Broadband Arrayed Waveguide Grating Multiplexers on InP

Transcription

1 Broadband Arrayed Waveguide Grating Multiplexers on InP Item Type text; Electronic Dissertation Authors Rausch, Kameron Wade Publisher The University of Arizona. Rights Copyright is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 11/04/ :31:27 Link to Item

2 Broadband Arrayed Waveguide Grating Multiplexers on InP by Kameron Rausch A Dissertation Submitted to the Faculty of the COLLEGE OF OPTICAL SCIENCES (GRADUATE) In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy In the Graduate College THE UNIVERSITY OF ARIZONA

3 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Kameron W. Rausch entitled Broadband Arrayed Waveguide Grating Multiplexers on InP and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy. Alan R. Kost David F. Geraghty Seppo Honkanen Date: November 15, 2005 Date: November 15, 2005 Date: November 15, 2005 Final approval and acceptance of this dissertation is contingent upon the candidate s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. Dissertation Director: Alan R. Kost Date: November 15, 2005

4 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: Kameron W. Rausch

5 4 ACKNOWLEDGMENTS I would like to express my deepest gratitude to my advisor, Dr. Alan Kost. His knowledge and expertise has been a real inspiration. I could not ask for a better advisor. I would also like to thank the rest of my dissertation committee, Dr. David Geraghty and Dr. Seppo Honkanen. Thanks for all of the interesting discussions and collaborations on past projects. I look forward to continuing these into the future. I would also like to thank two colleagues who created an unforgettable graduate experience. John Perreault and Souma Chaudhury, I will always look back and reminisce the interesting discussions we had during lunch. Lastly, I would like to acknowledge my family. Mom and dad, thank you for always believing in me. Newton, I can t imagine where I would be if you were not there to break up the long hours spent writing this manuscript and studying for prelims. My wife Caroline Rausch, without you, none of this would have been possible. Thank you for your patience while I pursue my dreams and ambitions. I owe you everything.

6 5 TABLE OF CONTENTS LIST OF FIGURES LIST OF TABLES ABSTRACT INTRODUCTION REFRACTIVE INDEX CALCULATIONS Bulk Material Refractive Index Waveguide and Modal Refractive Index Birefringence Minimization Temperature Dependence ARRAYED WAVEGUIDE GRATING DESIGN AND OPERATION Basic AWG Operation Performance Characteristics Design Variable Declaration AWG Design Focusing and Dispersion Waveguide Separation Star coupler Length Phased Array Waveguide Layout Waveguide Profile Bend Loss Final AWG Designs Thermal and Polarization Dependence Thermal Dependence Polarization Dependence PHOTOLITHOGRAPHY AND SEMICONDUCTOR PROCESSING Preliminary Tests Wet Chemical Etching Argon Ion Beam Etching Reactive Ion Etching Photolithography Reactive Ion etching

7 6 TABLE OF CONTENTS Continued 5 RESULTS AND DISCUSSION OF TESTED AWGS Waveguide Propagation Results AWG Transmission Temperature and Polarization Dependence Measurements Temperature Polarization Improving fiber to semiconductor coupling losses DESIGN OF ULTRA BROADBAND DEMULTIPLEXERS AWG Design AWG Comparison Calculations AWG PERFORMANCE OPTIMIZATION Multimode Waveguides Bend Loss as a Filter Waveguide Junctions SUMMARY Appendix A. MODELING REFRACTIVE INDEX WITH MATHCAD 107 Appendix B. SIMULATING AWGS WITH MATHCAD Appendix C. S-SHAPED AWG DESIGN REFERENCES

8 7 LIST OF FIGURES 1.1 Typical telecommunications datalink Band gap versus molar composition InP wafer with epi layers Refractive index dispersion for InGaAsP and InP Shallow ridge waveguide Slab waveguide mode Refractive index of the slab mode Zero birefringence waveguides Birefringence as a function of waveguide width Birefringence as a function of waveguide core layer thickness Birefringence as a function of layer t thickness Thermo-optic effect of InP Slab mode emanating from AWG Schematic representation of a four channel AWG Expanded view of a star coupler Shallow ridge waveguide used in AWG fabrication Slab waveguide with mode Crosstalk from evanescent coupling Schematic representation of image field Crosstalk due to field truncation Typical narrowband AWG phased array layouts Horseshoe geometry result of a broadband AWG Deep ridge waveguide transmission loss Bend loss illustration Bend loss as a function of cover layer thickness Bend loss as a function of radius Transmission channel width vs. Grating order Chemically etched waveguides Overcut and undercut waveguides Argon ion etched waveguides Preliminary reactive ion etching results Process flow schematic

