole and propagation loss. In fused silica, heat accumulation does not proceed for the laser exposures tested herein and the fundamental wavelength produces irregular structures with weak index contrast, incapable of eciently guiding red or infrared light. For the rst time, the higher uence provided by the second harmonic wavelength is shown to drive a stronger interaction, leading to higher index contrast waveguides with low propagation losses. Further improvement in waveguide transmission is found by optimizing the laser polarization and pulse duration, two parameters which have yet to be studied in high repetition rate fabrication. An optimum propagation loss of 0.2 db/cm will be demonstrated, which nearly equals the best result by Nasu et al. [31], but with a 1000-fold shorter writing time owing to high repetition rate fabrication. The optimum processing conditions in borosilicate and fused silica glass are applied to fabricate novel and high-performance optical devices. The directional coupler, a basic unit of optical circuits, is inscribed in borosilicate and fused silica and is demonstrated to have unprecedentedly high peak coupling ratio, showing the nesse of waveguide fabrication with high repetition rate femtosecond lasers. The directional coupler geometry is designed for wavelength demultiplexer operation at 1300 and 1550-nm wavelengths, and for nearly constant power splitting across the entire telecom band. The optimum recipe for waveguide writing in fused silica is applied to fabricate segmented waveguides which can act as Bragg grating waveguides, and also in lab-on-a-chip applications where waveguides intersect microchannels for sensing, counting and sorting of biomaterials. 5

36 In Chapter 2, a review of femtosecond laser waveguide writing and the related lasermaterial interaction physics are presented. The properties of fused silica and borosilicate glass are discussed and to later compare theory with experiment, optical waveguide and coupled-mode theory are reviewed using Maxwell's equations. In Chapter 3, the experimental and characterization techniques are discussed. The variable repetition rate femtosecond laser system is described and compared with other commercially available lasers suitable for waveguide inscription. The laser exposure procedures, and methods for insertion loss, mode characterization and refractive index prole measurement are presented. Chapter 4 presents the key results of diusion-only and heat accumulation eects in dening waveguide morphology in borosilicate glass. A rigorous optimization of laser exposure parameters is performed to reduce coupling and propagation losses of the written waveguides. A thermal model is presented that accurately predicts the diameter of laser-formed waveguides over a large range of exposure conditions. To address the issue of depth-dependent waveguide properties due to spherical aberration [33], the eect of numerical aperture is studied to determine the optimum lens for 3D fabrication. Thermal annealing studies are performed to test the resistance of waveguides written in the cumulative heating regime to thermal degradation. In Chapter 5, results of waveguide writing in pure fused silica glass are presented. Although heat accumulation does not proceed in fused silica due to less laser absorption and a higher melting point, waveguides with similar low loss behavior as borosilicate glass are obtained through optimization of all experimental variables. In Chapter 6, novel and high-performance optical devices are laser-fabricated in borosil- 6

37 icate and fused silica glasses using the laser recipes developed in the previous chapters. The devices have use in telecom, biophotonics and sensing applications. In Chapter 7, the results of waveguides written in fused silica and borosilicate are contrasted and the signicant achievements of this thesis are highlighted. Finally, Chapter 8 concludes the thesis by summarizing the key ndings and gives an outlook on future research and application directions. 7

38 Chapter 2 Background 2.1 Fabrication of waveguides in glass Glass is an excellent candidate for optical integrated circuits due to its high transmission at visible and near-infrared wavelengths, relatively low cost and ease of manufacture, and compatibility with existing optical ber technology. Polymers and semiconductors may also be used as substrates for optical integrated circuits, but are not emphasized in this thesis work. Over the past twenty years, planar lightwave circuit technology has become the industry standard for fabricating optical power splitters, wavelength multiplexers and arrayed waveguides gratings (AWGs) in glass for photonic networks [30]. Unfortunately, PLC technology is limited to planar geometries, preventing exible interconnection of waveguides, 3D crossing of waveguides and tap circuits [31]. PLC fabrication is also restricted to specic glass compositions. In 1996, Davis et al. showed that focused femtosecond laser pulses could inscribe optical waveguides in bulk glass along arbitrary 3D paths [8]. These fabrication techniques are reviewed below. 8

39 2.1.1 Planar lightwave circuit technology Planar lightwave circuits are typically fabricated by a multi-step ame hydrolysis deposition (FHD) [30] and reactive ion etching (RIE) method, as shown in Fig In FHD, SiCl 4 and GeCl 4 vapors are transported into an oxyhydrogen torch to form small SiO 2 and GeO 2 particles which are deposited on the substrate as two successive glass-particle layers that serve as the undercladding layer and the core. After deposition, the substrate with these two porous glass layers is heated for consolidation. The waveguide core ridges are then formed by photolithography and RIE. Finally, FHD is used again to cover the core ridges with an overcladding layer. This multi-step process is restricted to fabricating rectangular cross-sectional waveguides in two-dimensional planar geometries with only specic glass compositions. However, the FHD process is a well-established and mature fabrication technique that is capable of producing waveguides and optical circuits with excellent performance. Low waveguide losses in silica PLCs below 0.01 db/cm at telecom wavelengths have been demonstrated. Using a high index contrast core (index dierence = 1.5%), tight bends of 2-mm radius with negligible bend loss have been demonstrated, which is attractive for switches and large-scale AWGs in WDM (wavelength division multiplexing) telecom applications [30] Femtosecond laser writing of waveguides Peak intensities on the order of 10 TW/cm 2 can be driven by focused femtosecond laser pulses from modest-power commerical laser systems. Such intensities can drive strong nonlinear absorption, allowing for localized deposition of the laser energy in the bulk of glasses [34]. After several picoseconds, the laser-excited electrons transfer their energy to the lattice, leading to a permanent material modication. Depending on the laser and material pa- 9

40 (Si or glass wafer) a Flame hydrolysis deposition rc is 0.1 db. nique developed at NTT (Nippon Telegraph and Telephone Corp.) has the advantages of a high deposition rate and a large throughput. 7 FHD, as shown schematically in Figure 1a, is derived from the vaporphase deposition used for optical-fiber fabrication, which is capable of producing a huge glass preform. Raw materials, namely SiCl 4 and GeCl 4 vapors, are transported into an oxyhydrogen torch to form small SiO 2 and GeO 2 particles. GeO 2 is used to increase the refractive index of the core. Other dopants such as P 2 O 5 and B 2 O 5 are also added to control the sintering temperature of the glass layers. The high deposition rate circuits of the in FHD glass method [30]. is useful for fabricating optical waveguides because they require a thick glass layer of more than 20 m. Silica-based optical waveguides are fabricated on silicon substrates by a combination of FHD and reactive ion etching (RIE). 7 The waveguide fabrication process is shown schematically in Figure 1b. The first step is to use FHD to deposit two successive glass-particle layers that serve as the undercladding layer and the core. After deposition, the substrate with these two porous glass layers is heated to about 1300 C for consolidation. The waveguide core ridges are then formed by photolithography and RIE. Finally, FHD is used again to cover the core ridges with an overcladding layer. The core shape after RIE (before embedding) is shown in the top inset in Figure 1b. The shape was formed precisely and smoothly, with a well-defined rectangular profile. Core Undercladding Overcladding b Fabrication process Figure 2.1: Fabrication steps in ame hydrolysis method for producing planar lightwave Insertion Loss (db) demonstrated in fused silica [8, 26, 35], borosilicate [29, 36, 37], phosphate [9, 10], and chalco- Propagation Loss The propagation genide loss glasses of these [3841], wave-poly(methyguides is very important in constructing electric mode; TM transverse Figure 2. methacrylate) Insertion loss spectra (PMMA) for a polymer [16, 42], and lithium 10-m-long waveguide. TE transverse PLC-type devices niobate with a low [15, insertion 43, 44], silicon loss. [13], magnetic Ti:sapphire mode. [14] and quartz [45] crystals. Femtosecond laser FHD Consolidation RIE FHD + consolidation SiO 2 -GeO 2 particles SiO 2 particles Substrate Figure 1. Techniques for fabricating silica-based planar lightwave circuits (PLCs). (a) Flame hydrolysis deposition (FHD) and (b) fabrication process with a core shape after reactive ion etching (RIE). rameters, this laser modication may result in damaged and irregular scattering centers, or smooth structures with a positive refractive index alteration Compared to well-established PLC technology, femtosecond laser writing oers advantages of 3D patterning, maskless, TE 15 single-step fabrication, and1.5can be applied to many transparent materials. Femtosecond10 laser written waveguides with1.0 losses below 1 db/cm have been TM Wavelength (µm) Propagation Loss (db/m) MRS BULLETIN/MAY 2003 Such smooth structures of positive refractive index change, suitable for conning visible and infrared wavelengths by total internal reection, may be formed along arbitrary three-dimensional paths by using computer-controlled motion stages [8]. writing can provide a modest refractive index contrast of 10 3 comparable to the corecladding refractive index dierence of in single-mode ber (SMF), which imposes a 10

41 minimum bend radius of 50 mm to avoid excessive bend loss in femtosecond laser-written optical circuits [32]. A higher refractive index contrast is desirable for increasing the density of integrated optical circuits. The standard congurations for laser-writing of optical waveguides are shown in Fig In longitudinal writing, the sample is scanned parallel, either towards or away from the incident laser. In this conguration, the resulting waveguide structures have cylindrical symmetry, owing to the transverse symmetry of the focused Gaussian-shaped laser beam. The main disadvantage of the longitudinal writing geometry is that the waveguide length is limited by the working distance of the lens, which for a typical focusing objective with NA = 0.4, is approximately 5 mm. To overcome this issue, researchers have employed looser focusing lenses (NA 0.2) [46], requiring higher laser power to reach the intensity required for optical breakdown ( W/cm 2 [34]). At such peak powers ( 1 MW), the optical Kerr eect results in self focusing, which can balance the defocusing caused by the laser-induced plasma to produce laments which yield refractive index change structures elongated in the axial direction by up to several hundred microns [46]. Despite the long length of the laments, fabrication speeds are still relatively slow at 1 µm/s to build up enough refractive index increase to eciently guide light [47]. Another femtosecond laser writing geometry is using an axicon lens to form a Bessel beam, which has a very large depth of focus and a sharp central spot. It is possible to form an optical waveguide longitudinally, without translating the sample. With 100-Hz, 1-mJ, 35-fs pulses, good waveguides were formed after 3000 static laser shots [48]. Axicon focusing has the advantage of circular waveguide formation without the same limitation on waveguide length by the lens working distance. With Bessel beams, the waveguide length is only limited 11

42 LONGITUDINAL TRANSVERSE Figure 2.2: Longitudinal and transverse writing geometries for femtosecond laser waveguide fabrication in the bulk of transparent materials. In transverse (longitudinal) writing, the sample is scanned transverse (parallel) with respect to the incident femtosecond laser [49]. by the depth of focus of the Bessel beam, which can be made longer than 1 cm. In the transverse writing scheme of Fig. 2.2, the sample is scanned transversely relative to the incoming laser. The working distance no longer restricts the waveguide length and waveguides can be formed over a depth range of several millimeters, which is sucient exibility for many applications to provide 3D optical circuits. The disadvantage of the transverse geometry is that the waveguide cross section is roughly elliptical since the depth of focus (2z 0 ) exceeds the transverse spot size (2w 0 ) by a factor of 2z 0 /2w 0 = n/na, where n is the refractive index and NA is the numerical aperture. Since waveguides are formed with glasses with n 1.5 with typical NA of 0.25 to 0.85, the focal volume asymmetry n/na varies from 6.0 to 1.8. This asymmetry results in elliptical waveguide cross sections with elliptical guided modes, which couple poorly to SMF. To overcome this focal volume asymmetry, oil-immersion microscope objectives (NA > 1) may be used to provide n/na 1, but at the expense of increased lens cost and complexity and much reduced working distance. Another approach is to use astigmatic focusing by using a slit [50, 51] or cylindrical lenses [28] to reshape the beam to extend the beam waist to match the depth of focus and form cylindrically-symmetric waveguide cross sections. 12

43 Another solution to overcome the elliptical waveguide cross sections provided by focused femtosecond laser pulses in the transverse writing geometry is to employ a high repetition rate laser ( 1 MHz). At high repetition rates, heat accumulation between pulses together with spherically-symmetric heat diusion correct for the asymmetry caused by the mismatch between the depth of focus and spot size to yield cylindrically-symmetric waveguides. Fabrication with high repetition rate lasers further permits 1000-fold higher writing speeds compared with standard 1-kHz Ti:Sapphire amplied femtosecond lasers. Typically, high repetition rate lasers are oscillators which provide low pulse energies ( nj) [25, 29] so that high NA oil-immersion lenses are required. More recently, high-repetition rate solid state [52] and ber [53, 54] femtosecond lasers providing pulse energies of 1 µj have been developed. The higher pulse energies provided by these lasers permit a looser focusing condition, and as will be shown in this thesis, also provide nearly circular waveguide cross sections and mode shapes. 2.2 Interaction of femtosecond laser pulses with transparent materials A cursory review of the current understanding of the physics of ultrafast laser-material interactions is presented below. Nonlinear photoionization is discussed in Section 2.2.1, with energy relaxation and the resulting material modication discussed in Section In Section 2.2.3, linear and nonlinear propagation eects, which can distort the intensity distribution at the focus, will be discussed. 13

44 2.2.1 Free electron plasma formation Focused femtosecond laser pulses, having wavelengths in the visible or near-infrared spectra, have insucient photon energy to be linearly absorbed in glasses. To promote valence electrons to the conduction band, nonlinear photoionization is necessary, which proceeds by multiphoton ionization and/or tunneling ionization pathways depending on the laser frequency and intensity [55]. If there are initial free electrons in the conduction band, freecarrier absorption occurs, resulting in collisional ionization producing an electron avalanche. For irradiation of transparent materials, the simultaneous absorption of multiple photons is required to bridge the band gap. The rate of carrier production dn/dt by multiphoton absorption is related to the laser intensity: dn/dt = σ m I m (2.1) where m is the order of the multiphoton process, i.e. the number of photons required to bridge the bandgap E g, satisfying mhν > E g, and σ m is the cross section of the absorption process. Multiphoton absorption is the dominant mechanism for nonlinear photoionization at low laser intensities and high frequencies (but below that which is needed for single photon absorption). At high laser intensity and low frequency, nonlinear ionization proceeds via tunneling. The strong eld interacts with the Coulombic binding eld, resulting in an oscillation nite potential barrier, through which the valence electrons can tunnel through and escape to the conduction band [56]. As shown by Keldysh [57], multiphoton and tunneling photoionization can be described in the same theoretical framework. The transition between the processes 14

45 Figure 2.3: Schematic of tunneling (γ < 1.5) and multiphoton (γ > 1.5) and intermediate regimes (γ 1.5) of high-intensity photoionization in an atom [34]. can be described by the Keldysh parameter: γ = ω e me cnɛ 0 E g I (2.2) where ω is the laser frequency, I is the laser intensity at the focus, m e is the eective electron mass, e is the fundamental electron charge, c is the speed of light, n is the linear refractive index, E g is the bandgap, and ɛ 0 is the permittivity of free space. If γ is less (greater) than 1.5, tunneling (multiphoton) ionization dominates. For γ 1.5, photoionization is a combination of tunneling and multiphoton ionization. Tunneling and multiphoton ionization regimes can be visualized in Fig. 2.3, which shows a diagram of the photoionization of an electron in an atomic potential for dierent values of the Keldysh parameter. For electrons in a solid, they are promoted from valence to conduction band, rather than ionized to vacuum. For waveguide fabrication, typical laser and material properties result in γ > 1.5, so that multiphoton ionization dominates the excitation process [34]. Electrons present in the conduction band may absorb laser light by free carrier absorption as shown in Fig. 2.4(b). After sequential linear absorption of several photons, a conduction band electron's energy exceeds the conduction band minimum by more than the band gap energy. The hot electron can impact ionize a bound electron in the valence band, resulting 15

46 Figure 2.4: Illustration of multiphoton ionization (a) for seeding electrons for free-carrier absorption (b) followed by impact ionization (c) once the conduction band electron's energy has exceeded the bandgap energy [56]. in two excited electrons at the conduction band minimum, as shown in Fig. 2.4(c). These two electrons can undergo free carrier absorption and impact ionization, and the process can repeat itself as long as the laser eld is present and strong enough, resulting in an electron avalanche. For avalanche ionization, the conduction band electron density, N, increases according to: dn/dt = αin (2.3) where α is the avalanche ionization coecient [55]. Neglecting losses from recombination and electron diusion, which are negligible during the subpicosecond pulse duration, the net change in free electron density from avalanche and multiphoton ionization can be obtained by adding Eq. (2.1) and (2.3): dn/dt = αin + σ m I m (2.4) Avalanche ionization requires that sucient seed electrons are initially present in the conduction band. These seed electrons may be provided by thermally excited impurity of 16

47 defect states, or direct multiphoton or tunneling ionization. For subpicosecond laser pulses, absorption occurs on a faster time scale than energy transfer to the lattice, decoupling the absorption and lattice heating processes [34]. Seeded by nonlinear photoionization, the density of electrons in the conduction band grows through avalanche ionization until the plasma frequency approaches the laser frequency, at which point the plasma becomes strongly absorbing. The plasma frequency is dened by [56]: e ω p = 2 N (2.5) ɛ 0 m e For 1045-nm laser radiation, the plasma frequency equals the laser frequency when the carrier density is approximately cm 3, which is known as the critical density of free electrons. At this high carrier density, only a few percent of the incident light is reected by the plasma, so that most of the energy is transmitted into the plasma where it can be absorbed through free carrier absorption [34]. It is generally assumed that optical breakdown, or damage, occurs when the number of carriers reaches the critical value [34]. In glass, the laser intensity required to achieve optical breakdown is approximately W/cm 2 [34]. Since the lattice heating time is on the order of 10 ps, the absorbed laser energy is transferred to the lattice long after the laser pulse is gone. Because short pulses need less energy to achieve the intensity for breakdown ( W/cm 2 ), more precise machining is possible relative to longer pulses. Because photoionization can seed electron avalanche with femtosecond pulses, this results in deterministic breakdown, unlike longer pulses that rely on the low concentration of impurities ( 1 impurity electron in conduction band per focal 17

48 volume), which are randomly distributed in the material, to seed the electron avalanche [58]. Lenzner et al. found that for very short laser pulses (< 10 fs in fused silica and <100 fs in borosilicate glass), photoionization can dominate avalanche ionization and produce a sucient plasma density to cause damage by itself [59]. Schaer et al. showed that the contribution from avalanche ionization is greater at longer pulse durations and for materials with greater band gap energies [34] Relaxation and modication It is widely accepted that multiphoton/tunneling and avalanche photoionization from femtosecond laser pulses leads to an excitation of conduction band electrons. However, once the electrons have transferred their energy to the lattice, the physical mechanisms for material modication are not fully understood. The rst discovery of femtosecond laser induced refractive index modication in glass [8] has led to much research in a variety of glasses with many dierent choices of laser exposure parameters. Of the over 300 published works since the pioneering work by Davis et al., the observed morphology changes can be generally classied into three types of structural changes: isotropic refractive index change [60], a form-birefringent refractive index change (nanograting formation) [6163], and microexplosions leading to voids [64]. The resulting structure depends on the many exposure parameters (energy, pulse duration, repetition rate, wavelength, polarization, focusing numerical aperture, scan speed) but also the material properties (bandgap, thermal diusivity and others). However, in pure fused silica, these three morphologies can be observed by simply changing the incident laser energy [7, 63], as shown in Fig At low pulse energies ( 100 nj for 0.6-NA focusing of 800-nm, 100-fs pulses), but above 18

49 Figure 2.5: Illustration of the interaction physics of focused femtosecond pulses in bulk transparent materials. (a) The laser is focused below the sample surface resulting in a high intensity in the focal volume. (b) The energy is nonlinearly absorbed and a free electron plasma is created by multiphoton/tunneling and avalanche photoionization. (c) The plasma transfers its energy to the lattice on a 10 ps time scale resulting in one of three types of permanent modication (d): isotropic refractive index change at low pulse energy due to rapid quenching, birefringent nanogratings at moderate energy due to laser-plasma interference, and empty voids at high pulse energy due to microexplosion and shockwave propagation [7]. 19

50 the damage threshold, Chan et al. attributed the isotropic refractive index change within the focal volume to densication by rapid quenching of the melted glass [65]. In fused silica, the density (and refractive index) is increased when a glass is rapidly cooled from a higher temperature [66]. Micro-Raman spectroscopy has shown an increase in the concentration of 3 and 4 member rings in the silica structure in the laser exposed region, indicating a densication of the glass [65]. This argument is supported by the observation that in other glasses (e.g. phosphate and borosilicate) where the density decreases during rapid quenching, a negative refractive index change was observed [10]. An isotropic regime of modication is useful for optical waveguides, where smooth and uniform refractive index modication is required for low propagation loss. For higher pulse energies ( nj for 0.6-NA focusing of 800-nm, 100-fs pulses), birefringent refractive index changes have been observed in the bulk of fused silica glass, as rst reported by Sudrie et al. [61]. Kazansky's group argued that these periodic structures were due to the interference of the laser eld and the induced electron plasma wave [62]. In similarly exposed fused silica samples, Taylor's group observed periodic layers of alternating refractive index with sub-wavelength period after etching the laser-written tracks with HF acid (Fig. 2.6) [63]. The orientation of the nanogratings was perpendicular to the writing laser polarization, which oered preferential HF etching when the nanogratings were parallel to the writing direction (polarization perpendicular to scan direction) allowing the HF acid to easily ow through and etch the damage track, as shown in Fig Such etching of buried damage tracks can be applied to make buried microchannels for biological lab-ona-chip applications. The period of these nanostructures was found to be λ/2n, regardless of scan speed, which implies a self-replicating formation mechanism [67]. The authors have 20

51 Figure 2.6: Scanning electron microscope image of nanogratings formed at 65- µm depth (sample cleaved and polished at writing depth) with polarization parallel (a) and perpendicular (b) to the scan direction. Overhead view (c) of etched microchannels demonstrating polarization selective etching with parallel (top), linear 45 (middle) and perpendicular (bottom) polarizations [67]. proposed that inhomogeneous dielectric breakdown results in the formation of nanoplasmas resulting in the growth and self-organization of nanoplanes. With 800-nm wavelength, this model predicts a minimum nanoplane spacing of 275 nm in fused silica, which is in good agreement with the experimentally measured spacing of 250 ± 20 nm. Further development of this theory is needed to explain why nanogratings do not form in borosilicate glasses and why they only form in a certain window of laser pulse duration and energy in fused silica [67]. At high pulse energies (>500 nj for 0.6-NA focusing of 800-nm, 100-fs pulses) giving peak intensities of W/cm 2, pressures greater than Young's modulus are generated in the focal volume, which drives shockwave formation after the electrons have transferred their energy to the ions ( 10 ps). The shockwave propagates radially outward, losing energy by doing work against the internal pressure of the material (Young's modulus). The distance the shock travels denes the shock aected volume, at which point the shock wave converts into a sound wave and propagates through the material without inducing further damage [68]. The shockwave leaves behind a less dense or hollow core (void), depending on the laser and 21

52 Figure 2.7: Binary bits (voids) recorded in fused silica with 100-fs laser [69]. material properties. By conservation of mass, this core is surrounded by a shell of higher refractive index [64]. Figure 2.7 shows an example of voids formed by Mazur and coworkers in fused silica with a 100-fs laser for the purpose of three-dimensional memory storage. Hirao and Miura have suggested that the induced refractive-index change may be attributed to laser-induced color centers that alter the refractive index through a KramersKronig mechanism (a change in absorption leads to a change in refractive index) [70]. Although color centers have been observed in glasses after exposure to focused femtosecond laser pulses [71, 72], there has been no research that provides a direct quantitative link between color center formation and refractive index change. When forming waveguides in fused silica with an infrared laser, Saliminia et al. found photo-induced absorption peaks at 213 and 260 nm corresponding to SiE' (positively charged oxygen vacancies) and non-bridging oxygen hole center (NBOHC) defects, respectively. However, both color centers were completely erased after annealing at 400 C, although waveguiding behavior was still observed up to 900 C. Therefore, it is unlikely the color centers played a signicant role in the refractive index change [73]. Further, Streltsov and Borrelli found the thermal stability of the 22

53 color centers produced in borosilicate and fused silica glasses with femtosecond lasers is not consistent with that of the induced refractive index [72]. The above interpretations for the structural changes induced by focused femtosecond lasers were based on single pulse interactions, but can likely be extended to explain modication from multiple pulses within the same laser spot, assuming the repetition rate is low enough that thermal diusion has carried the heat away from the focus before the next pulse arrives [7]. In this situation, the ensuing pulses may add to the overall modication, but still act independently of one another. For high repetition rates, the time between laser pulses is less than the time for heat to diuse away, resulting in an accumulation of heat in the focal volume. If the pulse energy is sucient, the glass near the focus is melted and as more laser pulses are absorbed, this melted volume increases in size, until the laser is removed, and the melt rapidly cools into a structure with altered refractive index change. The size of the melted volume can be controlled by the number of pulses absorbed in a static laser exposure, or by the eective number of pulses in the laser spot size for a scanned exposure, N = 2w 0 R/v, where 2w 0 is the spot size diameter (1/e 2 of intensity), R is the repetition rate and v is the scan speed. For cumulative heating, the morphology of the structural change will be dominated by the heating, melting and cooling dynamics of the material in and around the focal volume [7]. The heat accumulation eect, rst observed in surface micromachining of glass [23] was extended to waveguide fabrication by Schaer et al. using a 25-MHz repetition rate Ti:Sapphire oscillator providing 5-nJ pulses [29]. The researchers were able to compensate for the low pulse energy of their laser by tightly focusing the light with a 1.4-NA objective. Figure 2.8 shows evidence of heat accumulation, with the size of modied zones written by 23

54 Figure 2.8: Optical microscope image of static laser exposures formed in borosilicate glass with 5-nJ, 25-MHz, 30-fs pulses focused with 1.4-NA objective. The number of pulses increases, by factors of 10, from 10 2 on the left to 10 5 on the right [7]. static laser exposures growing with the number of incident pulses. The researchers predicted a heat accumulation threshold of 1-MHz repetition rate in Corning 0211 borosilicate glass based on a characteristic time of 1 µs for heat to diuse out of the focal volume [29]. However, it will be shown in the present work that the strength of the heat source (absorbed pulse energy) strongly aects this heat accumulation threshold Propagation eects Linear eects such as dispersion, diraction, aberration and nonlinear eects such as self focusing, plasma defocusing and energy depletion inuence the propagation of focused femtosecond pulses in glass, thereby altering the energy distribution at the focus and the resulting refractive index modication Linear propagation To drive the high intensity ( W/cm 2 ) required to achieve optical breakdown in transparent materials, incident femtosecond laser pulses are typically focused with an external lens to achieve a small micrometer-sized focal spot. Neglecting spherical aberration and nonlinear propagation eects, the spatial intensity prole of a femtosecond laser beam can be well represented by the paraxial wave equation and Gaussian optics. The intensity distribution 24

55 of a Gaussian beam is: I(ρ, z) = ( ) 2 ) w0 exp ( 2ρ2 w(z) w 2 (z) (2.6) where the radial distance is ρ = x 2 + y 2 and z is the axial distance from the beam waist. The waist radius is: ( ) 2 z w(z) = w (2.7) with the diraction-limited minimum waist radius w 0 (1/2 the spot size) for a collimated Gaussian beam focused in a dielectric given by: z 0 w 0 = M 2 λ πna (2.8) where M 2 is the Gaussian beam propagation factor (beam quality) [74], NA is the numerical aperture of the focusing objective and λ is the free space wavelength. The Rayleigh range z 0 (1/2 the depth of focus) inside a transparent material of refractive index n is given by: z 0 = M 2 nλ πna 2. (2.9) Chromatic and spherical aberration cause deviation in the intensity distribution near the focus such that Eq. (2.6), (2.8) and (2.9) may no longer be valid. Chromatic aberration as the result of dispersion in the lens is corrected by employing chromatic aberration-corrected microscope objectives for the wavelength spectrum of interest. In this thesis work, an Ybamplied femtosecond ber laser with low 6-nm bandwidth reduces the eect of chromatic aberration. For lenses made with easily-formed spherical shapes, light rays which are parallel 25

56 to the optic axis but at dierent distances from the optic axis fail to converge to the same point, resulting in spherical aberration. This issue can be addressed by using multiple lenses, such as those found in microscope objectives, or employing an aspherical focusing lens. In laser micromachining, where the light is focused inside glass, the index mismatch of the air-glass interface introduces additional spherical aberration. High numerical aperture (NA > 1.0) microscope objectives, such as those used in biological imaging designed for oil immersion, correct for this spherical aberration where the index of refraction of the oil matches that of the coverslip glass. Dry objectives are also available that are specially designed for spherical aberration at various cover slip thicknesses by means of an adjustable collar [33]. When focusing femtosecond pulses with moderate pulse energies of 0.1-1µJ, optical breakdown can be reached with moderate numerical aperture (NA 0.5) microscope objectives or aspheric lenses. With such focusing, the long working distance ( 5 mm) prevents the use of index-matching oil. As such, the index mismatch between air and the glass sample causes a strong depth dependence for femtosecond laser-formed structures [33, 75]. Spherical aberration increases with numerical aperture, and becomes a signicant problem in laser fabrication for numerical apertures greater than 0.4, when the paraxial approximation breaks down [34]. To simulate the eect of spherical aberration on the intensity distribution at the focus, the scalar Debye diraction integral can be employed [76]. Figure 2.9 shows the simulated intensity distribution for 800-nm light focused 1 mm below the surface of glass for numerical apertures of 0.1, 0.2 and 0.6. Distortion in the intensity prole becomes more apparent with increasing NA, and occurs primarily in the axial direction. The asymmetry of the focal volume, 2z 0 /2w 0 = n/na, described in Section which assumes aberration-free focusing is no longer valid. Due to spherical aberration, the ratio of FWHM of the axial and 26

57 Figure 2.9: Intensity distribution of 800-nm wavelength laser focused 1 mm below the surface of glass with NA = 0.1, 0.2 and 0.6 [77]. transverse intensity proles for NA = 0.6 is nearly equal to the NA = 0.1 case. Dispersion from mirror reections and transmission through materials, in particular the microscope objective which contains several elements, can broaden the pulse width [37] which can reduce the peak intensity and alter the energy dissipation at the focus. However, dispersion can be neglected for the pulse durations of >200 fs employed in this research Nonlinear propagation The propagation of light in a medium is governed by Maxwell's equations: E = B t H = D t D = q + J (2.10) B = 0 where q is the free charge density, J is the current density vector, E and H are the electric and magnetic eld vectors, respectively, and D and B are the displacement vectors given by 27

58 D = ɛ 0 E + P B = µ 0 H+M (2.11) where µ 0 is the permeability of free space and P and M are the induced electric and magnetic polarizations, respectively. In nonmagnetic dielectrics such as glass, M = 0. For propagation in a dielectric, q = 0 and J = 0 so that combining Eqs. (2.10) with Eqs. (2.11) yields the wave equation: 2 E = 1 2 E c 2 t + µ 2 P 2 0 (2.12) t 2 where c = 1/ µ 0 ɛ 0 is the speed of light in vacuum. When light propagates through a dielectric material, it induces microscopic displacement of the bound charges, forming oscillating electric dipoles that add up to the macroscopic polarization which for amorphous glass with an inversion symmetry (χ (2) = 0) is given by: P = ɛ 0 [ χ (1) χ(3) E 2 ] E (2.13) where χ (i) is the i-th order susceptibility, with 4th and higher orders left out of Eq. (2.13) due to negligible contribution. The refractive index can be identied from Eq. (2.13) as: n = 1 + χ (1) χ(3) E 2 = n 0 + n 2 I (2.14) where n 0 = 1 + χ (1) is the linear refractive index, n 2 = 3χ (3) /4ɛ 0 cn 2 0 is the nonlinear refractive index and I = 1 2 ɛ 0n 0 c E 2 is the laser intensity. The spatial variation of the laser intensity can create a spatially varying refractive index 28

59 in dielectrics. Because n 2 is positive in most materials, the refractive index is higher at the center of the beam compared to the wings. This variation in refractive index acts as a positive lens and focuses the beam inside a dielectric as shown in Fig The strength of self focusing depends only on the peak power, which can be qualitatively understood as follows [34]. If the diameter of a collimated beam incident on a transparent material is doubled, the laser intensity and refractive index (Eq. (2.14)) are smaller by a factor of four. However, the area of the self-focusing lens is also increased by a factor of four, which compensates for the decrease in refractive index change, giving the same refractive power. If the peak power of the femtosecond laser pulse exceeds the critical power for self-focusing [34]: P c = 3.77λ2 8πn 0 n 2 (2.15) the collapse of the pulse to a focal point is predicted. As the beam self focuses, the intensity is sucient to nonlinearly ionize the material to produce a free electron plasma, which has its highest density in the center of the pulse and decreases outward in the radial direction due to the typical Gaussian spatial intensity prole. The plasma modies the real part of the refractive index according to: n = n 0 N 2n 0 N c (2.16) where the critical plasma density N c = ω2 ɛ 0 m e, is obtained from Eq. (2.5). For a Gaussian e 2 beam, the plasma-modied refractive index (Eq. (2.16)) is the smallest on the beam axis and the beam is defocused by the plasma, which acts as a diverging lens, that counters the Kerr lens self-focusing (Eq. (2.14)) [56]. A balance between self-focusing and plasma defocusing 29

60 Figure 2.10: Self-phase modulation and self-focusing of ultrashort pulses in a dielectric material [56]. leads to lamentary propagation, which results in axially elongated refractive index structures, which are undesirable for transversely written waveguide structures. Therefore, selffocusing is usually avoided in waveguide fabrication by tightly focusing the laser beam with a microscope objective to reach the intensity for optical breakdown ( W/cm 2 ) without exceeding the critical power for self focusing. In fused silica, n 0 = 1.45 and n 2 = m 2 /W [78] so that for λ = 800 nm, the critical power is 1.8 MW. From Eq. (2.15), the critical power is proportional to the square of the laser wavelength, therefore, lower critical powers result when working with the second and third harmonic frequencies of femtosecond lasers. Also, the critical power is inversely related to the nonlinear (and linear) refractive index, presenting a challenge in forming waveguides in exotic nonlinear materials such as heavy metal oxide (n 0 2, n m 2 /W [79]) and chalcogenide glasses (n 0 2.5, n m 2 /W [80]), polymers (n 0 1.5, n m 2 /W), lithium niobate (n 0 2.3, n m 2 /W [12]) and silicon (n 0 3.5, n m 2 /W [13]) crystals. Since the intensity I(t) of femtosecond laser pulses varies with time, the instantaneous refractive index also varies on time. The phase of the propagating pulse is modulated by the temporal envelope of the pulse itself, an eect known as self-phase modulation. The 30

61 instantaneous frequency varies with time according to: ω(t) = ω 0 2πn 2z λ di dt (2.17) where ω 0 is the carrier frequency and z is the distance traveled in the nonlinear medium. Self-phase modulation broadens the spectrum of the pulse by causing the leading part of the pulse to be red-shifted and the trailing edge to be blue-shifted due the approximately Gaussian temporal prole of the pulse, as shown in Fig Another factor which can inuence the nonlinear propagation of incident radiation is energy depletion before reaching the focus, an eect that is strongly dependent on pulse duration. At high pulse energy, high intensity forms before reaching the focal plane of the lens and nonlinear ionization can deplete the pulse energy well before the focus and cause a plasma with decreased refractive index which counters self-focusing [81]. More conned energy dissipation with longer pulses may be attractive for waveguide writing [43, 44], especially in highly nonlinear materials such as lithium niobate. 2.3 Glass composition Glass is an amorphous solid without long-range periodic order and exhibits a region of glass transformation behavior. Any material, inorganic, or metallic, formed by any technique, and exhibiting a glass transformation behavior is a glass. The glass transformation property is best explained by a graph of enthalpy (or volume) versus temperature, as shown in Fig First consider the glass when at temperatures above the melting point, T m, such that it is in the liquid state. Cooling to any temperature below the melting point normally results in crystallization, with the formation of long-range, periodic atomic order and characterized by 31

62 Figure 2.11: Enthalpy (or volume, inverse of density) versus temperature plot for glass under fast and slow cooling rates showing liquid, glass transition and crystalline states [82]. an abrupt decrease in enthalpy due to the heat capacity of the crystal. In glasses, crystallization is impeded by the kinetic barrier to atomic rearrangement due to a high viscosity, which increases with decreasing temperature. If the liquid is cooled below the melting point without crystallization, it becomes a supercooled liquid. As the supercooled liquid is further cooled, the enthalpy gradually decreases and the viscosity increases. Eventually, as the supercooled liquid is further cooled, the increasing viscosity prevents the atoms from reaching the equilibrium liquid structure, which causes the enthalpy versus temperature to deviate from the equilibrium line, following a curve of decreasing slope, until it becomes determined by the heat capacity of the frozen solid. The temperature region where the enthalpy is between that of a liquid and frozen solid is known as the glass transformation region, as indicated in Fig As shown in Fig. 2.11, a slower cooling rate will lead the enthalpy to follow the equilibrium curve to a lower nal enthalpy (higher nal density) for the room temperature glass. 32

63 Figure 2.12: Viscosity as a function of temperature for common optical glasses showing important glass temperatures [83]. By extrapolating the glass and supercooled liquid enthalpy lines, an intersection point is found that denes the ctive temperature, T f. This ctive temperature characterizes the thermal history of the glass. At this temperature, the structure is considered to be that of the supercooled liquid. It should be noted that fused silica displays an anomalous density change with ctive temperature (cooling rate). The density of the room temperature glass increases with ctive temperature (cooling rate) before reaching a maximum near 1500 C. The dependence of the nal density on the cooling rate was used by Chan et al. to explain the formation of positive refractive index change (increased density) in pure fused silica and negative refractive index change (decreased density) in phosphate glass exposed to 1-kHz femtosecond laser pulses [10]. Figure 2.12 shows the viscosity as a function of temperature for several glasses including 33

64 borosilicate and fused silica, that denes several important glass temperatures. The strain point is dened as the temperature below which glass can be rapidly cooled without introducing stresses. In the glass cooling process, stresses that develop above the strain point are permanent, while stresses that develop at temperatures below the strain point are temporary. Stresses that develop during the cooling process may be reduced or eliminated by heating the sample to the annealing point, known as the temperature at which stresses in the glass are relieved after several minutes, and then slowly cooling the glass to room temperature. The softening point is the temperature at which the glass deforms under its own weight and the working point represents the temperature at which the glass is easily deformed. Since the goal is to use femtosecond lasers to fabricate waveguides in glass which eciently guide light, the optical properties of glass are of great interest. Glasses are among the few solids which transmit light in the visible (and near-infrared) region of the electromagnetic spectrum. The refractive index of glass is inuenced by the interaction of light with the electrons in the glass. Low refractive index glasses have ions with low atomic number, which have both low electron density and polarizability. BeF 2 glasses have low refractive indices of 1.27, while glasses with Pb, Bi and Th have refractive indices ranging from 2.0 to 2.5. Pure fused silica has a refractive index of about Glasses have an ultraviolet (UV) absorption edge due to the electronic transition of a valence electron of a network anion to an excited state. In fused silica, this wavelength is approximately 140 nm ( 9-eV bandgap). By adding alkali oxides to pure silica, the network anions convert from a bridging to a non-bridging state, resulting in a shift in the absorption edge towards visible wavelengths [82]. In common borosilicate glasses, the absorption edge is about 310 nm, corresponding to a bandgap of 4 ev. Absorption in the infrared is commonly 34

65 Table 2.1: Thermal, structural and optical properties of glasses studied. All properties recorded at room temperature (25 C) [84]. Glass code Description D ( 10 3 cm 2 /s) ρ (g/cm 3 ) c p (J/g/K) E g (ev) n D Softening point ( C) Corning EAGLE 2000 Corning 7980 Alkaline earth aluminoborosilicate Fused silica due to vibrational transitions from Si-OH and Si-O bonds, and their overtones [82]. The overtone bands, particularly near 1400-nm wavelength are relatively weak for short samples, but can become very signicant for long lengths of optical ber used in telecommunications systems. Table 2.1 summarizes the important thermal, structural and optical properties of Corning EAGLE2000 borosilicate and Corning 7980 fused silica, the two glasses studied in this thesis. The variation of these properties with temperatures for application in a thermal model will be discussed later in Chapter Waveguide theory Solution to Maxwell's equations for optical bers In this section, the propagation of light in step-index, cylindrical optical bers is discussed. Such geometry will be shown to coarsely represent the refractive index prole of femtosecondlaser written waveguides and thus model the resulting modal beam proles. By taking the Fourier of transform of the electric eld: 35

66 Ẽ(r, ω) = E(r, t) exp(iωt)dt (2.18) Maxwell's equations, Eq. (2.10) and (2.11), can be recast to solve for the wave equation in the frequency domain: 2 Ẽ + n 2 (ω)k 2 0Ẽ = 0 (2.19) where k 0 = 2π/λ is the free-space wavenumber and the dispersive permittivity is assumed to be real because of low optical losses in the visible and near-infrared wavelengths. To take advantage of the cylindrical symmetry of an optical ber, the wave equation is written in cylindrical coordinates (radius ρ, azimuthal angle φ and is the z vertical position) in terms of the axial component E z : 2 E z ρ E z ρ ρ E z ρ 2 φ E z z 2 + n2 k 2 0E z = 0 (2.20) where the refractive index of the ber is n 2 in the core (ρ a) and n 1 in the cladding (ρ > a). Similar equations for the other components of E and H may be written, however, only two out of the six components are independent, with E z and H z usually chosen as independent components. Applying separation of variables and requiring the eld to be nite at the core-cladding interface and to vanish at innite radius, the general solution of Eq. (2.20) is: AJ l (k T ρ) exp(ilφ) exp(iβz), E z = CK l (γρ) exp(ilφ) exp(iβz), ρ a ρ > a (2.21) where J l and K l are the Bessel function of the rst kind and modied Bessel function of 36

67 the second kind of order l, respectively. In Eq. (2.21), l is an integer, β is the propagation constant, k T = n 2 2k0 2 β 2 and γ = β 2 n 2 1k0. 2 The same solution is found for H z but with dierent integration constants. The other four components of E and H can be found using Maxwell's equations. By applying the boundary condition that the tangential components of E and H are continuous at ρ = a, one obtains four equations with integration constants as unknowns. This leads to the following characteristic eigenvalue equation: [ J l (k T a) k T J l (k T a) + K l (γa) ] [ J l (k T a) γk l (γa) k T J l (k T a) + n2 1 K l (γa) ] [ ] 2lβ(n2 n 1 ) 2 2 = (2.22) n 2 2 γk l (γa) akt 2 γ2 For specic parameters k 0, a, n 1 and n 2, the eigenvalue equation can be solved to determine the propagation constant. For each azimuthal index l, the characteristic equation has multiple solutions yielding discrete propagation constants β lm (m = 1, 2,...). A mode is therefore described by the indices l and m, characterizing its azimuthal and radial distributions, respectively. The eective index n eff = β/k 0 gives more physical insight than the propagation constant, as the mode is guided and propagates when n 1 < n eff < n 2 but is otherwise a radiation mode for n eff n 1. The notation LP lm (linearly polarized) is adopted for weakly guiding bers when the axial eld components E z and H z are approximately zero (approximately TEM) and the guided rays are approximately paraxial. The linear polarizations in the x and y directions form orthogonal states of polarization. The two polarizations of mode (l,m) are degenerate with the same propagation constant and have the same spatial distribution. For the weakly guiding ber, n 1 n 2, and after applying derivative identities for the Bessel functions, Eq. (2.22) simplies to: 37

68 X J l±1(x) J l (X) = ± V 2 X 2 K l±1( V 2 X 2 ) K l ( V 2 X 2 ) (2.23) where X = k T a and V = k 0 a n 2 1 n 2 1. The eigenvalue equation can be solved graphically for a certain azimuthal index l, with the intersections of the left and righthand side of Eq. (2.23) giving the possible solutions X lm, from which, the corresponding propagation constants β lm can be determined. For V < 2.405, all modes except the fundamental LP 01 mode are cuto. Such bers support a single mode and are referred to as single-mode bers (SMFs). Since a Bessel-form electric eld distribution is cumbersome to use in practice, it is often approximated by a Gaussian distribution. For the LP 01 mode polarized along the x-axis, the transverse electric eld distribution can be written as: E x = A exp ( ρ 2 /w 2 0) exp(iβz) (2.24) where w 0 is the waist radius (1/2 the spot size). A comparison of the actual eld distribution with the tted Gaussian is shown in Fig for V = 2.4. The quality of t is very good for values of V near 2 [85], which is typical of the fabricated waveguides described in this thesis Evanescent coupling If two waveguides are suciently close such that their optical elds overlap, light will periodically transfer from one waveguide to the other. Formally, one can solve Maxwell's equations in both waveguides to determine the modes of the system. These modes are dierent than for the waveguides in isolation and the exact analysis is quite dicult. However, if we assume weak coupling between the waveguides, coupled-mode theory, analogous to time-dependent 38

69 is a universal function of V and g, provided we restrict ourselves to weakly guiding fibers r F 1.4 F 9 = CO V= 2.4 A, * 00 ACTUAL FIELD L :ooo GAUSSIAN APPROXIMATION W a F w S I o I Cb F F 0.0 L 0.(.0 I. S& r/a FIG. 8. Same as Fig. 4 with V = 2.4 and g = a J. Opt. Soc. Am., Vol. 68, No. 1, January 1978 optimally matched Gaussian distribution (solid dots) with V = 2.4. [86] V FIG. 10. Normalized Gaussian beam width parameter of V for several values of the exponent of the refractiv 9. Figure 2.13: Comparison of the shape of the fundamental mode eld (open circles) with the D. perturbation theory in quantum mechanics, is a good approximation. The eld is expressed as a linear combination of the normal modes of the unperturbed medium, where the amplitude coecients A m (m is an integer) vary with propagation distance, to account for the energy exchange between waveguides: E = m A m (z)e m (x, y) exp(i(ωt β m z)) (2.25) In Eq. (2.25), the mode amplitudes of the unperturbed system, E m (x, y), are normalized. To solve for the coupled mode equations, Eq. (2.25) is substituted into Eq. (2.19). Assuming a slowly varying amplitude due to weak coupling (neglecting d 2 A m /dz 2 ) and that there are only two waveguides, which support normal modes E 1 (x, y) exp(i(ωt β 1 z)) and E 2 (x, y) exp(i(ωt β 2 z)), the coupled mode equations for codirectional coupling (β 1 β 2 > 0) are [87]: 39

70 d A dz 1 + iκa 2 e i βz = 0 d A dz 2 + iκa 1 e i βz = 0 (2.26) where β = β 1 β 2. For the case of phase matching for identical waveguides with the same propagation constant ( β = 0), the solution of Eq. (2.26) is: A 1 (z) = A 1 (0) cos κz A 2 (z) = ia 1 (0) sin κz (2.27) where the light is launched at z = 0 in waveguide 1 such that A 2 (0) = 0. The coupling ratio is dened as the power in the cross port divided by the sum of the power at the two output ports: r = P 2 P 1 + P 2 = where the coupling coecient is : A 2 (z) 2 A 1 (z) 2 + A 2 (z) 2 = sin2 κz (2.28) κ = k2 ( ) 0 n 2 2β wg n 2 bulk E 1 (x, y)e 2 (x, y)dxdy (2.29) 2 where n wg is the refractive index in the waveguides and n bulk is the refractive index in the bulk, assuming a step refractive index prole. The integration in Eq. (2.29) is carried out over waveguide 2. The power coupling ratio for the phase-matched case results in sinusoidal oscillation of power between waveguides. The beat length for full power oscillation is inversely related to the coupling coecient: l B = π/κ. 40