9 8 LIST OF FIGURES Continued 4.6 Scanning electron image of shallow ridge waveguide Atomic force microscope image of etched surfaces Measured Fabry-Perot fringes for propagation loss Optical setup for propagation loss measurements Eight channel AWG transmission results Four channel AWG transmission results Phased array group and star coupler refractive indices Thermal spectral shift Birefringence effects on AWG transmission Flat-top pass band AWG spectrum Star coupler schematic showing the effects of index dispersion Output waveguide separation schematic Transmission loss of mispositioned waveguides Coupling to higher order modes as a function of waveguide offset Waveguide offset as a function of bend radius Input coupling versus waveguide width C.1 Exploded AWG layout with parameters

10 9 LIST OF TABLES 3.1 Final AWG design parameters AWG performance measurements

11 10 ABSTRACT Coarse Wavelength Division Multiplexing (CWDM) is becoming a popular way to increase the optical throughput of fibers for short to medium haul networks at a reduced cost. The International Telecommunications Union (ITU) has defined the CWDM network to consist of eighteen channels with channel spacings of 20 nm starting at 1270 nm and ending at 1610 nm. Four and eight channel AWGs suitable for CWDM were fabricated using a versatile S-shape design novel to InP. The standard horseshoe layout will not work on semiconductor for AWGs with a free spectral range (FSR) larger than 30 nm. The AWG design provides operation insensitive to thermal and polarization fluctuations, which is key for low cost operation and packaging. It will be shown that refractive index changes over the large operating wavelength band produced negligible effects in the transmission spectrum. Standard AWG design assumes refractive index is a constant over the operating wavelength band. As a result, the output waveguide separations are held constant on the second star coupler. As the channel number increases, secondary focal dispersion caused from a changing refractive index can have detrimental effects on performance. A new design method will be introduced which includes refractive index dispersion by allowing the output waveguide separations to vary. The new design is consistent with standard design but is applicable in materials with a linear index dispersion over an arbitrarily large wavelength band. Lastly, a method for increasing the transmission using multimode waveguides is discussed. Traditionally, single mode waveguides are required in order to prevent higher order waveguide modes creating ghost images in the output spectrum. Using bend loss and waveguide junction offsets, higher order modes can be filtered from the output, thereby eliminating ghost images and at the same time, increase transmission.

12 11 CHAPTER 1 INTRODUCTION The spread of voice, internet, and multimedia applications has placed a high demand for large transmission capacities in today s optical communication networks. Wavelength Division Multiplexing (WDM) has been the primary focus to meet this demand by increasing the aggregate transmission of a single fiber. Erbium doped fiber amplifiers are the major component for amplification within an optical fiber and the driving force in the spread of optical communication networks. The amplification band of an EDFA is limited to the C and L-bands of an optical fiber, which extends the wavelength range of 1530 nm to 1610 nm. In the past, emphasis has been placed on research into Dense Wavelength Division Multiplexing (DWDM) networks. The focus of these networks is to place many tightly spaced wavelength channels into the EDFA band. Present networks utilize the available band to its entirety. Increasing the transmission capacity with more channels requires a smaller wavelength channel spacing. WDM components with a channel spacing of 50 GHz (0.6 nm) are commercially available. The very tight channel spacing requires the lasers and components within the network to be thermally and polarization stabilized to prevent excess crosstalk and/or channel hopping. Thermoelectric coolers and hermetic sealing are typically used for temperature stabilization. Hermetic seals are expensive and thermoelectric coolers typically draw a few amps during operation. These requirements result in networks which are expensive to fabricate and operate. For medium to long haul networks, the high cost is acceptable since the network services many users and divides the cost up among them. In short haul networks, such as a Metro Area Networks (MAN) or fiber-to-home, cheaper networks are a necessity. Coarse Wavelength Division Multiplexing (CWDM)