71 Chapter 3 Experimental In this chapter, the femtosecond laser system for micromachining is reviewed in detail (Section 3.1). In addition, the procedures for sample preparation (Section 3.2) and waveguide characterization (Section 3.3) are discussed. 3.1 Femtosecond laser system IMRA femtosecond ber laser A crucial component to the proposed thesis was the novel ber-amplied laser, the IMRA µjewel D-400-VR, providing a pulse duration of 300 fs (FWHM of Lorentzian). Based on a partnership with IMRA America, our lab was able to purchase the rst commercial version of this laser for our waveguide writing studies. Providing a variable repetition rate between 200 khz and 5 MHz at a moderately high average power of 500 mw, the IMRA laser bridges a gap between high-energy kHz Ti:Sapphire regenerative ampliers and low-energy 80- MHz Ti:Sapphire oscillators, as shown in Table 3.1. Repetition rates of 200 khz to 2 MHz will be shown in Chapter 4 to be key in unraveling the contribution from thermal diusion and heat accumulation eects during waveguide writing in glasses. Based on prior work with other femtosecond laser systems, pulse energies of 1 µj focused with typical microscope 41

72 Table 3.1: Commercial lasers available for waveguide fabrication. Italicized systems were unavailable at the time time of laser purchase for this thesis work (2003). Laser model Technology τ(fs) R (khz) P (W) M 2 λ (nm) Spectra Physics Spitre Ti:S regen. amp or Coherent RegA Ti:S regen. amp or Spectra Physics Tsunami Ti:S osc High Q FemtoNOVA Yb cavity-dumped 400 1, IMRA µjewel D-400-VR Yb ber amp to 5, Amplitude Systemes Tangerine Yb ber amp , N/A 1030 Clark-MXR Impulse Yb ber amp to 25, objectives (NA = ) are expected to lead to strong nonlinear absorption resulting in refractive index modication in glasses [17]. In the case of low-repetition rate ampliers, the laser power must be attenuated 1000-fold to avoid creating damaged refractive index change structures. In the opposite extreme, high repetition rate ( 80 MHz) oscillators provide insucient energy ( 10 nj) to take advantage of modest NA to drive heat accumulation while maintaining large working distances and avoiding spherical aberration. Due to its all- ber approach (except free-space compressor), the IMRA ber laser is attractive for industry and research lab use because of its compact footprint and simple turn-key operation with no water cooling required. The IMRA laser provides an ideal combination of high average power and variable repetition rate, and was therefore selected over the cavity-dumped xed 1-MHz system from High Q and the traditional oscillator and regenerative amplier systems discussed above. Recently announced ber laser ampliers from Amplitude Systemes and Clark-MXR, unavailable at the time of our laser purchase in 2003, show excellent promise because of vastly increased power levels of 20 W, allowing for pulse energies >1 µj at > 10 MHz repetition rate. The IMRA µjewel laser uses chirped-pulse amplication to avoid excess ber nonlinear- 42

73 fiber stretcher fiber amplifier(s) bulk grating compressor fiber laser Figure 3.1: Chirped-pulse amplication in IMRA µjewel laser [88]. ities during propagation, as described pictorially in Fig Seeded by an Ytterbium-ber oscillator providing 300-fs pulses at 10-mW average power, a ber stretches the pulses to 200 ps to avoid excess nonlinearities and damage inside the ber during the amplication stage. After amplication, the pulses are recompressed using a bulk diraction grating to 300-fs duration pulses with 500-mW average power. The repetition rate is adjusted by acoustooptic downcounter between 200 khz and 5 MHz [88], giving a range of pulse energies from 100 nj at 5 MHz to 2.5 µj at 200 khz Beam delivery system During the rst six months of the PhD project, the author was responsible for designing the ultrafast laser lab, purchasing and installing the equipment and aligning all the optics. Haibin Zhang and Sergey Reznik also played crucial parts in the development of the laser lab. Haibin was mainly responsible for the purchase, design and implementation of the Aerotech motion stages and granite arch micromachining station in addition to the beam delivery optics for the Spectra Physics Ti:Sapphire laser. Sergey provided excellent technical support with several major contributions including design and construction of the optical table enclosure and several custom-designed mounts for laser experiments. The purpose of Sections 43

74 is to familiarize new users to the operating and alignment procedures for the IMRA ber laser for micromachining experiments. In addition to the laser system, procedures for operating/aligning the power attenuation module, beam delivery optics, acousto-optic modulator, autocorrelator, second harmonic conversion setup, translation stages, vision system and focusing lens will be described in detail. Figure 3.2 shows the beam delivery setup for the IMRA femtosecond ber laser. A trigger out from the laser was used to synchronize measurements with the pulse train (not used in this thesis work). The 200-ps pulse duration output from the laser head was directed with dielectric turning mirrors TM1 and TM2 into the compressor, where a grating compressed the pulse to 300 fs (Lorentzian FWHM) as discussed above. All mirrors (CVI Y ) before the second harmonic crystal (TM1-6 and FM1-3) were designed for high reection at 1045-nm wavelength. After the compressor, the laser power was varied using a half waveplate (Thorlabs WPH05M-1053) custom-mounted to a computer-controlled (via Aerotech A3200 controller) rotation stage (Aerotech ART310) before a polarizing beam splitter cube (CVI PBS ) which ensured linear, horizontal polarization (parallel to optical table surface). The average power was measured with a thermal power meter (Ophir 10A) at any point along the beam path, but typically just after aperture A1 for fundamental wavelength experiments and just after apertures A1 and A2 for second harmonic experiments. After the polarizer, the laser beam was directed with mirror TM3 towards mirror TM4 along the normal beam path (solid red line) or may be reected by the ip mirrors FM1 and FM2 for transmission to an acousto-optic modulator (AOM) or autocorrelator, respectively (dotted red lines). For the normal beam path, the beam was directed through apertures A1 and A2 to ensure correct alignment to the micromachining station (Fig. 3.3). An optional 44

75 second harmonic setup may be inserted between the apertures, which is described in detail in Section Mirror FM1 directed the beam towards the TeO 2 -based AOM (Neos LTD) powered by an RF driver with a digital modulation input (Neos DS). The AOM was used to modulate the pulse train for reducing the eective repetition rate (Section 4.1.2) or for writing Bragg grating waveguides [89]. For the input modulation, one of three devices were used: a digital delay generator (Stanford Research Systems DG535), function generator (Agilent 33220A) or the position-synchronized output (PSO) from the Aerotech A3200 motion controller. Mirror FM1 must be adjusted so that the beam passes through the alignment aperture A3. To achieve optimally fast response time ( 150 ns), the beam size was reduced to 1-mm diameter using a beam reducing telescope consisting of a converging lens (L1; 250-mm focal length; CVI PLCX C-1064) and diverging lens (L2; - 50-mm focal length, PLCC C-1064) before it passed through the AOM. The rst diraction order was directed through an identical, but reversed beam expanding telescope (L2' and L1') to restore the original beam size, at which point, the beam was directed back along normal beam path with mirrors TM5 and FM3. By angle tuning the AOM, the maximum diraction eciency was approximately 60%. To ensure the beam was aligned through apertures A4 and A2, mirrors TM5 and FM3 should be adjusted appropriately Micromachining station The beam passing through aperture A2 shown in Fig. 3.2 was directed upwards to mirror TM8 xed on the granite arch shown in Fig All mirrors (TM7-10; CVI HM ) shown in Fig. 3.3 have high-reection coatings to reect both the fundamental and sec- 45

76 Autocorrelator control box and PC (RS232) Aerotech motion stage controller Rotation stage with half waveplate Trigger out Granite arch Autocorrelator TM6 A2 L3' L4' Temperature controller HM LBO L4 TM5 L3 A4 FM3 AOM driver (BNC) L1' L2' AOM L2 L1 TM3 A3 A1 Polarizer TM4 FM1 FM2 Compressor TM2 TM1 IMRA laser head Optional SHG setup Figure 3.2: Beam delivery optics showing normal beam path (solid red line) and optional beam paths (dotted red lines) for autocorrelation and transmission through AOM. TM = turning mirror, FM = ip mirror, HM = hot mirror, A = aperture for alignment purposes. ond harmonic wavelengths. Using mirrors TM8 and TM9, the beam was aligned through apertures A5 and A6, and then directed by mirror TM10 to the aspherical focusing lens L5 (New Focus 5720 series). To rotate the linear polarization or achieve circular polarization, a half or quarter waveplate (WP) was inserted after aperture A5, as shown in Fig The numerical aperture of the aspheric focusing lenses were 0.25, 0.4, 0.55 and 0.65 yielding spot size diameters, 2w 0, (1/e 2 diameter of intensity) of approximately 3.4, 2.2, 1.6 and 1.4 µm, respectively, using Eq. (2.8). The focusing lens was mounted on a Newport LP-1A objective holder (2-axis translation with tip/tilt control) attached to the z-axis translation stage (Aerotech ALS130). The sample holder, focusing lens and motion stages were situated on a granite arch for increased stability and ease of sample alignment. Samples were translated transversely relative to the incident laser at speeds of 0.05 mm/s to the hardware limit of 100 mm/s using precise air-bearing motion stages (Aerotech ABL1000). Aerotech ABL1000 xy stages, ALS130 z stage and ART310 rotation stage (power automation) were connected to the Aerotech A3200 motion controller, which was interfaced to a desktop computer by FireWire connection. Software control was provided by G-code programs loaded in 46

77 the Nview MMI front-end. As described above, the PSO could be used to control the AOM or another TTL-controlled device within a user-dened laser processing region, as dened in a G-code routine. To align the beam directed from mirror TM10 towards the focusing objective L5, the lens was initially removed and the reection o an optical at placed directly on the air-bearing stage (black surface shown in Fig. 3.3) was observed on the nearly-closed aperture A5. The reected beam was adjusted to be collinear with the incident beam and perpendicular to the motion stage surface by adjusting mirror TM10 so that the reected beam propagated back through aperture A5. An infrared viewer (Newport IRV2-270) was used to observe the reected spot on the aperture. To ensure the focusing lens was perpendicular to the incident laser, the optical at was placed on the objective holder. The reected beam was again aligned so that it passed back through aperture A5 by adjusting the tip/tilt angles on the objective holder. The focusing lens L5 may then be secured to the objective holder and aligned with the incoming laser by translating the lens to achieve maximum power on target, as measured by a power meter (Ophir 10A) placed after the focusing lens. To avoid damage, the power meter should be placed as far away from the laser focus as possible so that the laser just lls the detector area. The glass substrate may now be placed on the sample holder and should be secured with magnets to avoid slipping during laser exposure scans. The collimated beam from the ber laser had a nearly Gaussian prole with M 2 = 1.3 and 4-sigma diameters 6Ö5 mm 2 prior to lens L5, as measured by a large-area CCD camera (Ophir BeamStar FX 66). This beam size slightly overlled the 5-mm clear aperture of the 47

78 Vision system A6 A5 TM8 TM10 WP TM9 Aerotech ALS130 L5 Aerotech ABL1000 TM7 Figure 3.3: Laser micromachining station on granite arch: output from femtosecond ber laser was directed towards the objective, which focused light below the surface of fused silica and borosilicate glass samples. WP = waveplate. 48

79 focusing lenses resulting in 400-mW average power at target. To place the laser focus at the sample surface, the Fresnel reection, which leaked through the nal mirror as indicated by the red arrow in Fig. 3.3, was directed with a mirror towards a FireWire-interfaced CCD camera (Sony XCD-X710) with a zoom lens (Computar L5Z6004). The best focus was obtained when the spot was smallest and brightest on the CCD camera. For focal plane nding, the laser power was attenuated with a neutral density lter with optical density of prior to mirror TM7 to avoid damaging the sample. Since the beam output from the ber laser was not perfectly collimated (divergence angle 0.6 mrad), there was a small error in the focus location (less than ± 10 µm) using this method. To ensure the focus was at the sample surface, laser tracks were written with small z osets (eg. z = -10,-5, 0,+5,+10 µm, where z = 0 µm corresponds to the smallest spot on the CCD camera) to check when an ablation line was produced, using energies just above the damage threshold for the best precision. The resulting ablation lines were visible by eye without the aid of microscopy. Alternatively, the plasma emission could be observed by eye during waveguide/ablation formation - a much dimmer emission was observed during ablation than waveguide writing in borosilicate glass with no plasma visible by eye when the laser focus was placed 10 µm above the surface. In fused silica, the contrast in the plasma emission during waveguide and ablation writing was less pronounced. To correct for the small angle of the sample surface relative to the motion stage platform, a tip/tilt stage (Newport TTN80) was used to ensure the reected laser spot remained at its smallest and brightest on the CCD over the entire sample area. The sample surface was assumed to be planar, so that by iteratively scanning to opposite extremes along the x and y axes, the tip/tilt controls were manually adjusted to optimize the parallelism of the sample surface relative to the stages. Using this procedure, 49

80 Focusing Lens Collimating Lens Figure 3.4: Setup for second harmonic generation of 522-nm light from incident 1045-nm radiation. The LBO crystal is placed at the focus of a telescope to maximize conversion eciency. the laser focus was placed at the sample surface within approximately ± 2 µm over the entire sample, due to the small nonuniformity of sample surfaces. Such variation in focus location has negligible eect on the properties of the buried waveguides reported in this thesis Second harmonic generation Among the various nonlinear crystals available, lithium triborate (LBO) was selected for second harmonic conversion because it oers non-critical phase matching (NCPM), a high damage threshold (45 GW/cm 100 ps), excellent transmission from UV to mid infrared, and a large acceptance angle with zero walk o angle. Figure 3.4 shows the setup for second harmonic conversion of incident 1045-nm light. The LBO crystal (Newlight Photonics) was placed at the focus of a telescope and was heated by an oven to 170 C for maximum conversion eciency. Since the energy per pulse from the ber chirped pulse amplication (FCPA) µjewel changes for dierent repetition rates, dierent focusing conditions were required for optimal conversion. Table 3.2 shows the conversion eciency, η, and focal length, f, at dierent repetition rates, R. These conversion eciencies are maximum values, obtained when launching the maximum incident fundamental power, P inc, at each repetition rate. The focal length was chosen to maximize conversion eciency but to avoid damaging the crystal. Lenses on 50

81 Table 3.2: Second harmonic conversion eciency and focal length at dierent repetition rates. R (khz) P inc (mw) f (mm) η (%) the infrared and visible wavelength sides were anti-reection coated for fundamental and second harmonic wavelengths, respectively. Referring to Fig. 3.2, lenses L3 (350-mm focal length; CVI PLCX UV-1064) and L3' (350-mm focal length; PLCX UV-532) were used for repetition rates of khz while lenses L4 (200-mm focal length; CVI PLCX UV-1064) and L4' (200-mm focal length; CVI PLCX UV-532) were used at repetition rates of 1-2 MHz. The hot mirror (HM; Thorlabs FM01) was used to transmit the converted green wavelength but reect the unconverted infrared wavelength. Optimal conversion eciency was achieved when the crystal was placed directly at the focus of the symmetric telescopes, with care taken to align the z-axis of the LBO crystal, indicated by an arrow on the crystal oven, with the incident fundamental laser polarization (horizontal and parallel to optical table). The generated second harmonic was polarized perpendicularly to the z-axis of the crystal (vertical and perpendicular to optical table) Autocorrelation To measure the duration of the pulses from the IMRA ber laser, a ip mirror was used to divert the beam from its normal beam path and towards the autocorrelator (APE PulseCheck). As shown in Fig. 3.5, the laser pulse entering the autocorrelator was divided into two parts with a beam splitter. Each part traversed an interferometer arm containing a retroreector. One of the retroreectors was mounted on a translation stage that continuously changed the 51

82 Use pulse to measure itself Use pulse to measure itself τ τ SHG SHG τ τ Figure 3.5: Intensity autocorrelation in non-collinear geometry: Pulses are split and passed through two arms with variable path length dierence before interfering at SHG crystal. When the pulses did not overlap temporally (left frame), no autocorrelation signal was detected. When pulse overlap temporally (right frame), an SHG autocorrelation signal was detected [90]. length of one interferometer arm (delay). The identical, time-shifted pulses are recombined and focused by a mirror, where they overlapped in a beta barium borate (BBO) crystal which is angle-tuned for maximum second harmonic generation (SHG) eciency at the laser wavelength. Light generated in the crystal was detected by a ltered photomultiplier tube (PMT). The electric eld at the SHG crystal is: E tot (t, τ) = 1 2 (E 1 (t) + E 2 (t + τ)) (3.1) and the second harmonic eld intensity is: I 2ω (t, τ) χ (2) 2 E 2 tot 2 = χ (2) 2 E 2 1 (t) + 2E 1 (t)e 2 (t + τ) + E 2 2(t + τ) 2 (3.2) The detector only selects the middle autocorrelation term 2E 1 (t)e 2 (t + τ) so that the integrated detector signal yields an intensity autocorrelation A(τ): 52

83 Table 3.3: Deconvolution factor for determining pulse width from autocorrelation width Temporal prole Deconvolution factor Square 1.0 Gaussian 2 Sech Lorentzian 2.0 A(τ) = I 2ω (t, τ)dt I 1 (t)i 2 (t + τ)dt (3.3) To quantify the chirp, which cannot be measured with intensity autocorrelation, collinear autocorrelation is needed so that all three terms in Eq. (3.2) contribute to the second harmonic intensity. This approach is not emphasized, as the compressed pulse from the IMRA laser is nearly transform limited. It can be shown that the full width at half maximum (FWHM) of the intensity autocorrelation function, τ ACF, is related to the FWHM of the laser pulse, τ, by a numerical factor referred to as the deconvolution factor γ = τ ACF /τ, which depends on the temporal shape of the pulse. If this factor is known, or assumed, the pulse duration can be measured using an intensity autocorrelation. As stated above, the phase cannot be measured. Table 3.3 shows the deconvolution factor for several pulse shapes. For the IMRA femtosecond ber laser, a Lorentzian best ts the temporal pulse prole. When using the PulseCheck autocorrelator with the IMRA femtosecond ber laser, the NIR-PMT (incident wavelength range nm; noting that the detectors are sensitive to the second harmonic wavelength incident on the autocorrelator) and NIR crystal should be used. For the second harmonic wavelength, the VIS I-PMT ( nm) should be used in conjunction with the VIS I crystal. These PMTs function for all repetition rates provided 53

84 Table 3.4: APE PulseCheck settings for IMRA laser Setting 1045 nm 522 nm Crystal NIR VIS I Detector NIR-PMT VIS I-PMT Gain Acquisition Free run Free run Scan range 5 ps 5 ps Sensitivity 1 1 Average Alpha by the IMRA ber laser (200 khz to 5 MHz). For lower 1-kHz repetition rates, photodiode detectors triggered by the laser must be employed. PMT detectors must not be used with the amplied Ti:Sapphire laser, as they can easily be damaged by the high pulse energies provided by the Spectra-Physics Spitre system. These sets include VIS-PD ( nm) with VIS I crystal or NIR-PD ( nm) and IR-PD ( nm), used with NIR crystal. Table 3.4 summarizes the measurement settings for autocorrelating with the IMRA ber laser. The gain should be set to 500 because of the nonlinear response of the PMT, however, other values may be used when aligning the autocorrelator. Before sending the beam to the autocorrelator with the ip mirror, the beam should be attenuated to 100-mW average power with an optical density of 0.5 to avoid damaging the PMT. The beam should rst be aligned so that it enters the entrance aperture. For easier alignment, the alignment aperture should remain in the down position. To align the beam inside the autocorrelator, the input mirror on the autocorrelator and the upstream ip mirror are adjusted until the alignment spot is aligned with the cross on the front control window. If two spots are observed, they may be united with the beam distance knob, which controls the separation between beams before they are focused on the SHG crystal. When the spots 54

85 are overlapped, there is no separation between the beams (collinear autocorrelation) and the resulting autocorrelation signal is stronger, which is useful for alignment purposes. The signal on the autocorrelation monitor can be optimized by adjusting the delay (temporal shift on the screen) and focus (position of focusing lens) knobs, and also the input mirrors. When the signal is clearly found, the beam distance should be increased for non-collinear intensity autocorrelation so that one beam is centered on the cross and the other is transversely displaced near the right side of the front control window. The autocorrelator is aligned for intensity autocorrelation when the background signal does not increase when the gain knob is increased. Another way to conrm the beam alignment is to verify that the SHG autocorrelation signal goes to zero when enabling both beam shutters. Further optimization of the beam distance may be required. Before recording the autocorrelation function, further optimization of the focus and outside mirror alignment may be needed to maximize the peak of the autocorrelation signal. The peak of the autocorrelation signal should be set close to the full scale range on the display by adjusting the input power, with the horizontal axis set to 5 ps so the 600 fs ACF pulse width is clearly visible. Figure 3.6 shows a typical autocorrelation trace with a Lorentzian t giving a pulse duration of τ = 311 fs (Lorentzian FWHM). 3.2 Sample preparation Waveguides were written in Corning EAGLE2000 borosilicate and 7980 fused silica glass samples, with properties described in Table 2.1. Samples measured mm 3 (waveguide length 25 mm) unless specied otherwise and were purchased from Precision Glass and 55

86 Figure 3.6: APE PulseCheck software showing Lorentzian prole of intensity autocorrelation function. Optics in Santa Ana, California. Samples were scribed from large sheets of mother glass with surface quality of 80/50 and surface roughness less than 1 nm. For borosilicate, samples were not polished before waveguide inscription because waveguides written in the heat accumulation regime taper away near the facets, so that edges must be ground by 200 µm followed by ne optical polishing. Samples were hand-polished in-house by our technician or commercially polished by BMV Optical Technologies in Ottawa, ON for the higher optical quality required for refracted near eld (RNF) or microscope characterization of the waveguide cross sections. For fused silica, samples were pre-polished at the facet edges because waveguides did not taper away near the end facets so that post-polishing was not required unless the sample was to be characterized by RNF. There was a small distortion in laserwritten waveguides as the laser passed through the end facet, but this eect had a negligible eect on the waveguide's insertion loss and mode prole in fused silica glass. 56

87 4 μm 4 μm 14 μm MFD = 10 μm Figure 3.7: Cross sectional (left) and overhead (right) view of good waveguide written in borosilicate glass. In the cross sectional view, the incident laser was incident from the top as shown by the red arrow. 3.3 Waveguide characterization After laser fabrication, waveguide morphology, insertion, coupling and propagation loss, mode prole, and refractive index prole were characterized, as described in this section. A majority of the thesis work was devoted to these characterization methods, which provided crucial feedback in discovering the optimum waveguide writing conditions Microscope observation After waveguide writing and sample polishing, the rst characterization step was to use white-light microscopy for the qualitative assessment of the cross sectional and axial laserinduced refractive index change. A standard Olympus BX51 microscope was used in transmission mode with dry microscope objectives with 50 or 100 magnication, depending on the feature size. Initial assessment from overhead was performed by placing the sample directly on top of a microscope slide on the microscope observation stage. Optimum waveguides had a uniform axial shape with a brighter central contrast relative to the bulk, indicative of a positive refractive index change. To observe cross sectional proles, samples were rotated 57

88 by 90 degrees so the facet faced the microscope objective. Ideal waveguides were those with a brighter circular core, similar to that of optical bers, which may suggest good optical connement of 1550-nm wavelength light with a circular mode shape, possibly well-matched to optical ber. The axial and cross sectional microscope image of a typical good waveguide are shown in Fig Fiber-based waveguide characterization Once reasonable quality waveguides were identied by microscope observation, a 633-nm wavelength HeNe laser (Melles Griot) was ber butt-coupled with SMF to the input facet of the sample to qualitatively test the guiding characteristics of the laser-written tracks using the characterization stage setup shown in Fig. 3.9, described in detail below. If there was sucient scattering loss, waveguiding was conrmed by observing the scattered streak by eye. Optimum ber alignment at the input facet was obtained when the scattered streak was brightest, and was used as a starting point for waveguide insertion loss and mode prole characterization at 1550-nm, described in Sections and , respectively. Waveguide mode proles and loss at 633-nm wavelength were not usually recorded, as the main focus was to demonstrate good device performance at the important telecom wavelengths ( nm). If red scattering was not visible, this indicated no waveguiding or low scattering, possibly from low-loss guiding of red light. In this case, red waveguiding was con- rmed by observing the far-eld diraction pattern on a white screen, as shown in Fig The bright central spot and concentric interference rings demonstrated that the laser-written track guided red light. 58

89 and butt-coupling. For end-fire coupling, Figure 3.5a shows a microscope objective lens (a) (b) Figure 3.8: Far-eld intensity distribution of 633-nm (c) wavelength light output from femtosecond laser-written waveguide. Figure 3.5 Launching probe laser light into the waveguides: (a) end-fire coupling and (b) butt coupling. The far-field beam pattern from the waveguide is shown in (c). In the telecom band, the waveguide mode prole, insertion loss and propagation loss used to focus the probing laser light to a few micron diameter spot size to match were characterized with an infrared laser butt-coupled to the input waveguide facet using waveguide size. Mismatch between the numerical aperture of the waveguide and the lens Corning SMF28e ber. Input/output bers and waveguide were manipulated with Luminos produce coupling losses. Butt-coupling, shown in Figure 3.5b, used a cleaved fiber to I3000 (3-axis) and I5000 (5-axis) 100-nm resolution manual positioners, respectively. An 31 overhead vision system consisting of a IEEE-1394 FireWire CCD camera (Sony XCD-V50) with variable zoom lens (Edmund VZM 300i) was interfaced to a computer for coarse visual alignment followed by precise ber alignment described below Insertion loss The waveguide insertion loss (IL) was obtained from the power transmitted P t (Newport 818-IG photodetector) through the waveguide by butt-coupling SMF28 ber at both the input and the output waveguide facet and normalized to the power propagated by directly butt-coupled input and output bers, P ref. Index matching uid was applied at the end facets to avoid Fresnel reection losses and improve measurement accuracy. If the power transmitted through the sample and the reference power are measured in dbm, the insertion 59

90 Figure 3.9: Sample characterization setup: input and output bers are aligned with sample using manual positioners. An overhead vision system linked to a computer monitor is used for visual alignment. loss is given by: IL (db) = Pref Pt. (3.4) Typically, the laser source used was a monochromatic laser tuned to 1550-nm wavelength (Photonetics Tunics-BT), but it was also possible to launch a broadband source (Agilent 83437A) consisting of four LEDs that cover the 1250 to 1650-nm telecommunications spectrum. With the broadband source, the power transmitted through the waveguide was collected by a butt-coupled single mode ber and transmitted to an optical spectrum analyzer (OSA; Ando AQ6317B) using the same alignment procedure used for insertion loss measurement. This insertion loss measurement method gives an upper bound for the insertion loss [91], because of the increased complexity in aligning three components in the ber-waveguide ber setup compared to the two components in the ber- ber setup. Therefore, the ber60

91 waveguide-ber power value may be articially too low, resulting in an overestimate of the insertion loss from Eq. (3.4). For experienced users, this overestimate is negligible (<0.05 db) considering the >1-dB insertion losses reported in this thesis. Another way insertion loss could be overestimated is when the waveguide is non-collinear with the input and output bers. This issue was partly addressed by xing the input, waveguide and output stages on a common rail, as shown in Fig To guarantee proper angle alignment, the sample and ber connections are viewed from above with the vision system with minimum magnication (0.75 ) for maximum eld of view. The sample, which is held to the waveguide stage with a vacuum holder, may be rotated manually or by using the yaw axis on the stage. The error in insertion loss measurement for 2.5-cm long waveguide samples studied in this thesis, was approximately ±0.05 db, as inferred from the standard deviation of repeated measurements on the same waveguides Mode prole measurement Before discussing the experimental setup for mode prole measurement, three IR camera technologies are reviewed. Vidicon is a storage-type camera tube in which a charge-density pattern is formed by the imaged scene radiation on a photoconductive surface which is then scanned by a beam of low-velocity electrons. The uctuating voltage coupled out to a video amplier can be used to reproduce the scene being imaged. PbSe photocathodes may be used to achieve a broad wavelength response from nm, as indicated in Table 3.5, which is the main advantage of vidicon technology compared to phosphor-coated charge-coupled device (CCD) and InGaAs technology. The drawbacks of vidicon include lag, a phenomenon when some of the output signal lingers after the incident light is interrupted, and a nonlinear 61

92 response, so that a gamma correction (0.6) is required. For the specic application of mode proling, the nonuniform response (shading) is the main drawback of vidicon technology. Coupled with the large footprint of such detectors, vidicon technology was ruled out for mode proling waveguides reported in this thesis, except when characterizing at 1300-nm wavelength (Section 6.1) since this wavelength could not be detected by the phosphor-coated CCD. The phosphor-coated CCD camera (Spiricon FireWire SCOR ) was primarily used for capturing mode proles of waveguides reported in this thesis. In a CCD, light is projected by a lens onto a photoactive region (an epitaxial layer of silicon composed of an array of capacitors), causing each capacitor to accumulate charge proportional to the light intensity at that location. The CCD acts as a shift register, with a controlling circuit converting the entire semiconductor contents of the array to a sequence of voltages, which it samples, digitizes and stores in memory. In the Spiricon SCOR , the CCD focal plane array is coated with a phosphor that emits visible radiation when illuminated with infrared radiation in the 1460 to 1625 nm wavelength range. Thus, the silicon photoactive region, which is sensitive to wavelengths from 190 to 1100 nm, can detect telecom wavelengths by means of the phosphor coating. Because the phosphor has a nonlinear response, a gamma correction (1.95) is required for accurate beam width measurements. The linearity correction also reduces the SNR from 58 to 30 db, an eect which can be counteracted by frame averaging to yield an SNR of 42 db. As shown in Table 3.5, the phosphor-coated CCD oers increased resolution, better uniformity and smaller size compared to vidicon technology. Another option for mode proling is InGaAs camera technology, such as the Sensors Unlimited SU320MS-1.7RT described in Table 3.5. InGaAs cameras oer a linear response, 62

93 Table 3.5: Cameras for mode proling at telecom wavelengths [9294] Model Spiricon SCOR Hamamatsu C2741 (N2606 tube) Sensors Unlimited SU320MS-1.7RT Sensor Phosphor-coated silicon CCD Vidicon tube InGaAs Pixels horizontal lines Pixel pitch µm 2 N/A µm 2 Area mm mm mm 2 Dimensions in in in 3 Spectral response SNR Advantages Disadvantages nm, nm 30 db (with gamma correction) Compact, high-resolution, low-cost Wavelength range, nonlinear response nm nm 46 db 66 db Broad wavelength spectrum, good sensitivity Lag, shading, nonlinear response, large footprint High sensitivity, linear and uniform response, excellent SNR High cost, large pixel pitch excellent SNR and wavelength operation across the entire telecom band, but suers from low pixel resolution requiring large magnication imaging (>60 ) for accurate beam measurements. Furthermore, InGaAs cameras are 4-times more expensive than phosphor-coated CCD cameras and are dicult to acquire due to their use in military applications. The high sensitivity of InGaAs cameras is ideal for detecting Rayleigh scattering for measuring waveguide propagation loss, but is problematic for mode proling, as large attenuation factors are needed to avoid saturating the camera. To capture the near-eld mode proles of the written waveguides, light from 1550 and 1300-nm wavelength tunable lasers (Photonetics Tunics-BT) was ber-coupled at the input, with the output facet imaged by 60 aspheric lens xed to an empty microscope tube, connected to a phosphor-coated CCD (Spiricon FireWire SCOR ) or Vidicon camera 63

94 (Electrophysics 7290) for and 1300-nm wavelengths, respectively. The high 60 lens magnication was chosen so that modes greater than 10-µm diameter lled more than pixels 2 on the CCD, resulting in accurate mode prole measurements (±0.5%). A back-illuminated 10-micron resolution target provided a calibration for the pixel pitch. Most mode proles were recorded at 1550-nm wavelength with the phosphor-coated CCD (Spiricon SCOR ), which was interfaced to the computer by FireWire. The intensity prole data was captured using the Spiricon software interface (LBA-FW-SCOR v4.81) shown in Fig Before capturing the mode, the laser was disabled and the Ultracal routine was initialized to reference the background light level. Once the calibration was completed, the capture process was initiated. For optimal measurements, the best focus was located by maximizing the signal on the CCD by translating the output stage in the axial direction. The laser intensity was then reduced to just below saturation (white level on screen) for the best signal to noise ratio. When recording the intensity data, it is necessary to enable the auto (yellow) and drawn (white) apertures in the Spiricon software. The drawn aperture is used to manually control the computation area for the beam diameter calculations. The drawn aperture should be set to about twice the diameter of the beam. As a guide, the yellow aperture gives the suggested region of interest for a given beam shape and size. As shown in Fig. 3.10, the white manual aperture is the same diameter as the yellow auto aperture. The beam diameter is indicated visually by the black aperture. The beam diameter may be measured in several ways. The most mathematically correct way to measure beam size is the so-called 4-sigma method, which is dened as 4 times the standard deviation of the energy distribution, evaluated separately for x and y axes. 64

95 Unfortunately, the 4-sigma method is more susceptible to noise, and for the experimentally measured mode prole shown in Fig. 3.10, where the phosphor coating introduces a slightly noisy background level, the 90/10 knife edge criterion is a better choice for beam diameter measurement. The 90/10 knife edge [95] method is the best approximation to the 4-sigma method and may be accessed in the software under Options\Computations. Of main interest are Width X and Width Y, shown near the top left of the program, which indicate the knife edge diameters along x and y axes, respectively. For a TEM 00 Gaussian beam, the widths correspond to where the intensity drops to 1/e 2 of its peak value. For the 1550-nm wavelength single-mode ber mode shown in Fig. 3.10, the beam diameter of 10.5 µm corresponds closely to a Gaussian t along x and y axes (shown below 90/10 knife edge data in Fig. 3.10). The correlation G c of the Gaussian t is dened as follows: G c = 1 Z S Z (3.5) where Z is the pixel intensity and S is the Gaussian surface intensity. Values of G c are between zero and one, with unity correlation indicating a perfect Gaussian representation of the intensity prole. The correlation for both axes of the ber mode was 0.94, indicating an excellent Gaussian representation. For the laser-written waveguides discussed in this thesis, the mode proles could be approximated by Gaussian distributions along x and y axes with correlations > 0.9, and therefore, the Gaussian t diameter was used to dene mode eld diameter (MFD). An image of the mode prole is included with Gaussian-t MFD values to give a complete description of the modal intensity distribution for the waveguides described 65

96 Figure 3.10: Screen-capture of Spiricon software for capturing intensity distribution of waveguide mode. in this thesis Coupling loss The coupling loss is dened here as the power loss when the light is coupled from a ber to the laser-formed waveguide or vice versa. When index matching uid is applied in the small ber-substrate gap, Fresnel reection losses can be neglected. The coupling loss is attributed to a mismatch between the waveguide and ber mode proles. This coupling eciency, η, can be estimated by the overlap integral of the two modes [96]: 66

97 η = Ψ 1(x, y)ψ 2 (x, y)dxdy 2 Ψ 1(x, y) 2 dxdy Ψ 2(x, y) 2 dxdy where Ψ 1 (x, y) = A exp ( (x 2 + y 2 ) /a 2 ) is the electric eld distribution of the Gaussian ber mode with MFD = 2a (10.5 µm at 1550-nm wavelength) and Ψ 2 (x, y) = B exp ( ( x 2 /d 2 x + y 2 /d 2 y is the electric eld distribution of the laser-formed waveguide mode, assumed to be elliptical Gaussian with MFD = 2d x and 2d y along x and y axes. When the assumed functional forms for Ψ 1,2 are substituted in Eq. (3.6), the single facet coupling loss expressed logarithmically is: (3.6) )) CL (db) = 10 log 10 4a 2 d x d y (d 2 x + a 2 ) ( d 2 y + a2) (3.7) MFD values were measured experimentally as discussed in Section , with Eq. (3.7) providing a theoretical estimate of the coupling loss. From the ±0.5% estimated error in mode eld diameter measurements, the error in coupling loss is estimated to be less than ±0.02 db/facet Propagation loss The waveguide propagation loss resulting from Rayleigh scattering and absorption may be measured in several ways. All methods suer from drawbacks with measurement accuracy typically degrading for shorter waveguides (< 5 cm) and for lower losses (< 1 db/cm). In the Fabry-Pérot technique, the small Fresnel reection from the air-glass interface sets up a Fabry-Pérot cavity for the light in the waveguide. By observing the fringe contrast of the power transmitted through the waveguide when the laser wavelength is tuned, the propagation loss can be determined [97]. Since the fringe contrast increases with decreasing 67

98 propagation loss, the measurement accuracy of the Fabry-Pérot technique improves with decreasing waveguide loss, unlike most measurement techniques. However, for small angular deviation between the waveguide and end facets, this adds additional loss, so that the propagation loss will be overestimated. Since it is dicult to align waveguides to within ±0.5, this makes the Fabry-Pérot technique inaccurate for the low (< 1 db/cm) propagation losses reported in this thesis. Another technique for measuring propagation loss is by observing the exponentially decaying scattered signal along the waveguide from overhead [98] by imaging with a standard CCD for visible wavelengths or an InGaAs camera at infrared wavelengths. Due to the weak intensity and noisy nature of the scattered signal, this measurement method is only accurate for moderately high waveguide loss (> 2 db/cm) and long waveguide lengths (>2 cm) [27]. Another diculty is that the scattering centers that produce the decaying streak are often randomly located along the waveguide length, so that dark regions absent of scattering centers would contribute to measurement error. A commonly employed technique for measuring propagation loss is by recording the insertion loss for a series of identical waveguides with dierent lengths. This can be accomplished by writing waveguides with identical conditions in dierent sample lengths or by cutting a long sample into dierent lengths. This technique requires long sample lengths (>5 cm) for reasonable accuracy but is prone to inaccuracies due to variation in the quality of facet cutting/polishing, in repeated exposures in dierent sample lengths, and in alignment for each sample. The most straightforward technique for measuring propagation loss is to use a very long sample, resulting in a large contribution from the propagation loss to the total insertion loss. 68

99 The propagation loss can then be determined by dividing the insertion loss by the sample length. Clearly, a longer sample length is required for waveguides with lower propagation losses or higher coupling losses. Unfortunately, the maximum travel range of the air-bearing motion stages used to fabricate the waveguides reported in this thesis limited the waveguide length to L 5 cm. Therefore, this method only provides an upper limit on the propagation loss. In this thesis, the propagation loss was measured indirectly by rst measuring the berwaveguide-ber insertion loss as in Eq. (3.4) and then subtracting the coupling loss from both facets, obtained from the overlap integral in Eq. (3.7). The propagation loss was then determined from: α = IL 2CL L (3.8) From the error in the measured insertion loss and coupling loss, the estimated error in propagation loss ±0.03 db/cm Refracted near eld prolometer Refracted near-eld (RNF) measurements of the cross-sectional refractive index proles were obtained with a commercial RNF tool (Rinck Elektronik) with spatial resolution of 0.5 µm and absolute refractive index resolution of 10 4 at 633-nm wavelength. As shown in Fig. 3.11, the laser beam was focused on the sample, and the intensity of the refracted light was measured to determine the refractive index. By scanning the sample along x and y axes, the variation in intensity was converted to a two-dimensional refractive index prole. Since waveguide mode proles were measured at 1550-nm wavelength, the refractive index must 69

100 Refractive Index Profiler Using Refracted Near Field Measurement Figure 3.11: Refracted near eld 2001 EXFO Electro-Optical forengineering measuring - All right the reservedcross sectional refractive3index proles of femtosecond laser-written waveguides [99]. be converted from 633 to 1550-nm wavelength using the Sellmeier equation to obtain an accurate map of the absolute refractive index prole. However, since the refractive index contrast (dierence between refractive index in the waveguide and the bulk) has negligible dispersion, the refractive index of the waveguide relative to the bulk is the same at both 633 and 1550-nm wavelengths. 70

101 Chapter 4 Waveguide fabrication in borosilicate glass In this chapter, which is the main part of this thesis, the central focus is to provide a new level of physical insight into laser waveguide writing in borosilicate glass at high repetition rates, where thermal diusion and heat accumulation eects act in concert (Section 4.1). These eects are examined against our criteria for optimizing laser exposure conditions to minimize waveguide propagation loss and provide low-loss coupling to SMF telecom ber (Section 4.2). The morphology of such low-loss waveguides is closely examined against a thermal diusion model that reveals the relative contribution of diusion-only and heat accumulation eects in dening the waveguide size and underlying modication temperatures. Finally, a thermal annealing study of the waveguides is performed to test the high temperature stability of the waveguides and to better understand the heat modication physics (Section 4.3). Section 6.5 provides a summary of the key results. 4.1 Heat accumulation versus thermal diusion eects In Section 4.1.1, a thermal diusion model is introduced to provide insight into thermal diusion and heat accumulation physics and in later sections, to draw comparisons with 71

102 experimental ndings. In Section 4.1.2, the eects of laser pulse energy and repetition rate on absorption and the resulting waveguide size are presented. In Section 4.1.3, the eects of heat accumulation and thermal diusion on the resulting refractive index proles will be discussed Heat diusion and accumulation model To calculate the size of thermally-induced modication zones over a broad range of laser exposure conditions requires knowledge of the temperature distribution as a function of time. A simple thermal diusion model is applied that assumes spherical Gaussian heat dissipation, so that temperature is calculated as a function of radial position. The model is therefore valid only for times after heat diusion has expanded an asymmetric laser-heating focal volume ( 1.6-µm transverse spot size Ö 4.4-µm depth of focus for NA = 0.55) to a nearly spherically temperature distribution, a condition that is valid for most of the exposure conditions examined here. The model also assumes a static laser exposure, and an eective number of laser exposure pulses, N = 2w 0 R/v, was therefore inferred from scan speed, v, and spot size, 2w 0, that considers the number of laser pulses delivered per spot diameter to mimic the scanning focused laser. This static exposure assumption was validated by the microscope observation of identical modication diameters for static and scanned exposures formed with the same net uence (same number of pulses per spot and same uence per pulse). The temperature distribution during waveguide formation was calculated with a nitedierence thermal diusion model governed by the thermal diusion partial dierential equation with spherical symmetry: 72

103 ( r T ) 2 = r2 T r r D t (4.1) where T (r, t) is the laser-heated temperature prole as a function of radial position r and time t, and D is the thermal diusivity. The laser dissipation was treated as a spherical Gaussian distribution with energy volume density E(r) = E 0 exp( r 2 /w0), 2 with beam waist, w 0, set to the 1/e 2 radius of the focused laser beam waist (w 0 = 0.8 µm). The value of E 0 depended on the absorbed laser pulse energy, which was inferred from measurement of the transmitted laser power, whose values varied with the laser power, scan speed, and repetition rate. Values were corrected for Fresnel reection loss at the air-glass interfaces. The temperature prole was augmented by an instantaneous temperature rise, T (r) = E(r)/c P ρ, each time a new laser pulse arrived. A specic heat capacity of c P = 971 J/kgK (average of C), diusivity of D = cm 2 /s (average of C), and density of ρ = 2370 kg/m 3 (room temperature) [84] were used. Radiative transport can be neglected for the present small size (tens of microns) of the laser-heated volume [100], and as evidenced by a transient thermal lensing study of laser-heated borosilicate glass for high temperatures ( 1000 C) [101]. In the transient lens method, a refractive index lens in the sample is observed by detecting a spatial deformation of a probe beam passing through the laser-induced plasma. As a change in temperature causes a refractive index change, the temperature distribution due to thermal diusion can be detected by the transient lends method for single-shot irradiation [101]. In their study, transient lens signals were well represented by a thermal diusion model, leading the authors to suggest that the energy emitted by thermal radiation can be neglected [101]. Carr et al. [100] noted that shock is a large heat transport factor in laser-heated fused silica, 73

104 Figure 4.1: (Electronic attachment: Fig4-1.mov, 3.3 MB). Simulated temperature prole evolution (0 to 25 µs) for static laser exposures (200-nJ absorbed energy/pulse) in Corning EAGLE2000 borosilicate glass for repetition rates of 200 khz (left) and 1.5 MHz (right). The horizontal red line at T s = 985 C is the softening point for EAGLE2000 used to dene the threshold radius for melting. but only in short time frames of 10 ns and short-distance ranges that can be neglected here where thermal diusion dominates over the long >500-ns time interval between laser heating pulses. The thermal model was developed in collaboration with Haibin Zhang, who improved upon the author's simplied analytical thermal diusion model with a nite dierence thermal diusion simulation written in MATLAB (Appendix A). The present author applied the nite dierence model to simulate the theoretical data presented in the gures shown in Section 4.1 of this thesis. Figure 4.1 shows the temporal evolution of the temperature prole obtained from Eq. (4.1) for repetition rates of 0.2 and 1.5 MHz for static laser exposures in EAGLE2000 glass. In both cases, the absorbed pulse energy was 200 nj and focused by a 0.55-NA lens to match typical waveguide writing conditions. The horizontal line at T s = 985 C is the softening point for EAGLE2000 and is used to dene the threshold radius for melting. At 1.5-MHz repetition rate, the strong laser-induced temperature rise within the 1.6-µm laser spot builds on top of a slowly building Gaussian heat distribution, yielding a melted volume which expands to sizes much larger than the spot size as further laser pulses are absorbed. At 200-kHz repetition 74

105 rate, where there is a 7.5-fold greater time between pulses (5 µs), signicant diusive cooling occurs between pulses, resulting in insignicant cumulative heating. At this repetition rate, single-pulse thermal diusion acts alone in determining the waveguide diameter, which is signicantly smaller than predicted for the 1.5-MHz case. However, we show in the next section that increased laser pulse energy at 200-kHz repetition rate will rst increase the diusion scale length, and then drive heat accumulation to produce a similar melt diameter as for the 1.5-MHz repetition rate case. To give further insight into increased heat accumulation at higher repetition rates, Fig. 4.2 plots the calculated temperature at a position r = 3 µm from the center of the laser heat source, recorded as a function of pulse number for repetition rates of 0.1, 0.5 and 1 MHz. Consistent with Fig. 4.1, an absorbed energy of 200 nj, 0.55-NA focusing and melting threshold of 985 C were assumed. At 100-kHz repetition rate, the temperature relaxes to below the softening point before the next pulse arrives, which results in minimal accumulation of heat and signicant temperature cycling during waveguide writing. At 0.5 and 1 MHz repetition rates, heat accumulation is strongly evident, leading to a melted volume which increases with pulse number (net uence) and repetition rate. Decreased thermal cycling with increased repetition rate is anticipated to lead to smoother waveguides with less propagation loss Waveguide diameters To compare experimental and theoretically calculated diameters, the temperature prole T (r, t) was rst calculated for exposure criteria given by the absorbed energy (dening E 0 ), 75