13 12 is a promising technique for increasing the bandwidth and flexibility of optical communication networks at a substantially reduced cost. The CWDM network, as defined by the standard G694.2 of the International Telecommunications Union, consists of eighteen channels extending from 1270 nm to 1610 nm [1]. The central wavelength of the network is 1440 nm. A relatively large channel spacing of 20 nm eliminates the need for temperature stabilization and reduces the overall network cost. The large channel spacing enables network components with the fabrication and operation tolerances relaxed, which results in a lower cost. The need for thermoelectric coolers to stabilize the laser wavelength and absorb the dissipated heat is lifted. The emission wavelength of lasers in a CWDM network would be allowed to drift with ambient temperature along with the other components in the network. A typical Wavelength Division Multiplexing (WDM) telecommunications data link is shown in Fig Key components in WDM systems are multiplexers and demultiplexers, which work to combine and separate wavelength channels. Many different technologies have been developed to realize multiplexers and demultiplexers in a WDM network. Some of those technologies include: thin film filters, Mach-Zender interferometers, ring resonators, and AWGs. In the next several paragraphs, I will highlight these multiplexers and demultiplexers. The technology for thin film filters is well developed and is currently in widespread use in optical WDM networks. Thin film filters consist of a Fabry-Perot cavity surrounded by many dielectric layers designed to increase reflectivity at a specific wavelength while allowing all other wavelengths to transmit through [2], [3]. A series of these cavities are required to extract all wavelengths from a fiber and place each channel on its own fiber. The number of Fabry-Perot cavities is dependent on the number of channels. A Mach-Zender multiplexer or demultiplexer consists of many individual Mach-Zender interferometers [4]. Each interferometer can only combine or separate all the incoming

14 13 LASER OPTICAL MODULATOR SOA PHOTODIODE 1 1, n i ADD 1 2 FIBER 2 DROP j m n MULTIPLEXER DE- MULTIPLEXER Figure 1.1: Schematic showing a typical telecommunications data link. Multiplexers and demultiplexers are key components used to separate and combine wavelengths in optical fibers. or outgoing wavelengths into the two input or output arms. To multiplex or demultiplex n channels, n-1 interferometers are needed. For example, a 1x16 Mach-Zender demultiplexer was fabricated using 15 interferometers [5]. Standard MZI multiplexers are not suitable for constant wavelength separation networks since they separate and/or combine signals on a constant frequency grid. By employing phase generating couplers, a uniform wavelength MZI multiplexer was demonstrated [6]. Ring resonators can also be used for multiplexing and demultiplexing [7]. If the resonant frequency of the ring matches the wavelength of the mode traveling in the straight waveguide, it can be coupled into the ring. Multiplexing is done by placing another waveguide tangent to the ring but on the opposite side. This waveguide is

15 14 used to couple the mode back into a straight waveguide for routing. Multiplexing or demultiplexing is accomplished by placing many ring resonators in series down a straight waveguide channel. The abovementioned multiplexers and demultiplexers are better suited for add/drop filters as shown in Fig. 1.1 or networks with a small number of channels because several cascaded stages are required for multiplexing or demultiplexing. Cascading stages increases device size, fabrication difficulty, insertion loss, and network complexity. A better multiplexer for large channel WDM networks is the Arrayed Waveguide Grating (AWG), sometimes referred to as a PHASAR. AWGs are a relatively new technology with increasing interest for applications in WDM networks. AWGs can be designed to suit a variety of applications in DWDM and CWDM networks. They have the ability for mass production and can be scaled for multiplexing and demultiplexing networks with many wavelength channels without increasing footprint size and insertion loss by the cascading of many components inherent to thin film filters, Mach-Zender interferometers, and ring resonators. AWGs are a generalized Mach-Zender interferometer and can replace many thin film filters, ring resonators, or Mach-Zender interferometers discussed above. Arrayed waveguide gratings can also be extended to optical routing [8],[9]. AWG multiplexers and demultiplexers are only different in the orientation of the device within the network. Multiplexers can be used as demultiplexers due to the reciprocity of light. Utilizing this, AWGs have been designed and fabricated that function concurrently as a multiplexer and a demultiplexer. The AWGs discussed in this thesis were tested as a demultiplexer and from now on, will be referred to as a multiplexer. CWDM AWGs have been fabricated on other material systems including acrylate polymers [10] and silica on silicon [11]. Extremely low insertion loss and crosstalk have been demonstrated due to the high transparency of these materials. The low index contrast between the core and the cladding minimizes coupling loss from fiber to device