106 Tempera ature o C MHz 500 khz 100 khz Pulse Number Figure 4.2: Finite-dierence model of glass temperature versus exposure at repetition rates of 100 khz, 500 khz and 1 MHz, at a radial position of 3 µm from the center of the laser beam. The absorbed pulse energy of 200 nj was the same at each repetition rate. The temperature driven at 100-kHz repetition rate saturates beyond 20 pulses, never exceeding the softening point. scan speed (dening number of pulses/spot, N) and repetition rate R (dening frequency of heat source). Solving for the maximum radius, r max, within the last heat cycle where T (r max, t) = T s = 985 C, was interpreted as the modication melt radius dening the radius of the heat-modied waveguide (similar to Fig. 4.1 and 4.2). In the model, there were no freely adjustable parameters. The objective was to study the eects of scan speed, repetition rate and pulse energy and apply the thermal model against the observed waveguide morphologies. Absorption was inferred from the power transmitted through the sample, after accounting for Fresnel reections from the air-glass interfaces. Experimentally measured absorption values represent an upper bound, as the power meter placed beneath the sample could not detect light scattered/reected by the laser-induced plasma. However, others have shown that only a small fraction ( 3%) of light is reected by the electron plasma under similar laser exposure conditions [34], thus validating the experimentally measured absorption values 76

107 reported here. Fig. 4.3(a) shows the fractional absorption as a function of laser repetition rate (R = 0.2, 0.5 and 1.5 MHz) for incident pulse energies of 100, 200 and 250 nj. The absorption values are shown for 15-mm/s scan speed, and were constant within experiment uncertainty (± 2%) for speeds of 2 to 80 mm/s, consistent with ndings in a previous study on Schott D263 borosilicate glass [102]. The absorption increases strongly with pulse energy due to an increased photoionization rate [55], until saturating as evident near 250 nj. Fig. 4.3(a) demonstrates preliminary evidence of heat accumulation eects, where for constant pulse energy, the absorption increases with repetition rate. Incomplete cooling between pulses presents a higher temperature glass to subsequent laser pulses, which then interact with thermally excited plasma to seed strong avalanche ionization [102]. The diameter of waveguides measured transversely from overhead transmission mode white-light microscopy is shown in Fig. 4.3(b) as a function of scan speed for incident laser pulse energies of 100, 200 and 250 nj and 1.5-MHz repetition rate, respectively. For all microscope measurements of transverse waveguide diameters reported in this study, the error in diameter measurement due to the microscope system resolution was ±0.24 µm (±2 pixels, with 0.12-µm/pixel calibration for 50 objective). Heat accumulation eects are clearly evidenced by the strongly increasing diameters with decreasing scan speed. Such a velocity trend would not be observed amongst pulses of the same energy if only thermal diusion was present. The solid lines in Fig. 4.3(b) are the waveguide diameters predicted by the thermal model, which are seen to closely follow the experimental data within 10% error at the higher pulse energies. Calculated values for 100-nJ pulse energy overestimate the diameter by 25%. The assumption of spherical symmetry in Eq. (4.1) is breaking down here as heat-modied diameters of 5-µm diameter or smaller no longer exceed an 77

108 Abso orptio on (a) 250 nj 200 nj 100 nj Repetition rate (MHz) (b) Diameter (μm) nj 200 nj 250 nj Scan speed (mm/s) Figure 4.3: Absorption (a) versus repetition rate for pulse energies of 100, 200 and 250 nj, and transverse waveguide diameter (b) versus scan speed for pulse energies of 100, 200 and 250 nj at 1.5-MHz repetition rate. Colored lines show calculated diameter. The black line at 2-µm diameter shows the approximate spot diameter (2w 0 ) of the laser. ellipsoidal-like heating volume of 2w 0 = 1.6-µm transverse diameter by 4.4-µm depth of focus, thereby overestimating the temperature. Discrepancy between theory and experiment is also attributed to the uncertain thermal properties of EAGLE2000 glass above 600 C. However, the close correspondence of theoretical and experimental data are strong evidence of the thermal role played in dening the waveguide structural size. Increased absorbed laser energy, for example, 40, 160, and 200 nj for respective incident pulse energies of 100, 200 and 250 nj at 1.5-MHz repetition rate in Fig. 4.3(a), resulted in signicantly higher initial temperatures. Heat accumulation eects were more pronounced, leading to 4-fold larger waveguide diameters for this increase in absorbed energy, as shown in Fig. 4.3(b). However, below an energy (uence) of 75 nj (3.8 J/cm 2 ), there was no evidence of thermal diusion or heat accumulation eects for all scan speeds tested, as the resulting waveguide diameter did not extend beyond the 2-µm (horizontal line in Fig. 4.3(b)) diameter of the laser spot size. Overhead microscope images of waveguides and their diameters are shown in Fig. 4.4(a) 78

109 for 250-nJ pulse energy, 15-mm/s scan speed and repetition rates of 0.2, 0.5 and 1.5 MHz. The higher contrast inner core is presumably due the very high temperatures within the laser spot size, as observed in Fig The outer cladding zone of weaker contrast is attributed to a lower temperature modication just above the melting point. As the repetition rate increases, thermal eects are signicantly more pronounced, with waveguides of 3, 7 and 26-µm diameter formed at repetition rates of 0.2, 0.5 and 1.5 MHz. Fig. 4.4(b) shows the waveguide diameter versus scan speed for 250-nJ pulse energy and 0.2, 0.5 and 1.5-MHz repetition rates, along with diameters predicted by the thermal model. As expected, the transverse waveguide diameter increases with increasing net exposure, through increased repetition rate and increased dwell time (decreasing scan speed). There is also good agreement (±10%) observed between theoretical and experimental values of waveguide diameter. The widely varying diameters in Fig. 4.4(b) cannot be accounted solely by thermal diusion, given the pulse energy was xed at 250 nj. The large increase in diameter together with the steepening slopes as repetition rate increases are strong evidence of heat accumulation. Because of asymmetrically higher laser exposure at higher repetition rate in Fig. 4.4(b), it is more appropriate to compare melt diameters based on the net exposure uence: NF = 2w 0R F p (4.2) v where w 0, R, and v were previously dened, F p = E p /πw 2 0 is the uence per pulse, and E p is the incident laser pulse energy. Equation (4.2) indicates two approaches for driving uniform uence exposure along the waveguides for variable repetition rate: scan speed can be increased to maintain a constant ratio of R/v, or laser pulse energy can be reduced to 79

110 (a) 26 m 7 m 3 m (b) Diameter ( m) MHz 500 khz 200 khz Scan speed (mm/s) Figure 4.4: Overhead microscope images (a) of waveguides fabricated with 250-nJ pulse energy, 15-mm/s scan speed at repetition rates of 1.5 MHz (top), 0.5 MHz (middle) and 0.2 MHz (bottom) and (b) waveguide diameters plotted against scan speed for 250-nJ pulse energy and repetition rates of 0.2 MHz (blue triangles), 0.5 MHz (green circles) and 1.5 MHz (red squares). The circled data points show melt diameters at the same net uence of 2 kj/cm 2. Calculated thermal model values of the melt diameter are shown by the solid lines. maintain a constant value for F p R. The former approach is represented by the open circles in Fig. 4.4(b) where the melt diameters of 5, 8 and 26 µm were obtained for identical net uence exposure of 2 kj/cm 2, corresponding to identical ratios of R/v = 0.2 MHz / 2 mm/s, 0.5 MHz / 5 mm/s, and 1.5 MHz / 15 mm/s, respectively. The data clearly shows strong heat accumulation eects by the large 5-fold increase in waveguide diameter even when scan speeds are scaled down with increasing repetition rate to deliver uniform uence exposure. Alternatively, waveguide structural diameter formed under constant average power of P = E p R = 200 mw is shown in Fig. 4.5(a) for varying scan speed. Under these conditions, the melt diameters increase strongly with increasing dwell time (decreasing v), as expected, but values otherwise remain nearly constant (within 15%) at each scan speed where net uence exposure is the same for each of the 0.2, 0.5 and 1.5 MHz repetition rates. This apparent absence of heat accumulation eect arises from a fortuitous combination of exposure 80

111 (a) Diameter (μm) MHz 0.5 MHz 0.2 MHz Scan speed (mm/s) Abs sorption (b) Repetition rate (MHz) d energy ( J) Absorbe Figure 4.5: Transverse waveguide diameter (a) as a function of scan speed for repetition rates of 0.2, 0.5 and 1.5 MHz at a constant average power of 200 mw. Data points are experimental diameters and solid lines are diameters predicted by thermal model; corresponding values of absorption and absorbed energy (b) versus repetition rate at 200-mW average power. conditions where much higher pulse energy is now delivered at lower repetition rate. This higher energy drives up absorption to 75% to match values previously only seen at higher repetition rate as shown in Fig. 4.5(b). In this way, the 8-fold higher pulse energy at 0.2 MHz drives signicantly more laser energy of 0.75 µj into the glass each pulse in contrast with 0.1 µj/pulse dissipation at 1.5 MHz, as shown by the right vertical axis data in Fig. 4.5(b). Much stronger thermal diusion is now driven at low repetition rate, extending the modication zone dramatically to match that produced by low-energy absorption accumulation at high repetition rates. In Fig. 4.5(a), good agreement between theory and experiment is observed at a repetition rate (pulse energy) of 1.5 MHz (133 nj), but discrepancies are noted for 500 khz (400 nj) and 200 khz (1 µj) rates at scan speeds below 10 mm/s. At these lower repetition rate conditions, the combination of high pulse energy (>400 nj) and low scan speed (<10 mm/s) resulted in damaged tracks visible by optical microscope inspection. Moreover, these damage tracks caused high scattering of laser light in the focal volume that led to overestimated absorption values in Fig. 4.5(b), and therefore predict overly large 81

112 (a) 6 μm (b) Diffusion dia ameter ( m) Experiment Theory Pulse energy (nj) Figure 4.6: Overhead microscope image (a) at 100Ö magnication showing thermal diusion from single-pulse modication zones irradiated with 1-µJ pulse energy at 100-mm/s scan speed and 40-kHz repetition rate. Pulses were focused 150-µm below the surface with a 0.55-NA lens. Comparison of experimental (blue diamond) and calculated (red square) modication diameters (b) from single-pulse diusion eects as a function of incident laser pulse energy. modication diameters for the 200 and 500-kHz data when speeds were less than 10 mm/s. As the theoretical and experimental data in Fig. 4.5 converge at higher scan speeds (lower temperatures), it is likely that the uncertainty of the specic heat and thermal diusivity at elevated temperatures also contributes to deviation between theory and experiment observed at the lower scan speeds. The combination of diusion and accumulation thermal events in Fig. 4.5 is somewhat unique at the present 200-mW power level in balancing structure diameter and is shown in Section 4.2 to provide the lowest insertion-loss waveguides for coupling to SMF. This balancing of waveguide diameter at constant net uence is not available by velocity tuning (constant R/v data points in Fig. 4.4(b)) which always increases waveguide diameter as repetition rate increases. 82

113 (nj) nergy hold pulse e Thres mm/s 10 mm/s 40 mm/s Repetition rate (MHz) Figure 4.7: Experimental values of threshold pulse energy for onset of heat accumulation as a function of laser repetition rate for scan speeds of 2, 10 and 40 mm/s and NA = 0.55 focusing. To estimate the onset of heat accumulation eects, it was rst necessary to experimentally verify the range of diusion-only eects for a single pulse exposure. This was done by lowering the laser repetition rate to 40 khz with an acousto-optic modulator and increasing the scan speed to 100 mm/s such that modication tracks opened up into nearly isolated interaction spots of 2.5-µm spacing as shown in Fig. 4.6(a). For this example of relatively strong laser interaction at 1-µJ pulse energy, thermal diusion dened a faint 6-µm diameter zone that extends 4-fold larger than the 1.6-µm spot size, also seen as bright circular spots in Fig. 4.6(a). Figure 4.6(b) plots the experimental values of diusion diameter as a function of pulse energy, together with melt diameter predicted by the thermal diusion model for reaching 985 C in a single laser pulse. There is very good agreement above 4-µm diameter, while theory overestimates values at lower pulse energy as is expected when the spherical diusion diameter (2r max = 4 µm) is less than the 4.4-µm depth of focus, as explained above. The onset threshold for heat accumulation is dened here as the minimum laser pulse 83

114 energy required to increase the waveguide diameter 2-fold over the diameter produced by diusion in a single-pulse interaction as determined in Fig. 4.6(b). Experimental values for this energy threshold are shown Fig. 4.7 as a function of repetition rate (200 khz to 2 MHz) and for various scan speeds (2, 10, and 40 mm/s) and should be compared with the singlepulse damage threshold of 50 nj (2.5 J/cm 2 uence) for creating a structure visible under an optical microscope, which was invariant with repetition rate. In contrast, the energy threshold for heat accumulation decreases sharply from values of 900 nj at 200 khz to 80 nj at 2 MHz and is only weakly dependent on scan speed, varying from 750 to 1100 nj at 200 khz compared with 80 to 90 nj at 2 MHz for scan speeds of 2 to 40 mm/s. In this R = 0.2 to 2 MHz range, the diusion scale length D/R decreases from 1.6 to 0.5 µm, indicating that the eective laser heating volume shrinks dramatically with increasing repetition rate, thereby reducing the threshold pulse energy for heat accumulation. For R > 1 MHz, the thermal diusion scale length of 0.7 µm falls inside the laser waist radius of w 0 = 0.8 µm, resulting in an asymptotic limit of the heat accumulation threshold energy to a minimum value of 80 nj at 2-MHz repetition rate in Fig Beyond 2 MHz, the available laser pulse energy was below this value, preventing the observation of heat accumulation eects in the present borosilicate glass. Similarly, when the laser was operated at 100-kHz repetition rate, the 2-µJ maximum pulse energy available was insucient to drive heat accumulation eects beyond a large thermal diusion diameter of 8 µm. Hirao and coworkers inferred a 10-µs cooling time (to <100 C) in borosilicate glass (Corning 0211) when exposed to a single laser pulse of 220-fs duration and 600-nJ energy focused by a 0.4-NA lens [101]. While this suggests a 100-kHz threshold for heat accumulation, the data in Fig. 4.7 indicates that this threshold is in fact variable with the repetition rate, and strongly dependent on 84

115 the laser pulse energy and scan speed, and is also likely dependent on other changes in laser parameters (wavelength, pulse duration), spot size and material. Note that by dening the relative increase in melt diameter compared to single-pulse diusion zones as a higher factor (e.g. 4-fold) leads to higher threshold pulse energies, although similar trends as shown in Fig. 4.7 would still be observed. The experimental and well-matched theoretical results presented in Figs. 4.3 through 4.7, conclusively show that both thermal diusion and heat accumulation play signicant competing roles in dening the waveguide morphology at repetition rates greater than 200 khz. The threshold pulse energy for driving sucient thermal diusion to initiate heat accumulation was observed to be decrease with increasing repetition rate, before approaching a minimum modication threshold at 1 MHz repetition rate when the diusion scale length falls below the laser's waist radius Cross sectional refractive index proles High-resolution refracted-near eld (RNF) measurements [99] provided cross-sectional refractive index proles of waveguides across a wide range of laser exposure conditions. RNF proles in Fig. 4.8 present the interesting case in Section where waveguides of similar diameter were generated across the 0.2 to 2 MHz range of repetition rates by holding constant the net uence exposure with a xed 200-mW power. Here, waveguides were written with a 0.55-NA lens, 150-µm depth, 25-mm/s scan speed and repetition rates of 0.2, 0.5, 1, 1.5, and 2 MHz. As will be shown in Section 4.2, this combination of average power and scan speed also provided optimum waveguides for low-insertion loss at each repetition rate. The core-cladding structure seen in Fig. 4.8 is similar to other waveguides formed with 85

116 high-repetition rate lasers [103] and is the result of rapid cooling of the melted volume. Insight into the core-cladding structure can be gained from the animation in Fig The core of the waveguide structure is attributed to the high temperatures induced within the 1.6-µm spot size by each laser pulse, while the outer lower-contrast cladding is formed by a more slowly evolving near-gaussian temperature distribution, with the overall size determined by the largest diameter where the temperature exceeds the softening point. Because of the variable temperature across the modied zone, the cooling rates are highly nonuniform [29], and therefore are expected [10] to lead to a nonuniform distribution of the nal glass density. The refractive index contrast prole will follow this density prole. The depth of the small, dark spot near the bottom of the structures in Fig. 4.8 was observed to be independent of average power (50 to 400 mw), repetition rate (0.2 to 5 MHz), and writing speed (5 to 80 mm/s), except for pulse energies >1 µj at 200-kHz repetition rate, where the spot shifted towards the sample surface by several microns. This spot is attributed to the focal plane location, with the images showing that most of the laser energy was deposited upstream of this focal plane. With increased pulse energy, with repetition rate and scan speed held xed, the modied zones moved closer to the surface, but the dark focal spot remained at the same depth, showing no evidence of self focusing, except when pulse energies >1 µj exceeded the critical self-focusing power of 3 MW in borosilicate glass at 1045-nm wavelength [34]. At 200-kHz repetition rate, the waveguide has an elliptical-like central core guiding region (elongated white region) with peak refractive index change of n = in a 3.4Ö6.9-µm 2 area, and an outer elliptical-like heat-modied cladding of peak n = in a 11.1Ö18.0- µm 2 area that is dened by diusion from an asymmetric focal volume. The waveguide is 86

117 R = 0.2 MHz R = 0.5 MHz R = 1 MHz R = 1.5 MHz n n (electric field to sample surface), TE (electric fiel of the input light source. All spectra were recorded w interfaces for all spectral recordings and insertion l R = 2 MHz n Results and discussion 3.1 Low-loss waveguide writing 10 m n The present BGWs comprised of a periodic array o centre-to-centre separation, as defined by 0.52-mm/ rate. Each voxel was formed by a single laser p response [16]. Over the wide 100-fs to 2-ps pulse du and homogenous modification tracks were observed w durations in the range of 100 fs to 1.5 ps and pulse en tracks appeared faint, discontinuous, or invisible f appeared inhomogeneous and damaged above 7 μj. propagation losses were found at pulse energies on threshold for generating guiding tracks. Figure 4.8: Cross-sectional refractive index proles from RNF measurements of waveguides written with 0.55-NA focusing, 200-mW power, 150-µm depth, 25-mm/s scan speed and repetition rates of 0.2, 0.5, 1, 1.5, and 2 MHz. The writing laser was incident from the top. elliptical ( 1.6:1 aspect ratio) due to thermal diusion from a laser heating volume extended vertically by self focusing eects as well as by minor heat accumulation at this repetition rate. A progression towards more narrow and elongated structures is expected as the repetition rate is further reduced, approaching the cross section typically observed in 1-kHz repetition rate fabrication, as shown in Fig provided polarization control of the launch light in birefringence. Unpolarized light from the broadban then focused into the BGWs by a 30X objective len modes (45 linear polarization) in the BGWs, while t AQ6317B) with 0.01-nm resolution. Index matc stability of the BGWs, samples were heated in a tub temperature and optically characterized after coolin mode profile, Bragg wavelength, and grating strength n At 500-kHz repetition rate, owing to increased heat accumulation, a more circular guiding Figure 4.9: Cross sectional microscope image of waveguide written in EAGLE2000 with 1- khz repetition rate Ti:Sapphire laser (pulse duration 100 fs, energy 3 µj, scan speed 0.5 mm/s, NA = 0.55) [104]. 87 Fig. 2. Microscope images in top view (top row) and near-field mode profiles of 1560-nm light (bottom ro energy and 0.52-mm/s scan speed. Pulse durations ar

118 and cladding cross section are observed with a central core of peak n = in a 3.7Ö5.4-µm 2 area that forms an optical guide. Also noted is a new small region of positive refractive index change formed immediately below the main guiding region. At 1-MHz repetition rate, this region below the core has increased in size and magnitude to a peak of n = in a 2.2Ö3.1-µm 2 area. This region is now responsible for waveguiding of 1550-nm light but the mode also extends into the weaker central core (peak n = ) to yield two transverse modes when formed with a higher power laser exposure (> 250 mw). At 1.5-MHz repetition rate, the guiding region has clearly transitioned to below the central core to form a small and slightly elliptical region ( 2.1Ö3.1-µm 2 area) of peak n = Interestingly, the central region is no longer guiding, and dominated by a large volume of negative refractive index of n = Despite the ellipticity, the mode prole at 1550-nm wavelength is circular, as described below. At 2-MHz repetition rate, the guiding region has a peak n = Above this repetition rate, the pulse energy dropped below the heat accumulation threshold of 90 nj (Fig. 4.7) to form suciently strong guiding structures and future work with more powerful femtosecond laser sources are therefore required to extend this study. For repetition rates of 0.2 to 2 MHz, the transverse cladding diameter was nearly constant at 11 µm, consistent with Fig. 4.5, where diameters were measured from overhead by whitelight microscopy. The peak refractive index change in the guiding region increased from to with 0.2 to 2 MHz increase in repetition rate. The vertical distance between the focal plane (small dark spot) and the center of the waveguides decreased from 12 µm at 200-kHz repetition rate to 3 µm at 2-MHz repetition rate, due to weaker self-focusing and preferential absorption further downstream expected as pulse energy decreased from 1000 to 88

119 100 nj over this same range. To quantitatively model the complex structures found in the refractive index proles as shown in Fig , one requires experimental verication of evolving temperature proles [49] that our group is presently studying with time-resolved and imaging spectroscopy [105] as well as accurate models of glass density changes for the diering cooling rates [66]. Other sources of refractive index modication such as shockwave propagation also lead to formation of rareed cores surrounded by dense shells [64, 106], features that also appear to contribute to the refractive index changes seen in Fig More advanced theoretical models that account for these additional processes are expected to delineate the ner features of the refractive index proles shown in Fig Waveguide processing window The properties of femtosecond laser written waveguides in bulk glass depend strongly on laser exposure conditions such as repetition rate, scan speed, average power, wavelength, pulse duration, polarization, numerical aperture, and focus depth. The rst three parameters were found to play the strongest role in controlling waveguide properties in EAGLE2000, and are discussed in Section Section presents the eects of pulse duration and polarization on waveguide properties. In Section 4.2.3, the spectral response of the insertion loss will be presented while in Section 4.2.4, the role of numerical aperture on spherical aberration for fabricating deep waveguides for 3D applications will be discussed. Waveguides could also be formed in EAGLE2000 with frequency doubled 522-nm wavelength light, but without any signicant advantage over the present 1045-nm wavelength results. 89

120 Figure 4.10: Classication of waveguide properties as a function of average power and scan speed for 1.5-MHz repetition rate and NA = 0.55 focusing at 150-µm depth: red, blue and black squares indicate low (< 3 db), medium (3 6 db) and high (>6 db) insertion loss, respectively, and black diamonds indicate waveguides that support multiple transverse modes Repetition rate, scan speed and average power Figure 4.10 summarizes waveguide properties as a function of average laser power and scan speed for 1.5-MHz repetition rate and NA = 0.55 focusing at 150-µm depth. Insertion loss (IL) has been classied by red, blue, and black squares representing low (<3 db), medium (3 to 6 db) and high (>6 db) insertion loss, respectively. Waveguides exhibiting multiple transverse modes and typically damaged morphology, written with the highest laser exposures (high power and dwell time) are found at the top-left corner (black diamond data points) of the graph. Conversely, the bottom-right corner indicates underexposed waveguides where the index change was too low to eciently guide 1550-nm light. At 1.5-MHz repetition rate, the lowest insertion losses for ber-waveguide-ber coupling (IL = 1.2 db; 2.5-cm long waveguide) were observed over a large mm/s range of scan speeds but in a narrow 200 ± 10 mw average power range (encircled data in Fig. 4.10). 90

121 L (db) I (a) Repetition rate (MHz) MF FD ( m) (b) CL (db/facet) Repetition rate (MHz) db/cm) Figure 4.11: Measured insertion loss and mode eld diameter (a) and coupling and propagation loss (b) versus repetition rate for waveguides written with 200-mW average power and 15-mm/s scan speed. Waveguides were formed 150 µm below the surface with a 0.55-NA lens. The waveguide lengths were 2.5 cm. Similar analysis was carried out for waveguides formed with 0.2, 0.5, 1 and 2-MHz repetition rates and in all cases, revealed a surprisingly similar processing window of 200 mw power and 10 to 25 mm/s scan speed for lowest insertion loss waveguiding. The minimum insertion loss at each repetition rate is presented in Fig. 4.11(a). Over the wide repetition rate range, the generated waveguides had similar shape ( 2.5 µm core and 11 µm cladding diameters) but generated a small increase in refractive index contrast of to 0.01 as shown in Fig. 4.8 that is responsible for the decrease in the waveguide mode-eld diameter (MFD) also plotted in Fig. 4.11(a). The mode eld diameters are an average of Gaussian t diameters (1/e 2 of intensity) along x and y axes and have a greater than 90% correlation for all modes measured. This 200-mW exposure window appears consistent with the optimum 250-mW power found by Osellame et al. for generating low-loss waveguides in phosphate glass at repetition rates of 505 to 885 khz [9]. The decreasing IL with increasing repetition rate in Fig. 4.11(a) is associated with increasingly stronger heat accumulation eects beginning at 0.2 MHz that result in stronger refractive index change and smaller MFD for best coupling to optical bers at 1.5 MHz. The 91

122 increased insertion loss from 1.5 to 2 MHz is attributed to inadequate laser pulse energy (100 nj) at 2 MHz for driving sucient laser heating above the 90-nJ threshold for heat accumulation. Beyond 2-MHz repetition rate, only narrow 2-µm diameter waveguides were formed that were barely guiding and showed no evidence of heat accumulation eect. A large part of the insertion-loss variation in Fig. 4.11(a) follows from the variation of MFD, also plotted in the same graph, which leads to large coupling loss with optical ber when the waveguide MFD does not match the 10.5-µm MFD of the ber (1550-nm wavelength). The expected facet coupling loss (CL) values shown in Fig. 4.11(b) were estimated using an overlap integral (Eq. (3.7)) between the measured waveguide mode prole and a Gaussian representation of the ber mode (10.5-µm diameter), yielding a minimum coupling loss of < 0.1 db/facet in the 1-2 MHz range. Removing this facet coupling loss from the insertion losses in Fig. 4.11(a) provided an estimate of the waveguide propagation losses, α, (Fig. 4.11(b)) according to Eq. (3.8). The propagation loss is approximately constant with repetition rate but reaches a minimum of 0.35 db/cm at 1.5-MHz repetition rate, where ber coupling and heat accumulation are both the most ecient. From Section 3.3.2, the estimated error in insertion loss, coupling loss and propagation loss were 0.05 db, 0.02 db/facet, and 0.03 db/cm, respectively. The refractive index proles of waveguides written with 0.55-NA lens, 200-mW power, 150-µm depth, 1.5-MHz repetition rate and scan speeds of 5, 15 and 30 mm/s are shown in Fig Due to the decreased net uence, the cladding and guiding region diameters and also the peak refractive index change decrease with increasing scan speed. As shown in Fig. 4.11, a scan speed of 15 mm/s provided the lowest insertion loss of 1.2 db at 1550-nm wavelength with 10-µm MFD allowing ecient coupling to single-mode ber. The highest 92

123 5 mm/s n 15 mm/s 30 mm/s n m Figure 4.12: Refractive-near eld measurements of cross-sectional refractive index proles for waveguides written with 0.55-NA lens, 200-mW power, 150-µm depth, 1.5-MHz repetition rate and scan speeds of 5, 15 and 30 mm/s. The writing laser was incident from the top. exposure at 5-mm/s scan speed led to high loss (Fig. 4.10), while 30-mm/s speed resulted in weakly conned modes of 15-µm MFD, coupling poorly to ber. At the maximum scan speed of 100 mm/s, the MFD increased to 20 µm. The refractive index prole for the optimum waveguide at 15-mm/s scan speed (1.2- db insertion loss, 0.3-dB/cm propagation loss) was used to conrm the accuracy of the RNF measurements, as shown in Fig The RNF data was imported into a numerical mode solving routine (Lumerical MODE Solutions 2.0) and the resulting mode prole shows excellent agreement with the experimentally measured mode prole, conrming the accuracy of the RNF measurements. The red arrow indicates the relative position of mode and waveguide cross section Pulse duration and polarization No detectable dierence in insertion loss or mode size was found when waveguides were formed with linear (electric eld vector parallel or perpendicular to scan direction) or circular polarization in EAGLE2000 borosilicate glass. Waveguide properties in EAGLE2000 were 93

124 RNF profile Simulated mode Observed mode 10 m m Figure 4.13: Waveguide fabricated with 1.5-MHz repetition rate, 200-mW power, 0.55-NA lens, 150-µm depth and 15-mm/s scan speed: Cross sectional refractive index prole (left), simulated mode prole (middle) and measured mode prole (right). Red arrow indicates position of mode relative to waveguide cross section. also invariant to pulse duration when varied from 300 to 700 fs (Lorentzian FWHM) by translating a prism in the compressor. Longer pulses were not possible due to the limited travel range of the compressor prism. These results are compared with waveguides formed in fused silica and discussed in more detail in Ch Spectral response of insertion loss Using a broadband light source, the insertion loss versus wavelength for waveguides written with scan speeds of 8 to 20 mm/s (average power 200 mw, repetition rate 1.5 MHz) is shown in Fig. 4.14(a). Since the laser-written waveguide mode size is expected to a have a similar wavelength dependence as the ber-coupled mode, the trend in the spectral response in Fig. 4.14(a) is a character of the propagation loss. Other than a peak near 1390-nm wavelength, the insertion loss decreases as the wavelength increases, which is attributed to Rayleigh scattering from sub-wavelength variations in the refractive index in the laserexposed waveguide. An overtone resonance at 1.24 µm [85]may also explain the increased insertion loss for shorter wavelength guided light. For the optimum waveguide written at 94

125 (a) Insertion n loss (db) Wavelength (nm) 8 mm/s 10 mm/s 12 mm/s 15 mm/s 20 mm/s (b) loss (db) Insertion Wavelength (nm) Figure 4.14: Insertion loss versus wavelength for 5-cm long waveguides fabricated in EA- GLE2000 with (a) 300-fs ber laser and 8 to 20-mm/s scan speed (1.5-MHz repetition rate, 200-mW power) and (b) 100-fs, 1-kHz Ti:Sapphire laser [107]. 15-mm/s scan speed, the insertion loss decreases from 3 db at 1300-nm wavelength to 2.2 db at 1550-nm wavelength (note the 2-fold longer sample length compared to results shown above). At the fastest scan speed of 20 mm/s, the overall insertion loss is higher than at 15 mm/s due to increased coupling loss from a larger mode size. At 20 mm/s, the loss decreases by 0.5 db as the wavelength is increased from from 1300 to 1550 nm, while for the slowest scan speed of 8 mm/s, the loss decreases by 1.5 db as the wavelength increased from 1300 to 1550 nm. The peak near 1390-nm wavelength is attributed to absorption due to the overtones from IR vibrations of the hydroxyl defects from residual water vapor in the glass [85]. A similar trend was observed in waveguides formed in the same glass with a 1-kHz, 800-nm Ti:Sapphire laser, as shown in Fig. 4.14(b). The peak at 1550-nm wavelength can be ignored in the comparison with Fig. 4.14(a), as it is due to a Bragg resonance intentionally formed in the waveguide [108]. 95

126 4.2.4 Spherical aberration One key advantage of femtosecond laser writing of waveguides is the ability to form structures in three dimensions. However, spherical aberration due the air-glass refractive index mismatch distorts the intensity distribution at the focus, as discussed in Section Such redistribution results in waveguide properties which change dramatically with depth [33, 77, 109]. One solution to reduce the distortions is to use a high numerical aperture (>1.0 NA) oil-immersion objective, with refractive-index matching greatly reducing the effect of spherical aberration. These objectives have been used with high-repetition rate, low energy ( 100 nj) femtosecond oscillators [9, 24, 25]. Such focusing is benecial in forming nearly circular structures by reducing the oset between the depth of focus and spot size (2z 0 /2w 0 = n/na), and also avoiding undesirable self-focusing and lamentation eects due to the lower peak power required for waveguide fabrication [34]. However, the maximum depth of waveguides written with this approach is limited by the short working distance ( 200 µm) of large-na oil-immersion objectives. In a study by Hnatovsky et al., the authors proled refractive index modication in glass as a function of focusing depth when writing with dry microscope objectives [33]. With a relatively high 0.75-NA objective, they compensated for spherical aberration from the airglass refractive index mismatch with an adjustable collar for spherical aberration correction at various focusing depths (up to 1.5 mm). This approach introduces additional control challenges when waveguide bends are formed in the vertical direction, as the collar must be adjusted in real-time, as the waveguide is written. As spherical aberration is less pronounced at low numerical aperture [33, 34], the depth 96

127 dependence of waveguide properties can be dramatically reduced with low NA (< 0.3) objectives. However, with commonly employed 1-kHz femtosecond lasers, this leads to very elliptical waveguide cross sections due to an absence of cumulative heating. Recently, Diez- Blanco et al. [77] used a 0.26-NA objective to avoid spherical aberration, in conjunction with the slit reshaping method [51] to achieve circular waveguide cross sections with a 1-kHz Ti:Sapphire femtosecond laser. The slit blocks a signicant fraction of the incident light so this method is not useful for high-repetition rate lasers which oer signicantly less pulse energy of 100 nj to 1 µj. The recent development of high-energy ( 1 µj), high repetition rate ( 1 MHz) femtosecond solid-state [52] and ber [53, 103] lasers allows the use of moderate numerical aperture (NA 0.5) lenses to drive heat accumulation and melting in waveguide formation. Thermal diusion compensates for the axially elongated focal volume to yield nearly circular waveguide structures with circular mode proles, as shown in Fig In the present study, aspheric lenses of NA = 0.55, 0.4 and 0.25 were used to study the depth eect for waveguide fabrication in Corning EAGLE2000 glass and dene practical working distances for laser writing of 3D optical circuits. For the 0.55-NA focusing applied in Section at optimum exposure conditions of 200 mw, 1.5 MHz, and 15 mm/s, waveguides with similar low loss and mode size could only be obtained in a narrow depth range of d = 50 to 200 µm. Figure 4.15 shows the MFD of these waveguides to increase 60% from 10 µm at 50-µm depth to 16 µm at 300-µm depth, spherical aberration precluding a deeper waveguide writing range. Much deeper waveguide writing was possible with the 0.25-NA lens, but 5-fold lower peak intensity at the maximum 97

128 Mode field diameter (μm) NA 0.4 NA Depth (μm) Figure 4.15: Mode eld diameter versus focusing depth for waveguides formed with 1.5-MHz repetition rate, 15-mm/s scan speed with 0.55 NA (230 mw) and 0.4 NA (200 mw) exposure condition in EAGLE2000 borosilicate glass. available laser power (400 mw) yielded only small diameter waveguides and weak refractive index change. A better balance was found with the 0.4 NA lens, providing only a small increase in MFD from 11.0 to 13.5 µm as the depth was increased from d = 50 to 520 µm. The measured propagation loss of 0.35 db/cm was nearly independent of focal depth. In comparison to 0.55-NA focusing, a 15% higher average power of 230 mw was necessary to partially compensate for the 38% larger spot size. It is possible to achieve a constant insertion loss by increasing the power with increasing depth to compensate for the distortion of the intensity distribution due to spherical aberration. However, this approach reduces the control one has for forming uniform cross-section waveguides in the 3D fabrication process. To model the eect of spherical aberration from the air-glass interface on the intensity distribution near the focus, the vectorial Debye integral was applied to model the intensity distribution near the focus. The theory is based on the diraction of a plane monochromatic electromagnetic wave focused through a planar dielectric interface [76]. By neglecting the depolarizing eect of the objective, which is only signicant for convergence angles greater 98

129 Figure 4.16: Coordinates used to calculate the intensity distribution at a point P inside glass: ρ is the radial distance from the propagation axis, z is the depth below the focus in the absence of the second medium, and d is the distance from the surface to the diractionlimited focus. than 45 (NA > 0.7), the vectorial model can be simplied with a scalar approximation [110]. The scalar 3D intensity point spread function (PSF) can be written as: I(ρ, z, d) = β 0 cos φ1 (τ s + τ p cos φ 2 ) J 0 (k 0 ρn 1 sin φ 1 ) exp (iφ + ik 0 zn 2 cos φ 2 ) dφ 1 2 (4.3) where as depicted in Fig. 4.16, ρ = x 2 + y 2 is the radial distance from the propagation axis, z is the depth below the focus in the absence of the second medium, and d is the distance from the surface to the diraction-limited focus. In Eq. (4.3), β = arcsin (NA/n 1 ) is the half-angle of the light convergence cone, NA is the numerical aperture of the focusing lens, k 0 = 2π/λ 0 is the wave number in vacuum, n 1,2 is the refractive index in medium 1,2, and φ 1 and φ 2 are the angles of the ray convergence in the rst and second media, respectively, which are related through Snell's law: ( ) n1 φ 2 = arcsin sin φ 1 n 2 99 (4.4)

130 The function describing the spherical aberration due to the refractive index mismatch is: Φ = k 0 d (n 1 cos φ 1 n 2 cos φ 2 ) (4.5) The Fresnel amplitude transmission coecients for s and p polarizations are given by: τ s = 2 sin φ 2 cos φ 1 sin (φ 1 + φ 2 ), τ p = 2 sin φ 2 cos φ 1 sin (φ 1 + φ 2 ) cos (φ 1 φ 2 ) (4.6) Figure 4.17 shows the normalized axial intensity I(0, z, d)/i(0, 0, 0) calculated at various depths for numerical apertures of 0.55, 0.4, 0.34 and 0.25 NA. The intensity distribution in the transverse direction ρ is weakly aected by spherical aberration [33, 75] and is not described here. The eect of spherical aberration is best demonstrated in Fig. 4.17(a) for the highest NA of Focusing to a depth of 225 µm, the peak intensity is observed to drop below 0.8 and the FWHM of the distribution increases relative to shallow focusing conditions (< 75 µm). Recalling that low-loss waveguides could only be fabricated up to 200 µm below the surface (Fig. 4.15), the depth where the peak intensity drops to 0.8 of its near-surface value is used to predict the maximum writing depth from these intensity calculations. In Fig. 4.17(b), the axial intensity distribution is plotted for 0.4-NA focusing, showing much slower drop in intensity with depth in comparison to the 0.55-NA case. The depth where the peak intensity reduces to 0.8 increased to 600 µm, consistent with experimental observations of rapidly increased mode size and insertion loss. Theoretically, similar low-loss waveguides could be written through the entire 1-mm sample thickness by slightly underlling the 0.4-NA lens. Figure 4.17(c) shows that with 0.34-NA focusing, the threshold depth can 100

131 Figure 4.17: Normalized intensity along axial direction for various focusing depths for (a) NA = 0.55, (b) NA = 0.4, (c) NA = 0.34 and (d) NA = be increased to 1 mm to match the thickness of samples used in the experiments. With a 38% increase in spot size compared to 0.4 NA, only a slight increase in power is expected to be necessary for optimum waveguide writing with 0.34-NA focusing. Focusing with a 0.25-NA lens (Fig. 4.17(d)) reveals no degradation in the axial intensity prole over a >5-mm depth range, greatly exceeding the 1-mm thickness of samples used in this study. As mentioned earlier, the lower uence (55% larger spot than 0.4 NA) provided by this lens yielded smaller and weaker waveguide structures, even with the maximum available power of 400 mw. If higher power were available, 0.25-NA focusing may allow circular and low-loss waveguides formed over a similar depth range demonstrated with low NA slit shaping at 1-kHz repetition rate [77]. However, the increased average power needed when focusing with low NA (< 0.4 NA) lenses may lead to undesirable self focusing ( 3-MW critical power [34]), resulting in elongation of the waveguide in the axial direction and formation of poor quality waveguides. 101

132 4.3 Thermal stability of waveguides For the rst time, the thermal stability of femtosecond-laser written waveguides formed in the cumulative heating regime is reported. Waveguides were written at 230-mW power, 1.5- MHz repetition rate, 0.4-NA, 150-µm depth and 8-20-mm/s scan speed. After waveguide characterization, the EAGLE2000 sample was baked for 1 hour in a tube furnace in repeated heating and testing cycles of increased temperature in 100 C steps. A peak temperature of 800 C was tested that exceeds the annealing point of 722 C, the temperature at which stresses are relieved after several minutes, but remains below the softening point of 985 C at which the glass deforms under its own weight. For reference, the strain point of 666 C is the temperature below which glass can be rapidly cooled without introducing stresses. Figure 4.18 shows the mode prole (top) and overhead morphology (bottom) of the waveguide written with intermediate 15-mm/s scan speed for increasing annealing temperature. There is little change in the mode size and waveguide morphology at temperatures up to 500 C. At 600 C, the mode diameter increased 10% and there is less contrast in the cladding. At 700 C, the mode diameter increased 40% compared with the unheated sample (25 C), and the cladding is barely visible. At the last heating step of 800 C, the mode was undetectable due to high losses and the cladding has completely disappeared. Figure 4.19 shows the thermal annealing trends for the mode eld diameter (a) and insertion loss (b) for scan speeds of 8 to 25 mm/s. Above 500 C, the MFD and IL for all waveguides tested increased with temperature, with the degree of degradation being smallest for the waveguides written with the lowest speed or highest net uence. Glass has a frozen-in structure that depends on the cooling rate which corresponds to a ctive temperature of the 102

133 C 500 C 600 C 700 C 800 C 10 m Figure 4.18: 1550-nm mode prole (top) and overhead microscope (bottom) image at dierent annealing temperatures for waveguide fabricated in EAGLE2000 with 230-mW power, 1.5-MHz repetition rate, 0.4-NA, 150-µm depth and 15-mm/s scan speed. equilibrium melt [66]. Waveguides fabricated with the highest net uence are expected to cool fastest from the highest temperatures, creating modication structures with the highest ctive temperatures, as discussed in Section Therefore, waveguides written at the highest exposure required annealing at higher temperatures to undo the thermal history of the laser-modied glass and restore its properties to that of the unmodied bulk. Further, the disappearance of the cladding before the central core in Fig is attributed to a lower ctive temperature in the outer cladding due to lower temperatures and slower cooling rates as seen in Fig For the waveguide written with the minimum laser exposure (fastest speed of 20 mm/s), the 600 C anneal step increased the MFD and IL by 10% and 3.5 db, respectively, and the waveguide mode became undetectable after the 700 C step. In contrast, the maximum net exposure waveguide (8 mm/s) survived all annealing steps, accumulating only a small 5% and 0.7 db increase, respectively, in MFD and IL across all annealing steps to 800 C. By heating the sample above the annealing point (722 C) and then slowly cooling it, the radial stress that may be developed during waveguide formation is relaxed [35]. For 103

134 (a) diam meter ( m) Mode field Temperature (ºC) 8 mm/s 10 mm/s 12 mm/s 15 mm/s 20 mm/s (b) ) (db) Inse ertion loss Temperature (ºC) 8 mm/s 10 mm/s 12 mm/s 15 mm/s 20 mm/s Figure 4.19: Mode eld diameter (a) and insertion loss (b) versus baking temperature for waveguides fabricated with 230-mW power, 1.5-MHz repetition rate, 0.4 NA, 150- µm depth and scan speeds of 8 to 20 mm/s. The EAGLE2000 borosilicate glass sample was baked for 1 hour at each temperature. waveguides written at slow speeds of 8 and 10 mm/s, the mode eld diameter and insertion loss showed strong resistance to heating at 800 C. This indicates that the stress-optic contribution to the refractive index modication is small. Thermal annealing did not improve waveguide losses, which others have reported in fused silica and attributed to stress relaxation [35] and reduction of waveguide roughness and refractive index uctuations [111]. Waveguides written in EAGLE2000 glass with 1-kHz repetition rate were much less stable than the present 1.5 MHz results, undergoing an 80% increase in MFD after annealing at 500 C, and resulting in undetectable guiding at 1550 nm after annealing at 750 C [104]. The higher temperature stability of waveguides written with 1.5-MHz repetition rate is attributed to the higher ctive temperatures driven by the cumulative heating regime. 4.4 Summary Repetition rate was used as an experimental variable for the rst time in femtosecond laser writing of waveguides to delineate the roles of thermal diusion and heat accumulation at high repetition rates. For the rst time, a threshold energy for heat accumulation was iden- 104

135 tied as a function of repetition rate and scan speed. For 0.55-NA focusing, the pulse energy threshold for heat accumulation was found to vary from 900 nj at 200 khz to 80 nj at 2 MHz, showing that a stronger source for thermal diusion is needed to overcome the longer time interval between pulses at low repetition rates. A nite-dierence thermal diusion model was applied to model the temperature prole as a function of time and accurately predicted experimentally measured waveguide dimensions as a function of all exposure conditions. With the average power held constant at 200 mw, strong heat diusion at 200-kHz repetition rate compensated for a lower pulse delivery rate to form similar 11-µm diameter zones at repetition rates up to 2 MHz, where heat accumulation is more ecient. Waveguides written at 200-mW power and 15-mm/s scan speed were found to have the minimum insertion loss at each repetition rate, with the minimum propagation loss of 0.3 db/cm achieved with 1.5-MHz pulse delivery rate. The useful range for 3D fabrication was extended from 200 µm [37] to 500 µm by exploring a lower numerical aperture (0.4) writing condition, which reduced the eect of spherical aberration. Thermal annealing tests of waveguides written in the optimum processing window revealed excellent resistance to temperatures up to 800 C, showing excellent promise for long-term stability and in applications requiring high temperatures. The results contribute a comprehensive and pioneering study of laser waveguide writing in EAGLE2000 borosilicate glass, an important industrial glass used in at panel and liquid crystal display (LCD) devices. 105

136 Chapter 5 Waveguide fabrication in fused silica glass Fused silica glass is an excellent candidate for integrated optical circuits because of its excellent transparency in the visible and near infrared, resistance to high temperatures and compatibility with many biomaterials. Although many groups have demonstrated laserwritten waveguides in fused silica, few have been able to fabricate waveguides with low propagation and coupling losses at 1550 nm wavelength. Nasu et al. demonstrated very low 0.1 db/cm propagation losses in fused silica [31], but their method required multiple overlapping scans at scan speeds of 10 µm/s which is very slow for potential device fabrication. In this work, the high repetition rate femtosecond ber laser was applied to greatly improve fabrication speeds with exposure conditions optimized to achieve low propagation losses at telecom wavelengths. 5.1 Static laser exposures Figure 5.1 shows optical microscope images of Corning 7980 fused silica glass modied by static laser exposures of 450-nJ pulse energy focused with 0.65-NA aspheric lens (1.4-µm spot size diameter) with varied repetition rate and number of pulses. From overhead, transverse 106

137 waveguide diameters of 2 µm nearly identical to the laser spot size were observed for all exposure conditions, showing no evidence of heat accumulation or strong thermal diusion. This absence of heat accumulation is partly attributed to the 9.1-eV bandgap of fused silica, which is more than twice that of borosilicate (Table 2.1). Indeed, Streltsov and Borrelli [72] have observed less absorbance in fused silica compared with borosilicate glass. Further, more laser energy is necessary to heat fused silica to its 1585 C softening point, which is 1.6-fold higher than in borosilicate glass (Table 2.1). Also, the thermal diusivity of Corning 7980 fused silica is 1.5-fold higher than EAGLE2000 borosilicate (Table 2.1), so that heat diuses away from the focal volume at a faster rate in fused silica, inhibiting a buildup of heat between laser pulses. A combination of higher uence, higher repetition rate, and shorter laser wavelength may provide the necessary conditions for driving cumulative heating eects in fused silica. Osellame et al. recently observed nonuniform structures in fused silica using a 30-nJ, 26-MHz Ti:Sapphire oscillator and a 1.4-NA oil-immersion objective [37]. These refractive index structures showed evidence of cumulative heating but were not suitable for waveguiding. 5.2 Waveguide processing window Despite the absence of heat accumulation in fused silica, it will be shown that through optimization of the laser power, scan speed, repetition rate, wavelength, polarization and pulse duration, the fabrication of uniform waveguide structures with low insertion loss is possible. The focusing numerical aperture was held constant at 0.55 NA to provide a good compromise between spherical aberration and self-focusing. 107