16 15 and vice versa, further reducing loss. The best performing AWGs fabricated to date used silica on silicon technology. Unfortunately these materials are inherently passive and currently, monolithic integration with active devices is limited. Erbium doped fiber amplifiers have a gain bandwidth which is much smaller than the extent of the CWDM wavelength range. For amplification outside the EDFA band, semiconductor optical amplifiers (SOA) are used. Semiconductor optical amplifiers extend the gain bandwidth by having the ability of tuning the amplification wavelength band, thereby increasing the possible gain band to cover the entire region of the CWDM network. AWGs on InP are highly desirable for several reasons. They have the ability to drastically reduce the size of the device because of the high refractive index contrast possible in semiconductor waveguides and AWGs on InP can be monolithically integrated with active components, such as lasers and photodiodes. Integration of optoelectronic components is inevitable because of the advantages it offers network administrators and technicians. Integrated components are cheaper to fabricate than if the components were fabricated separately and are more robust because of fewer optical connections between devices, which also reduces insertion loss. AWGs on InP are highly desirable in CWDM networks because they have the potential for monolithic integration with SOAs, which could potentially provide gain over the entire CWDM band as discussed above. The arrayed waveguide grating was first proposed by Smit in 1988 [12]. Vellekoop and Smit had an operational device in 1989 using visible wavelengths [13]. Takahashi et al. fabricated the first AWG using near-infrared telecommunication wavelengths in 1990 [14]. Research for developing AWGs on InP has been almost entirely limited to dense wavelength division multiplexing [15]. Broadband AWGs on InP include a two channel device designed for the duplexing of 1.31 m and 1.55 m wavelengths [16] and an eight

17 16 channel AWG with a 3.2 nm channel spacing [17]; however, the channel spacing in these devices are not suitable for CWDM operation. In this thesis, the focus will mainly be on broadband AWGs which conform to the International Telecommunications Union (ITU) standard for a Coarse Wavelength Division Multiplexing (CWDM) network with a channel spacing of 20 nm. Four and eight channel AWGs, suitable for CWDM multiplexing were fabricated on InP. The required large free spectral range prohibited the use of the standard horseshoe style AWG design. A more versatile S-shape design was used instead. These were the first AWGs fabricated on semiconductor suitable for CWDM and the first to utilize an S-shape design on semiconductor. Over a broad range of wavelengths, the refractive index changes considerably and has effects on the transmission spectrum, which are proportional to the free spectral range. The refractive index dispersion was modeled using the effective index technique and together with the AWG design equations were used to predict the positions of the transmission peaks as a function of wavelength, polarization, and temperature. The positions were found to coincide very accurately with the measured spectral peaks which validates the use of the effective index technique as an invaluable tool for modeling AWGs. The effective index technique was then used to simulate the effects refractive index dispersion has on the transmission spectrum as the channel number or free spectral range is increased. It will be shown that the path length difference introduces a first order wavelength dependent focal dispersion. Refractive index causes a secondary focal dispersion which, if unaccounted for, can be a source of excess loss as the channel number increases. This can have some detrimental effects on the overall performance. A new model with refractive index dispersion is derived which can be used for designing AWGs over an arbitrarily large wavelength band. The new design is compared to the standard design which ignores index dispersion via an AWG designed to cover the entire CWDM

18 17 network. The AWG consists off 18 channels separated by 20 nm, beginning at 1270 nm and ending at 1610 nm. The positions of the waveguides for the outside channels were found to have a maximum error of 14%, which translates into a wavelength channel spacing error of 14% and a maximum additional loss of 2.5 db. Lastly, a brief review is given on methods of reducing insertion loss with emphasis placed on semiconductor AWGs. Then a novel technique, which uses a property of the waveguide and the wide spectral peaks of the channels, is introduced for increasing transmission through AWGs. Wider waveguides can increase coupling from the input fiber and at the star coupler-phased array interface due to a higher overlap integral. With a few exceptions, waveguides are required to be single mode since multiple modes can cause ghost images in the transmission spectrum and greatly increase crosstalk, especially in DWDM. In shallow ridge waveguides, control of the bend radius can be used as a selective filter for separating out the higher order modes in the form of bend loss. With this filter, wider multi-mode waveguides can be used without producing ghost images. Wider waveguides are possible in CWDM since the transmission spectral peaks are much wider than DWDM. The outline for this thesis is as follows. The model for calculating the refractive index measurements from interpolated experimental results along with the effective index method are presented in chapter 2. In chapter 3, the principles and design of conventional AWGs, suitable for narrowband applications, will be discussed. Chapter 4 covers the fabrication of AWGs including the photolithography and processing. The results with discussion of the fabricated and tested AWGs are given in chapter 5. In chapter 6, the design and simulation of broadband AWGs is presented, which takes into consideration refractive index dispersion. Methods of improving the overall performance of AWGs is discussed in chapter 7 along with a new concept to increase the transmission of AWGs