138 4x10 7 4x10 6 4x10 5 4x10 4 4x10 3 pulses 1 MHz 500 khz 50 m 200 khz 100 khz MJ/cm 2 Figure 5.1: Optical microscope images showing laser-modied zones formed in Corning 7980 fused silica with 450-nJ energy, 1045-nm wavelength pulses focused with 0.65-NA lens. Total pulse (top) and uence accumulation (bottom) is shown for each column and the laser repetition rate (100 khz to 1 MHz) is indicated for each row. Laser direction is normal to page Optimization of wavelength With the fundamental wavelength of 1045 nm, weak and irregular damage tracks were observed for all exposure conditions (scan speed, repetition rate, and pulse energy) and these were unable to guide visible or telecom wavelengths. Figure 5.2 shows an overhead microscope view of typical tracks written with 1045-nm wavelength. Since other exposure variables had been widely explored at 1045-nm wavelength, the laser was frequency doubled with an LBO crystal in the hope of driving strong absorption and forming smooth and low-loss waveguides. The frequency-doubled 522-nm light oers a theoretically 2-fold smaller spot size that compensates for the 50% of incident power that is lost in the conversion process, resulting in a 2-fold higher maximum uence compared to the fundamental wavelength. This together 108

139 Figure 5.2: Overhead microscope images of laser modication tracks in fused silica written at 1045-nm wavelength with 1-MHz repetition rate, 175-mW average power, and 0.2 to 50-mm/s scan speed. with stronger multiphoton ionization processes was thought to contribute to the formation of higher contrast modication tracks. Figure 5.3 shows typical tracks formed with 522-nm wavelength with experimental setup described in Section Compared to the fundamental wavelength, tracks written with the green wavelength were smoother and showed stronger contrast, which is attributed to the higher maximum uence. It is possible that the lower order of multiphoton absorption results in enhanced nonlinear photoionization and increased absorption. However, for the same uence, a similar absorption of 40% was recorded for 522 and 1045-nm wavelengths in fused silica. For wide bandgap materials such as fused silica and CaF 2, avalanche ionization plays a more important role than photoionization in increasing the concentration of free carriers. As a result, a similar damage threshold was found by Schaer et al. in fused silica for fundamental (800 nm) and second harmonic (400 nm) wavelengths from a 40-fs Ti:Sapphire oscillator [34]. With the longer pulse duration provided by the present ber 109

140 Figure 5.3: Overhead microscope images of laser modication tracks in fused silica written at 522-nm wavelength with 1-MHz repetition rate, 175-mW average power, and 0.5 to 10-mm/s scan speed. laser ( 220 fs), avalanche ionization is expected to play an even stronger role in comparison to multiphoton absorption. Table 5.1 shows the optimum scan speed and pulse energy for low-loss waveguides at repetition rates of 0.25, 0.5, 1 and 2 MHz. The writing wavelength was 522 nm with polarization parallel to the scan direction. Also shown in Table 5.1 are the net uence and resulting mode eld diameter and insertion loss, measured at 1550-nm wavelength. The optimum insertion loss decreases with increasing repetition rate, reaching a minimum of 0.9 db at 1 MHz. Nearly the same pulse energy of 200 nj and net uence of 30 kj/cm 2 was required to achieve the lowest-loss waveguide with mode diameter of 11 µm at repetition rates of 0.25 to 1 MHz. At 2 MHz, the insertion loss (and mode size) increased dramatically. The maximum pulse energy of 95 nj was required to achieve the optimum waveguides, well below the ideal 200- nj energy needed at repetition rates of 0.25 to 1 MHz. If more laser power were available, we anticipate that lower loss ( 1-dB insertion loss) waveguides could also be generated at 110

141 Table 5.1: Exposure conditions, MFD and IL of lowest loss waveguides written in fused silica at repetition rates of 0.25, 0.5, 1 and 2-MHz repetition rate (522-nm wavelength). Sample length 2.5 cm. Laser polarization was parallel to the scan direction. Repetition rate (MHz) Pulse energy (nj) Scan speed (mm/s) Net uence (kj/cm 2 ) Mode eld diameter (µm) Insertion loss (db) >20 >10 db repetition rates above 1 MHz Optimization of polarization In fused silica, femtosecond-laser modied structures are highly polarization dependent due to the formation of nanogratings perpendicular to the writing polarization [61,62,67]. Therefore, the eect of polarization on refractive index morphology and guiding characteristics was explored. Linear polarizations parallel and perpendicular to the scan direction and circular polarization were provided by a half and quarter waveplate, respectively, as described in Section 3.1. The optimum writing condition for perpendicular and circular polarization was 1-MHz repetition rate, 175-nJ pulse energy and 0.75-mm/s scan speed, identical to the case of parallel polarization in Table 5.1. However, the resulting cross sectional prole and guiding characteristics of the optimum waveguide for each polarization were signicantly dierent. Figure 5.4 shows the cross sectional phase contrast microscopy images for the optimum waveguides written with circular, parallel and perpendicular polarizations. The images colors were inverted for clarity to oer direct comparison with transmission microscopy. The 111

142 location of the geometric focus, 75 µm from the surface, coincides with the transition between the bright and dark regions. Since the images were recorded with phase contrast microscopy, the bottom region was conrmed to have a positive index change and therefore responsible for guiding light, while the top region was composed of negative refractive index change. For all incident polarizations, the overall dimensions of the modied zones were 3 µm 25 µm, greatly exceeding the theoretical diraction-limited focal volume of the laser. The transverse spot size and depth of focus for focusing 522-nm light with the 0.55-NA lens were 2w 0 = 0.80 µm and 2z 0 = 2.2 µm, respectively. The elongated structures in Fig. 5.4 appear similar to those reported by Couairon et al. [112] and Burakov et al. [113] in which buried structures were fabricated with peak powers greater than the critical power for self focusing in fused silica. The waveguide shapes showed reasonable agreement with theoretical models of the electron density during waveguide writing in bulk fused silica [112, 113]. The electric eld at the focus was modeled by these groups with the nonlinear optical Schroedinger equation, accounting for propagation eects including dispersion, diraction, self focusing, plasma defocusing and energy loss from photoionization [113, 114]. The elongated shape of the structures shown in Fig. 5.4 is attributed to an absence of heat accumulation and thermal diusion eects. Further, multiple modication zones are attributed to a combination of plasma defocusing and self focusing eects, as the peak power is equal to the 0.8-MW critical power for self focusing in fused silica (Eq. 2.15) [115]. By varying the pulse energy from near threshold (50 nj) to the optimum 175 nj, the apparent focus location shifted towards the surface by 5 µm, indicating that self focusing plays a role in dening the optimum waveguides in fused silica. Further modeling work, also accounting for the multi-pulse interaction used in the present experiments, may 112

143 Figure 5.4: Cross sectional phase contrast microscopy images of waveguides written at circular, parallel and perpendicular polarizations at 1-MHz repetition rate, 175-nJ pulse energy, 0.75-mm/s scan speed. elucidate the detailed features of the refractive index zones. Shown in Table 5.2 are the mode eld diameter and insertion loss at 1550-nm wavelength for the waveguides shown in Fig The insertion loss was minimum for parallel polarization at 0.9 db, although the waveguide properties were similar to the case of circular polarization where a 1.4-dB insertion loss was measured. The dierences observed in the waveguide morphologies for circular and parallel versus perpendicular polarizations was also seen in the guiding properties, where for perpendicular polarization, a larger mode size and larger insertion loss of 13.5 µm and 2.4 db, respectively, were measured. In the only published study on the inuence of polarization on waveguide properties, Ams et al. reported that in the fabrication of waveguides in fused silica with a 1-kHz, 120-fs Ti:Sapphire laser, circularly polarized light yielded better transmission for straight and curved waveguides compared to linear polarization. Despite the dierent repetition rate and pulse duration used in the studies, a reasonable comparison can be made due to the 113

144 Table 5.2: Insertion loss and mode eld diameter (1550-nm wavelength) as a function of writing polarization for 1-MHz repetition rate, 175-nJ pulse energy and 0.75-mm/s scan speed Polarization Insertion loss (db) Mode eld diameter (µm) Circular Parallel Perpendicular lack of heat accumulation in the current study. In the present work, parallel polarization yielded the optimum straight waveguides, although it is expected that circular polarization to be optimal for writing curved waveguides for two reasons: rst, the smaller mode size for circular polarization (Table 5.2) results in less bend loss; second, the nanogratings formed by circular polarization are disordered [67], which unlike the case of linear polarization, results in waveguide properties that do not vary along the waveguide bend Optimization of pulse duration Since the nonlinear pulse propagation [81] and the formation of nanogratings [63] in fused silica are dependent on the pulse duration, the eect of the pulse duration on the resulting waveguide properties was explored. By misaligning the compressor prism, it was possible to extend the pulse duration from its nominal value of 300 fs to a maximum of 700 fs at 1045-nm wavelength (Lorentzian FWHM). The intensity autocorrelation traces after second harmonic generation are shown in Fig. 5.5, where pulse durations of (i) 220 fs, (ii) 280 fs and (iii) 400 fs were measured at 522-nm wavelength (Lorentzian FWHM). Table 5.3 shows the optimum pulse energy, mode diameter and insertion loss at 1-MHz repetition rate, 0.75-mm/s scan speed and parallel polarization for the pulse durations shown in Fig Figure 5.6 gives a graphical representation of the pulse duration dependence 114

145 1045 nm 522 nm (i) (ii) (iii) Time delay (ps) Figure 5.5: Intensity autocorrelation function (ACF) for pulse durations of (i) 200 fs, (ii) 280 fs and (iii) 400 fs measured at 522-nm wavelength and FWHM of Lorentzian. Incident fundamental (1045 nm) ACF shown in red and second harmonic (522 nm) ACF shown in green. Table 5.3: Insertion loss and mode eld diameter as a function of pulse duration for 1-MHz repetition rate, 0.75-mm/s scan speed and parallel polarization Pulse duration (fs) Pulse energy (nj) Insertion loss (db) Mode eld diameter (µm) of the insertion loss and mode prole. The insertion loss is 0.9 db at the nominal pulse duration of 220 fs and reaches a minimum of 0.7 db at 280 fs before increasing to 1.1 db at 400 fs. As the pulse duration was increased, the mode size decreased from 12.2 µm at 220 fs to 9.9 µm at 400 fs. Note that for other repetition rates and polarizations, a similar trend was observed. The corresponding microscope images of the waveguide cross sections are shown in Fig At 280 fs, the smoothest guiding region was observed, which could explain the lowest insertion loss of 0.7 db at this pulse duration. Since the waveguide length was 2.5 cm, the upper limit for propagation loss is 0.3 db/cm. The eect of pulse duration on the nonlinear propagation is evident, with the longest pulse showing a signicantly dierent morphology, with a shorter axial length and more irregular guiding region compared to the lower pulse 115

146 Insertio on loss (db) Pulse duration (fs) Figure 5.6: Insertion loss versus pulse duration for waveguides fabricated in fused silica with 1-MHz repetition rate, 0.75-mm/s scan speed and parallel polarization. Mode proles at 1550-nm wavelength are shown at each data point. 116

147 220 fs 280 fs 400 fs 5 m Figure 5.7: Cross sectional microscope images of waveguides written at pulse durations of 220 fs, 280 fs and 400 fs as specied in Table 5.3. The laser was incident from the top and the dashed red line shows the approximate location of the focal plane, 75 µm below the surface. durations. The waveguide structures shifted downwards as the pulse duration was increased and is attributed to the decreased peak power for increased pulse duration, which reduces the eect of self focusing Spectral response of insertion loss Similar to borosilicate glass (Section 5.2.4), the insertion loss was measured in fused silica waveguides as a function of wavelength (Fig. 5.8). A similar trend is observed, with the loss decreasing from from 2.2 db to 1.3 db from 1250 to 1550-nm wavelength, except for a peak near 1390-nm wavelength, attributed to IR vibrational overtones from the OH defect. In Corning 7980 fused silica, there is a relatively high concentration ( 1000 ppm) of OH impurities [84], leading to a higher 0.5-dB/cm loss at 1390-nm wavelength corresponding to the 1.2-dB peak in Fig. 5.8 for the 2.5-cm sample length. 117

148 Insertio on loss (db) Wavelength (nm) Figure 5.8: Insertion loss versus wavelength for 2.5-cm long waveguides fabricated in fused silica with 1-MHz, 220-fs ber laser (0.55 NA, 522-nm wavelength, 0.7-mm/s scan speed, 150-mW average power). 5.3 Summary In this chapter, a high repetition rate ber laser was applied to fused silica glass to examine the potential for low-loss waveguides. The fundamental wavelength was frequency doubled to 522-nm wavelength to increase the maximum per-pulse uence on target and drive strong index modication in fused silica glass, which absorbs less light than borosilicate glass. With an optimum 1-MHz repetition rate, low-loss waveguides were formed in fused silica, but with an absence of heat accumulation due to less absorption, a higher melting point and a higher thermal diusivity compared to borosilicate glass. The eects of pulse duration and writing laser polarization were studied for the rst time on femtosecond laser inscribed waveguides in fused silica, with a low propagation loss of 0.2 db/cm obtained with a relatively long pulse duration of 280 fs and parallel polarization. 118

149 Chapter 6 Device fabrication Since this rst discovery of femtosecond laser fabrication of waveguides by Hirao and coworkers in 1996 [8], various optical devices have been written inside glasses such as sensors [116,117], power splitters [118], and three-dimensional (3D) circuits [19,103,117,119]. Despite the promise of femtosecond laser waveguide writing, there have been few reports of characterization of such optical devices in the low-loss telecom wavelength (1550 nm), [18,116119] and no reports at the zero-dispersion wavelength (1310 nm) or across the entire telecom band ( nm). In Section 6.1, detailed characterization results for femtosecond laser written buried directional couplers in borosilicate glass are presented, the rst such device characterized at the important telecom wavelengths of 1310 and 1550 nm. The couplers show markedly improved coupling eciency and insertion loss relative to other results [18,120]. The directional coupler is an important building block in optical circuits that opens new opportunities for fabricating Mach-Zehnder interferometers, optical interleavers, sensors and power splitters in novel 3D architectures. In Section 6.2, the spectral performance of femtosecond laserwritten couplers is characterized across the full telecommunications band ( nm). Using knowledge of the coupling coecient and the additional phase from curved transition 119

150 regions, a coupler that demultiplexes 1300 and 1550 nm wavelengths is demonstrated. In Section 6.3, the directional couplers are designed to give a wavelength attened response for power splitting applications. At small separation distances, the wavelength response of the coupling coecient and additional phase cancel out to yield a nearly constant coupling ratio with wavelength. Using both symmetric and asymmetric designs, wavelength-attened responses are demonstrated at various coupling ratios including 0, 50 and 100%. In Section 6.4, lab-on-a-chip, sensing and telecom devices fabricated in fused silica glass are presented. In Section 6.5, the results in this chapter are summarized. 6.1 Directional coupler The present directional couplers were fabricated with exposure conditions of 200-nJ pulse energy, 1-MHz repetition rate, and 20-mm/s scan speed to yield low loss waveguides in Corning EAGLE2000 borosilicate glass at 1550-nm wavelength. The ideal repetition rate of 1.5-MHz for low-loss waveguides described in Section 4.2 was found after this directional coupler study. A MFD of 12.0 µm at 1550-nm wavelength was found at 20-mm/s scan speed, closely matching that of SMF (10.5-µm). Using a SMF at the waveguide output facet, this waveguide yielded a 2-dB insertion loss for the 5-cm long waveguide. Bend loss was investigated by measuring the insertion loss in a single arm of the directional coupler as shown in the inset of Fig. 6.1 for various bend radii, R. The central region oset from the input/output arms was xed at 50 µm so that the arc length of the two S-bends varied from 4.0 to 9.8 mm for bend radii varying between 10 and 60 mm. The measured bend loss, which refers to the dierence in insertion loss between one arm of the directional coupler and that of a straight waveguide, includes pure bend loss and bend tran- 120

151 Figure 6.1: Bend loss (dierential insertion loss between coupler arm and straight waveguide) versus radius of curvature for waveguides written with 20-mm/s scan speed, 200-nJ pulse energy and 1-MHz repetition rate in EAGLE2000 borosilicate glass. Inset shows one arm of the directional coupler under test with four bends of radius R. sition loss at inection points in the arm. The contribution from propagation loss due to a dierent arc length of the coupler arm compared to the straight waveguide is negligible here. The bend loss, or dierential insertion loss, is plotted in Fig. 6.1 as a function of bend radius for 1310 and 1550 nm. A bend radius of 40 mm ( 0.1 db loss) was chosen for the directional couplers because the loss rapidly increases for smaller bend radii. Directional couplers were dened by symmetric double S-bend waveguides with 40-mm radius of curvature in the layout shown in Fig The top optical microscope image of the evanescent coupling region shows similar waveguide structure to those described in Section 4.2 with a core and cladding diameter of 3 and 12 µm, respectively. In total, 140 directional couplers were fabricated, with waveguide separation distance d (center to center) varied from 7.5 to 22.5 µm and interaction length L varied from 2 to 30 mm. Also shown in Fig. 6.2 are the 1550-nm wavelength near-eld intensity distributions of the launch ber mode at port 1 121

152 and the waveguide modes at output ports 2 and 3. A 50/50 splitting ratio is demonstrated in Fig. 6.2 for a separation distance and interaction length of d = 17.5 µm and L = 20.6 mm, respectively. The output modes are nearly identical in shape and the power ratio was 50:50±1%. The index modication zone was approximated to be a cylindrical step prole of 3- µm diameter, as the refractive index contrast in the core is primarily responsible for light guiding as shown in Section 4.2. From the analytic Bessel function solution describing the intensity prole of the weakly-guiding cylindrical waveguide [121], a refractive index change of best matched the experimentally measured waveguide MFD of 12.0 µm. Such index change is comparable to those measured experimentally by RNF in Section 4.2. At 1550-nm and 1310-nm wavelengths, the V -parameter (Section 2.4.1) was 1.2 and 1.0, respectively, indicating single-mode operation since V < Only at a visible wavelength of 650 nm does the V -parameter exceed 2.405, predicting multimode operation. Indeed, multimode operation was observed when launching 635-nm light into the waveguides written in EAGLE2000. The measured insertion losses in either arm of the symmetric 50/50 coupler in Fig. 6.2 were identical within experimental uncertainty to that of a straight waveguide, conrming the insignicant <0.1 db loss in Fig. 6.1 for 40-mm radius of curvature. At 1310 nm, the insertion loss of the directional coupler was 2.5 db while at 1550 nm, the insertion loss was slightly lower at 2.2 db. This loss compares favorably to the 3 3 directional couplers written by Suzuki et al. [18], who reported 6.7-dB insertion loss at 1530-nm wavelength. The 3-fold improvement in insertion loss may be due to the 6-fold longer pulse duration of the writing laser and dierences in exposure conditions and the type of glass. 122

153 Figure 6.2: Schematic of 3-dB directional coupler and optical microscope image of waveguides in coupling region (top) together with mode proles of 1550-nm laser light from launch ber at port 1 and from output facets at ports 2 and 3. 50/50 coupling was demonstrated at d = 17.5 µm and L = 20.6 mm, using writing conditions of 200-nJ pulse energy, 20-mm/s scan speed, 150-µm focal depth and 1-MHz repetition rate. In the waveguide mode proles shown at the output, the writing laser was incident from the top. The power splitting was next characterized as a function of interaction length, L, and separation distance, d. Referring to Fig. 6.2, a coupling ratio, r, is dened as power at the cross port P 3, normalized to the total power at output ports 2 and 3 can be derived from coupled mode theory (Section 2.4.2): where δ = r = P 3 = κ2 P 2 + P 3 δ 2 sin2 (δl) (6.1) (β 1 β 2 ) 2 /4 + κ 2, β 1 and β 2 are the propagation constants of the adjacent waveguides, κ is the coupling coecient, which decreases with increasing core separation, d. Ideally, the coupling ratio modulates sinusoidally between 0 and 1 with varying L. Deviation from 100% power transfer is due to a dierence in the propagation constants β 1,2, presumably caused by a drift in laser power during exposure or the modication zone of the rst written waveguide aecting the refractive index modication of the second waveguide. Data for the through port coupling ratio, dened as 1 r, is plotted in Fig. 6.3 versus 123

154 Figure 6.3: Through port coupling ratio dependence on interaction length for separations d = 7.5, 12.5 and 17.5 µm at 1310 and 1550-nm wavelengths. Sinusoidal curve ts shown are shown as solid lines. interaction length for core separation distances of d = 7.5, 12.5 and 17.5 µm at wavelengths of 1310 and 1550 nm. The modulation depth consistently reaches near unity and closely follows the expected sinusoidal response (solid and dashed curves in Fig. 6.3) for all data ranges. At 1550-nm wavelength, the minimum through port coupling ratio is -19 db (1%) corresponding to 99% maximum coupling ratio. The modulation range is slightly lower at 1310-nm wavelength, yielding a minimum of -12 db, corresponding to 93% coupling ratio. Impressively, the coupling performance for the case of d = 7.5 µm is not hindered by slight overlapping of the outer waveguide cladding zones which have 6-µm radius. The results are a signicant improvement over the 2 2 directional couplers demonstrated by Minoshima et al. [120], which yielded a sharp decrease in the maximum coupling ratio from 0.6 to 0.08 as the separation distance increased from 8 to 12 µm. One reason for their low coupling is due to the mismatch in propagation constants that arises for the dierent bend radii used in the two arms of their coupler. Coupler beat lengths were obtained from the data presented in Fig. 6.3 and are plotted in Fig. 6.4 as a function of the separation distance, d. The solid (dashed) curve for 1550-nm 124

155 (1310-nm) wavelength is derived from the analytical calculation of the coupling coecient for the case of cylindrical step-index proles [121, 122]: κ = (2 )2 a ( X 2 K 0 V 2 X 2 d/a ) ( (6.2) V 3 V 2 X2) K 2 1 where κ = π/l B is the coupling coecient, l B is the beat length for full power oscillation, a is the waveguide radius, d is the center-to-center separation, = 1 n 1 /n 2, V = 2πan 2 2 /λ, λ is the free-space wavelength, and n 1,2 is the refractive index of the bulk and the waveguide core, respectively. The core parameter X = k T a was determined from the eigenvalue relation for the fundamental mode of a weakly guiding ber (Eq. (2.23)): X J 1 (X) J 0 (X) = V 2 X K ( 2 1 V 2 X ( 2) (6.3) K 0 V 2 X2). In solving Equations (6.2) and (6.3), a diameter 2a = 3 µm and index change of n 2 n 1 = were assumed. Consistent results were also provided by numerical analysis (Lumerical MODE Solutions 2.0). The analytical model slightly overestimated the experimental data in Fig. 6.4, which is attributed the simplied cylindrical geometry assumed for the refractive index proles, which have more complex proles as shown in Section 4.2. As expected, beat length increases with waveguide separation since the coupling coecient falls exponentially with increasing distance [123]. Beyond 17.5-µm separation, beat lengths become nearly as large as the 50-mm long substrate. At 1310-nm wavelength, a smaller MFD of 8.6 µm reduces the coupling between adjacent waveguides and yields longer beat lengths than for 1550 nm. The good quality of directional couplers presented here represents a signicant advance 125