19 18 that utilize multimode waveguides in the design without affecting performance. This thesis will conclude with a summary in chapter 8.

20 19 CHAPTER 2 REFRACTIVE INDEX CALCULATIONS The devices of this thesis cover a broad band of wavelengths and are fabricated out of a very specific composition of In 1 x Ga x As y P 1 y. Since the refractive index of all the different InGaAsP compositions at all wavelengths have not been measured, a model was developed to curve fit the experimental data as a function of wavelength and molar compositions x and y [18]. Shallow ridge waveguides were used in the fabrication of the AWGs in this thesis. The effective index method was used to calculate the effective indices of the core, cladding, and finally the mode for the shallow ridge waveguide. In this chapter, the model used to calculate the refractive indices of the bulk InP and InGaAsP material will be introduced. These can then be used to calculate the refractive indices of the ridge waveguide profile. 2.1 Bulk Material Refractive Index For telecommunication devices, InP is the semiconductor of choice. The bandgap of InP and its lattice matched composition of In 1 x Ga x As y P 1 y can be tuned over the wavelength range 920 nm to 1650 nm. The band gap wavelength of the In 1 x Ga x As y P 1 y layer in the devices was designed to be far away from the operating band of the AWG devices, which extends from 1270 nm to 1610 nm. A band gap λ g equal to 1100 nm will keep refractive index dispersion and absorption at a minimum. Choosing a composition of In 1 x Ga x As y P 1 y which is lattice matched to InP places restrictions on the possible values of x and y. The lattice matching condition of x in

21 20 Figure 2.1: The band gap wavelength versus molar composition y. A value for y equal to 0.33 was chosen to give a band gap of 1100 nm. terms of y is the following. x = y y (2.1) A polynomial equation to the second power was used to fit the measured band gap energy E 0 versus molar composition y for InGaAsP lattice matched to InP. E 0 = y 2 (2.2) in which E 0 is in electron volts. The composition y which provides a band gap wavelength λ g equal to 1100 nm is found by solving the roots of Eq The molar composition of y equals 0.33 and from Eq. 2.1, x equals The band gap wavelength λ g is shown in Fig. 2.1 as the molar composition is changed. The semiconductor wafer used to fabricate the AWGs consisted of a 0.3 µm thick In 0.85 Ga 0.15 As 0.33 P 0.67 layer sandwiched

22 21 Figure 2.2: The epi layers were grown on an InP substrate using MOCVD. between two 1.56 µm thick InP layers as illustrated in Fig The epi-layers were grown on an InP substrate by a commercial foundry using metal-organic chemical vapor deposition (MOCVD). The photoluminescence peak which corresponds to the absorption edge, was measured at λ g equal to 1100 nm. Typical materials, glass for example, use the Sellmeier equation or the simplified Cauchy formula to fit an analytical equation to experimental data [19]. The Sellmeier equation is an empirical equation which can incorporate an arbitrary amount of absorption resonances to match the materials physical properties. On semiconductor, a similar expression is used to curve fit an analytical equation to experimental data. The absorption resonances used in this model correspond to the valence/conduction band transition E 0 and the split off/conduction band transition E The following equation is used to curve fit an analytical formula to the experimentally measured refractive indices of InP. [ {A n(ω) = f(χ 0 ) ( E0 E ) ] } f(χso ) + B (2.3) in which A is the strength of the E 0 and E transitions, B is constant arising from higher order band gaps and do not add dispersion to the material, the function f(x) = 2 1+x 1 x x 2 is a fitting parameter dependent on χ 0 and χ so, which are the

23 22 Figure 2.3: The refractive index dispersion for In 0.85 Ga 0.15 As 0.33 P 0.67 and InP. Over the entire CWDM band, the refractive index changes by more than 2%. This small change has a much larger effect on the AWG transmission. energies associated with the E 0 and E transitions. The empirical A and B parameters required to make Eq. 2.3 fit experimental data are written in terms of the molar composition y. A = y (2.4) B = y (2.5) The refractive indices for the In 0.85 Ga 0.15 As 0.33 P 0.67 and InP layers are shown in Fig The refractive index of the In 0.85 Ga 0.15 As 0.33 P 0.67 and InP layers at λ equal to 1.55 µm is and respectively.