156 Figure 6.4: Beat length as a function of separation distance for 1.31 and µm wavelengths. Experimental data points are shown along with analytic representations (solid and dashed lines). in laser fabrication technology of potential interest for telecom and sensing applications. The couplers provide near-unity power transfer at small separation distances (7.5 µm) and short beat lengths ( 1.5 mm). Insertion losses of 2 db are already attractive for many applications and improvements are anticipated with further optimization of laser exposure conditions. Laser writing speeds of 5 seconds per coupler are appealing as are the opportunities for generating novel 3D optical structures not possible with standard planar lithographic techniques. 6.2 Wavelength demultiplexer Wavelength multi-demultiplexers play a vital role in wavelength division multiplexing (WDM) optical networks and sensor applications. Wavelength multiplexers have been demonstrated in planar-lightwave circuits (PLC) using directional couplers, oering the potential for miniaturization and mass production [124], but are limited to specic glass compositions with planar geometries. The most common fabrication method for wavelength demultiplexers is using two bers fused into a single tapered element by heating and drawing. The adiabatic 126

157 taper at the input and output result in undesirable device lengths of several centimeters [123]. Furthermore, the ber approach cannot be integrated on a photonic chip for added functionality. In comparison to the commonly employed fused ber taper technique for fabricating wavelength demultiplexers, femtosecond-laser writing enables the close and accurate placement of adjacent waveguides resulting in small interaction lengths of 1 mm in combination with curved transitions of 5-mm length, allowing for devices shorter than 1 cm, with wellpredicted responses from coupled mode theory, as demonstrated in Section 6.1. For use as wavelength multiplexer/demultiplexers, directional couplers must be functional across the entire telecommunications band. The operation of femtosecond-laser-written directional couplers has been demonstrated at visible ( nm) [47] and near-infrared ( nm) [120] wavelengths, but there have been no couplers characterized across the full telecommunications spectral band ( µm) spanning original (O), extended (E), short (S), conventional (C), long (L) and ultra-long (U) bands. Furthermore, directional couplers were fabricated without the aid of a model for tailoring spectral performance for wavelength multi-demultiplexing. In this work, femtosecond laser-written directional couplers are characterized across the full telecommunications band, showing ideal zero to unity oscillation of coupling ratio versus wavelength and interaction length, in agreement with coupled mode theory. A simple empirical model permitted the design and demonstration of a direction coupler geometry optimized for wavelength demultiplexing of 1.3 and 1.55-µm wavelengths that may serve in passive optical networks (PONs) [125] for ber-to-the-home (FTTH) applications. Straight optical waveguide sections in Corning EAGLE2000 borosilicate glass were opti- 127

158 Input port 1 2 R d 4 L 3 Through port Cross port Figure 6.5: Directional coupler geometry with center-to-center separation d, interaction length L and S-bend radius R = 50 mm mized for minimum insertion loss at 1550-nm wavelength as described in Section 4.2. Directional couplers were written with the optimum 1.5-MHz repetition rate, 200-mW (133-nJ) average power (pulse energy) and 12-mm/s scan speed. Similar to the directional couplers described in Section 6.1, symmetric couplers were fabricated with the S-bend geometry shown in Fig The center-to-center separation was varied from d = 8 to 15 µm and the interaction length was varied from L = 0 to 7.6 mm. The separation between input ports 1 and 4 and output ports 2 and 3 was (100 + d) µm. Light was launched into port 1 and output power at the through (P 2 ) and cross (P 3 ) ports was measured at ports 2 and 3, respectively, as identied in Fig As expected, identical coupling behavior was observed when launching light from input port 4. For a directional coupler with curved transition regions, the power coupling ratio, r(λ), can be derived from coupled mode theory [126] yielding: r (λ) = sin 2 (κ (λ) L + φ(λ)) = sin 2 (κ (λ) L eff ) (6.4) where κ(λ) is the coupling coecient, which is inversely related to the beat length, l B = π/κ(λ), for full power oscillation. The phase term φ(λ), referred to as the bending phase, is due to coupling in the curved transition regions and depends on the bend radius and 128

159 separation distance d. A wavelength-dependent eective interaction length L eff (λ) = L + φ(λ)/κ(λ) is introduced to account for the net coupling from the straight and curved regions. The conditions for demultiplexing of λ 1 = 1300 nm and λ 2 = 1550 nm can be derived for the directional coupler with S-bends using Eq. (6.4) with the requirement r(λ 1 ) = 1 and r(λ 2 ) = 0 (1300 nm at cross port, 1550 nm at through port), leading to the desired eective interaction length at wavelengths λ 1 and λ 2 : L eff,1 = L + φ 1 /κ 1 = 2m 1 1 l B,1 ; L eff,2 = L + φ 2 /κ 2 = m 2 l B,2 (6.5) 2 where m 1,2 are positive integers chosen such that l B,1 > l B,2. The minimum lengths are satised by m 1,2 = 1: L eff,1 = 1 2 l B,1; L eff,2 = l B,2 (6.6) For the case of the straight directional coupler, φ 1 = φ 2 = 0 and Eq. (6.6) simplies to: L eff,1 = L eff,2 = L = 1 2 l B,1 = l B,2. (6.7) Another possibility for demultiplexing of λ 1 = 1300 nm and λ 2 = 1550 nm is r(λ 1 ) = 0 and r(λ 2 ) = 1 (1550 nm at cross port, 1300 nm at through port). This requirement is satised by: L eff,1 = m 1 l B,1 ; L eff,2 = 2m 2 1 l B,2 (6.8) 2 The minimum length is satised by m 1 = 1, m 2 = 2 (m 1,2 = 1 does not satisfy l B,1 > l B,2 ): 129

160 L eff,1 = l B,1 ; L eff,2 = 3 2 l B,2 (6.9) For the straight coupler, Eq. (6.9) simplies to: L eff,1 = L eff,2 = L = l B,1 = 3 2 l B,2 (6.10) It is useful to analyze the demultiplexing criterion for the straight directional coupler (Eqs. (6.7) and (6.10)), particularly when the coupling contribution from the bending phase is small. At rst glance, Eq. (6.7) appears to specify a smaller length than Eq. (6.10). However, in Eq. (6.7), the ratio of beat lengths at 1300 and 1550 nm is 2 whereas in Eq. (6.10), the ratio is 1.5. As shown in Fig. 6.4 the ratio of beat lengths at 1300 and 1550 nm increases with separation distance d. Therefore, one needs a larger separation, and therefore larger beat length to satisfy Eq. (6.7) compared to Eq. (6.10). For the direction couplers written with the exposure conditions described above, a separation of d = 8 µm led to nearly identical beat lengths of l B,1 = 1.8 mm and l B,2 = 1.7 mm, which is unable to demultiplex λ 1 and λ 2 unless a very large device is used. A larger separation of d = 10 µm resulted in l B,1 = 1.5 l B,2 = 3.8 mm, which satises the interaction length specied by Eq. (6.10). A large separation of d = 15 µm was needed to provide a 2-fold dierence in beat lengths to satisfy Eq. (6.7), but this resulted in beat lengths > 10 mm. Therefore, Eq. (6.10), with L = l B,1 = 1.5 l B,2 = 3.8 mm, is the minimum interaction length for a straight directional coupler fabricated with our experimental setup. As will be shown below, the curved transition regions introduce a small phase correction to the straight coupler analysis. Therefore, for a curved coupler, the demultiplexing criteria in Eq. (6.9) leads to the smallest 130

161 device size for this WDM application. The two criteria for demultiplexing in Eq. (6.9) can be satised using a numerical method such as the beam propagation method to determine the optimum separation distance d, interaction length L and bend radius R. However, this requires knowledge of the refractive index prole at all wavelengths, which is dicult to accurately measure in the present devices. Instead, an empirical approach was applied where a sequence of directional couplers were fabricated and the measured coupling ratio versus interaction length was used (Eq. (6.4)) at each wavelength (1250 to 1650 nm) to determine κ(λ) and φ(λ) representations at a specic coupler separation distance d. In this study, the bend radius was held xed to avoid signicant bend loss. The separation d was estimated from the simplied straight coupler criterion in Eq. (6.10) and the interaction length L (two possible solutions) was chosen to satisfy the curved coupler criteria in Eq. (6.9). As described earlier, 10-µm separation distance provides 1.5-fold dierence in beat lengths at 1300 and 1550-nm wavelengths. The coupling ratio versus interaction length is plotted in Fig. 6.6(a),(b) and demonstrates a beat length of 3.87 mm at 1300-nm wavelength (a), 1.5 times larger than the 2.57-mm beat length at 1550-nm wavelength (b). Accurate sinusoidal representations of the coupling ratio versus length were observed for all wavelengths between 1250 and 1650 nm, conrming the validity of Eq. (6.4) derived from coupled mode theory. From the least squares curve ts of the coupling ratio versus length at each wavelength, the coupling coecient and bending phase spectra were calculated and are shown in Fig. 6.6(c) for 10-µm separation distance. The slope of the coupling coecient and bending phase are both positive, therefore, for any choice of interaction length L, the total phase 131

162 Coupling ratio Coupling ratio (a) Interaction length (mm) 1.4 (b) Interaction length (mm) 1.4 Coupling coefficient (rad/mm) Extra phase (rad) (c) Wavelength (nm) 0.0 Figure 6.6: Measured (solid square) coupling ratio versus interaction length at (a) 1300 nm and (b) 1550 nm wavelengths, and sinusoidal curve ts (solid lines) for d = 10 µm. The beat length is 3.83 mm and 2.57 mm at 1300-nm and 1550-nm wavelength, respectively. Coupling coecient and bending phase (c) versus wavelength for directional coupler with 10-µm center-to-center separation. 132

163 Table 6.1: Coupling coecient and bending phase at 1300-nm and 1550-nm wavelengths for d = 10 µm. Wavelength Coupling coecient, bending phase, Beat length, φ/κ (mm) λ(nm) κ (rad/mm) φ (rad) l B (mm) κ(λ)l + φ(λ) will increase with wavelength monotonically, resulting in a nearly sinusoidal relationship between the coupling ratio and wavelength. As described in the next section, φ (λ) > 0 for all separation distances, but only for d 8 µm is κ (λ) > 0. Short separations of d < 8 µm lead to κ (λ) < 0 and a wavelength-attened response, which is undesirable for demultiplexing, and is discussed below in the context of broadband power splitters. For typical interaction lengths of L > 2 mm, the coupling coecient's contribution to the total phase is about 3-fold greater than the bending phase over the entire spectrum, so that the straight coupler criterion for demultiplexing (Eq. (6.10)) is a reasonable estimate for the separation distance. Larger bend radii of R > 50 mm will lead to a larger contribution from the bending phase, which is undesirable for simple device design, since the straight coupler criterion (Eq. (6.10)) becomes a worse estimate for the separation distance. The coupling coecient, bending phase, ratio of coupling coecient to bending phase and beat length are summarized in Table 6.1 for wavelengths λ 1,2 = 1300, 1550 nm. To meet the conditions in Eq. (6.9), the interaction length L for demultiplexing operation is L 1,2 = 3.23, 3.10 mm. The discrepancy between the two values (L 1 L 2 ) means that demultiplexing of 1300 and 1550-nm wavelengths with zero crosstalk cannot be achieved. The wavelength response of the coupling ratio across the full telecommunications band ( nm) is shown in Fig. 6.7 for interaction lengths L = 0, 0.8, 1.6 mm in (a) and L = 133

164 0.8 mm (a) (b) 5.2 mm L = 3.2 mm L = 0 mm 1.6 mm 6.8 mm Figure 6.7: Measured coupling ratio versus wavelength for interaction lengths of (a) L = 0, 0.8, 1.6 mm and (b) 3.2, 5.2, 6.8 mm for d = 10 µm. 3.2, 5.2, 6.8 mm in (b). As expected from Eq. (6.4) and Fig. 6.6(c), the spectral responses are nearly sinusoidal with the period of oscillation decreasing with increasing interaction length. To the author's best knowledge, Fig. 6.7 is the rst demonstration of nearly 0 to 100% sinusoidal wavelength response for a femtosecond laser-written coupler, conrming the directional couplers are symmetric with identical propagation constants in adjacent arms, despite the close proximity of the waveguides resulting in an overlap of the heat-modied claddings. The noisy parts of the spectra in Fig. 6.7, at 1250, 1350, 1500 and 1600 nm arise from low power emission points in the broadband source that consists of four LEDs with center wavelengths of 1310, 1430, 1550 and 1650 nm. For L = 3.2 mm in Fig. 6.7(b), strong demultiplexing discrimination of 1300 and 1550 nm wavelengths is observed with r(1300 nm) = and r(1550 nm) = This interaction length shows excellent agreement with the interaction lengths of 3.2 and 3.1 mm predicted by Eq. (6.9). The crosstalk, a gure of merit for demultiplexing, is r(1300 nm)/r(1550 nm) = db. This result is comparable to the -20 db crosstalk achieved by other fabrication techniques [124, 127]. Improvement in crosstalk is expected through ner scaling of the 134

165 separation distance and bend radius, leading to a convergence of the interaction lengths for demultiplexing operation. 6.3 Broadband power splitter Directional couplers are typically wavelength sensitive as their operation depends on the interference of even and odd supermodes with propagation constants that vary with wavelength. Wavelength sensitivity is desirable in certain applications such as wavelength demultiplexing described in the previous section, but not for broadband power splitting, commonly required in wavelength division multiplexing (WDM) systems and power monitoring applications. To overcome the wavelength sensitivity, several designs have been proposed which include tapered ber couplers [122], bent couplers [128], Mach-Zehnder interferometers (MZIs) [129], and asymmetric directional couplers [130, 131]. Y-splitter branching devices were avoided due to the excess loss introduced by the Y-junction and the increased fabrication complexity in joining the output arms. For completeness, this section presents results of broadband power splitting with femtosecond laser-written directional couplers. This work was a collaborative eort with experimental and detailed theoretical analysis performed by the present author, and colleague William Chen, respectively. A more complete analysis will be reported in William Chen's MASc thesis. The broadband responses were observed at short separation distances, d, through compensation of the wavelength dependence between the straight and curved regions in a directional coupler. For the symmetric coupler, the coupling ratio spectrum is given by (6.4). Wavelength attening of the coupling ratio results when the total phase κ(λ)l + φ(λ) is independent of wavelength. 135

166 Figure 6.8: Directional coupler implementation for wavelength-attened power splitter. The rst arm was written at 12 mm/s and the second arm was written at 8 mm/s (asymmetric), 12 mm/s (symmetric) or 20 mm/s (asymmetric). As depicted in Fig. 6.8, the directional coupler design was either uniformly symmetric or uniformly asymmetric, following Takagi's nomenclature [130]. The couplers were fabricated in Corning EAGLE2000 borosilicate glass using the same experimental conditions as the previous Section 6.2. A scan speed of 12 mm/s was used to dene the rst arm with the second arm scanned at a speed of either 12 (symmetric), 8 (asymmetric) or 20 mm/s (asymmetric). The center-to-center separation distance d ranged from 6 to 10 µm. The interaction length L was varied from 0 to 2.5 mm in steps of 0.25 mm. The experimentally determined values for coupling coecient and bending phase are presented against wavelength for the symmetric coupler in Fig. 6.9 for separations of d = 6, 6.5, 7.5, 10 µm. Similar to the previous section, the wavelength dependence of the coupling coecient and bending phase were obtained by least squares ts of the coupling ratio versus interaction length Eq. (6.4), for wavelengths between 1250 and 1650 nm. For all wavelengths and separation distances, the data were accurately represented by Eq. (6.4) indicating that coupled mode theory was valid over the geometries tested in Fig As the separation distance increases, both the coupling coecient and bending phase decrease due to the exponentially decaying evanescent tail of the waveguide mode. For 10- µm sepa- 136

167 ration distance, both the coupling coecient and bending phase increase with wavelength. Regardless of interaction length L, the total phase (sum of coupling coecient and bending phase) increases with wavelength, preventing a wavelength-attened response. However, such behavior is desirable for applications requiring sinusoidal modulation of the coupling ratio, such as wavelength multiplexing applications demonstrated in Section 6.2. As the separation distance decreases below 10 µm, the slope of the coupling coecient is reduced, eventually becoming negative over the entire wavelength range. In this case, broadband coupling behavior is possible through suitable choice of interaction length, L. A common but incorrect view is that the coupling coecient increases monotonically with wavelength [130]. The transition of the coupling coecient from positive to negative slope at small separations can be understood by analyzing in the functional form of the coupling coecient (Eq. (2.29)): κ k2 0 E1 (x, y)e 2β 2 (x, y)dxdy. Since the integral is taken over waveguide 2, increasing wavelength (less connement of the modes) results in E 1 increasing, but E 2 decreasing. The rst term outside the integral k2 0 2β approximately varies as 1/λ. Therefore, it is not surprising that the coupling coecient can decrease with wavelength at a certain separation distance. The coupling ratio versus wavelength for 6-µm separation distance and interaction lengths of 0, 0.5, 1, 1.5, 2, and 2.5 mm is shown in Fig It is important to note that with 6-µm center-to-center separation, the second waveguide fabricated in the coupler was written into the cladding of the rst waveguide. The 12-µm diameter claddings overlap by 6 µm, yet the adjacent waveguides show negligible dierence in propagation constants as evidenced by the zero to unity sinusoidal variation in coupling ratio with interaction length. This underscores the robustness of the high-repetition rate femtosecond-laser writing process, particularly 137

168 Figure 6.9: Coupling coecient (solid lines) and bending phase (dashed lines) versus wavelength for symmetric coupler with separation distances of 6, 6.5, 7.5 and 10 µm. in comparison with direct UV laser writing of PLCs, where a decrease in photosensitivity contributed to a propagation constant oset of closely spaced waveguides [132]. Broadband unity coupling with greater than 400-nm bandwidth (±5%) was achieved for L = 1 mm as seen in Fig The common view in the literature is that the coupling ratio modulates nearly sinusoidally from zero to unity in the wavelength domain for a symmetric directional coupler [130]. However, for all the interaction lengths tested, the modulation clearly does not follow this trend. This is not due to breakdown of couple mode theory, but rather due to the balance between the κ(λ)l and φ(λ) terms in Eq. (6.4) as described above. To achieve at wavelength response at coupling ratios less than unity, in particular for the most challenging coupling ratio of 3 db, an asymmetry between the adjacent waveguides was introduced by scanning the second arms at a dierent speed (8 or 20 mm/s). Note that over the scan speed range (8 to 20 mm/s) yielding low-loss waveguides, the peak coupling ratio ranges from 60% to 90% as wavelength is varied, above the desired 50% optimum 138

169 Figure 6.10: Coupling ratio versus wavelength for symmetric coupler with separation distances of 6 µm and interaction lengths of 0, 0.5, 1, 1.5, 2, and 2.5 mm. Table 6.2: A list of the broadband couplers, their geometries and bandwidths ( ±5%). r (%) v (mm/s) d (µm) L (mm) BW (nm) >400 >400 >400 >400 > >400 >350 >400 to atten the wavelength response for 3-dB couplers [123]. The best broadband responses obtained with symmetric (r = 100%) and asymmetric (r = 0, 10, 20, 35, 50, 60, 70, 90%) designs are shown in Fig The coupler geometries, bandwidths and scan speeds are summarized in Table 6.2. Coupling ratios from zero to unity were obtained with ±5% bandwidth (BW) ranging from 300 to 400 nm, comparable to PLC wavelength-attened power splitters written by photolithography [130] and direct UV laser writing [131]. 139

170 Figure 6.11: The spectral responses of couplers with the largest bandwidths for coupling ratios of 0, 10, 20, 35, 50, 60, 70, 90 and 100%. Coupler geometries and exposure conditions are summarized in Table 6.2. The femtosecond laser writing technique applied in this study presents a number of advantages over the existing fabrication technologies. Fused ber technology is not suitable for integration, while photolithography requires expensive clean room technology and is not ideal for fast prototyping of custom components. In comparison to direct UV writing, femtosecond laser writing allows faster writing speeds by about 10 fold and does not require additional photosensitization procedures [131]. In addition, femtosecond laser writing can write structures in 3D outside of the plane and is applicable to a wide variety of transparent materials, while UV photosensitivity of most glasses is too weak to be practical beyond PLC applications. 140

171 6.4 Fused silica devices As detailed in the previous chapter, heat accumulation could not be driven in fused silica but despite this, low-loss waveguides could still be formed with 1-MHz repetition rate, 150-mW average power, parallel polarization and 280-fs pulse duration at 522-nm wavelength. These optimum parameters were applied to fabricate devices in fused silica that take advantage of its favorable properties, for lab-on-a-chip, telecommunication and sensing applications. Lab-on-a-chip or biochip devices are powerful functioning laboratories where large instrumentations have been miniaturized to oer high diagnostic sensitivity for small sample volumes, with high speed throughput useful in a large number of applications [133]. The integration of photonic functions oers new approaches for detection, spectral diagnostics, manipulation, and analysis of bio-samples. By intercepting microchannels with waveguides, the optical detection of cells and bio-materials is possible by observing the uorescence [134] or transmission [133] signal. To intercept surface microchannels, which typically have diameters of µm, buried waveguides with depths of < 30 µm are required. In borosilicate glasses such as Corning EAGLE2000, it is not possible to fabricate waveguides with depths less than 50 µm because the extended heat zone results in ablation at the surface. In fused silica, where the ablation threshold is higher and the heat-aected zone is smaller, much shallower waveguides can be formed to a minimum depth of 15 µm, with excellent guiding properties. At 10-µm depth, the glass at the surface begins to ablate, and the waveguide losses increase. Figure 6.12 shows a waveguide fabricated at 15 µm below the surface and the corresponding mode prole at 1550-nm wavelength. The insertion loss and mode size are similar to the best 141

172 Figure 6.12: Fused silica waveguide for intercepting surface microchannel fabricated at 15 µm below the surface with the corresponding mode prole at 1550-nm wavelength. waveguides demonstrated in the previous chapter. Future work will involve integration with surface microchannels fabricated with the 157-nm F 2 laser, which has demonstrated very low roughness ( 10-nm RMS) in ablating surface features in fused silica [135]. The 3D advantage of femtosecond laser writing has been exploited to form buried microchannels in fused silica glass [67, 136]. Buried microchannels allow a higher density and can avoid the issues in planar microuidics such as unwanted microchannels crossings and sealing of the lab-on-a-chip. As rst demonstrated by Hnatvosky et al., laser modication tracks such as those used for optical waveguides can be etched by HF acid to form microchannels below the glass surface [67]. This work was extended by Maselli et al., where they demonstrated the formation of channels with circular cross sections by using astigmatic beam shaping [136]. In our group, Stephen Ho (PhD candidate) has applied the laser recipes developed in Section 5.2 for waveguide writing in fused silica to stitch together an array of waveguides that open up after HF etching, producing microchannels with arbitrary cross sections [137]. Cross sections of rectangular, square, elliptical or circular proles with arbitrary 142

173 Figure 6.13: Integrated optouidic sensor: buried microchannel between input and output reservoirs intercepted by buried waveguide [137]. size are possible using this technique. Figure 6.13 shows an integrated optouidic sensor with reservoirs, which may be used for cell counting by observing a change in the waveguide transmission, or for cell detection, by observing the uorescence signal at the output waveguide. Particle ow can be driven by capillary electrophoresis. The etched microchannels with orthogonal probing waveguide are buried 75 µm below the surface. As described in Section 6.2, the wavelength (de)multiplexer is a critical component for passive optical networks and was demonstrated with very low cross talk in borosilicate glass. As proof of principle, directional couplers were written in fused silica with the same coupler geometry and characterized across the entire telecom spectrum, as shown in Fig The coupling ratio spectra show sinusoidal spectra with peak ratios of near unity, demonstrating excellent reproducibility of the closely-spaced (10-µm separation) waveguides. My colleague Haibin Zhang recently discovered a single-step method for writing waveguides with integrated Bragg gratings, referred to as Bragg grating waveguides (BGWs) [89]. By externally modulating the intensity of the incoming laser with an acousto-optic modulator (AOM), periodic voxels were formed in fused silica along the waveguide which can act 143