24 Waveguide and Modal Refractive Index The effective index technique is a very useful tool in modeling the refractive index profile and propagation constant of shallow ridge waveguides. Using the refractive indices above for the bulk material, the effective index method reduces a 2-D waveguide crosssection to a 1-D slab waveguide, greatly simplifying the simulation of optical devices. The effective index method was used in this thesis to simulate the wavelengths peak in the output spectrum and the polarization and thermal dependence of AWGs. The basic premise of the effective index method [20],[21] is that the fields are separable in the x and y directions. U(x, y) = X(x)Y (y) (2.6) Inserting this equation into the wave equation, 2 U(x, y) = k 2 [n 2 (x, y) n 2 eff] (2.7) results in two separable differential equations which can be solved independently of each other. 1 d 2 Y (y) + [k 2 n 2 (x, y) k 2 n 2 Y (y) dy eff(x)] = 0 (2.8) 2 1 d 2 X(x) + [k 2 n 2 X(x) dx eff(x) β 2 ] = 0 (2.9) 2 Solving the above differential equations and using the boundary condition that the fields should be continuous, the dispersion relation for the TE mode of the shallow ridge waveguide is: sin(κd 2φ) = sin(κd)exp[ 2(σs + ψ)] (2.10)

25 24 where ) ( σ φ = tan 1 κ) ( σ ψ = tanh 1 γ κ = k n 2 c n 2 eff (2.11) σ = k n 2 eff n2 s γ = k n 2 eff n2 a The dispersion for the TM mode is found in a similar fashion. The equations for φ and ψ in Eq become: ( ) σn φ = tan 1 2 c κn 2 s ( ) σn ψ = tanh 1 2 a γn 2 s (2.12) The effective index of the core ncore eff and cladding nclad eff is found by solving the transcendental equation (Eq. 2.11) for the waveguide profile in Fig.?? with the height s equal to the rib plus cover layer for the core and just the cover layer for the cladding. The calculations were performed in Mathcad. The program is located in Appendix A. The refractive index of the core and cladding layer are shown in Fig Now that the index profile has been reduced to a 1-D problem (Fig. 2.5), the effective index of the mode nmode eff can be found by solving the wave equation (Eq. 2.7) again with the appropriate boundary conditions. The dispersion relation for the TE mode is found below. k 0 w nmode 2 ncore 2 eff 2 nmode2 eff = atan eff nclad 2 eff ncore 2 eff nmode2 eff + (m num 1) π 2 (2.13) in which, w is the width of the ridge waveguide, ncore eff and nclad eff are the effective indices of the core and cladding region of the slab waveguide, m num is 1,2,3... and represents the mode number, and k 0 is the free space wavenumber. The dispersion equation

26 25 t h rib cladding n a n r s d core n c substrate n s Figure 2.4: Schematic representation of a shallow ridge waveguide. for the TM mode adds a ncore 2 eff /nclad2 eff term inside the arctangent argument. The effective index of the fundamental TE and TM modes are displayed in Fig. 2.6 for a waveguide of width 2.5 µm. 2.3 Birefringence Minimization In optical fiber, even though the TE and TM are orthogonal, they are coupled to each other over large distances from irregularities associated with the waveguide. To prevent excess polarization dependent loss (PDL), it is desirable to use waveguides which have little or no birefringence since the input polarization state is possibly an unknown. Designing the phased array waveguides such that the effective indices are equal is the conventional way of fabricating polarization independent AWGs. A common technique for fabricating waveguides with zero birefringence is designing symmetric guiding and cladding layers for the two orthogonal directions. Two examples of waveguides which can be designed to have zero birefringence are shown in Fig. 2.7 [15].

27 26 Figure 2.5: Illustration of a slab waveguide highlighting the variables in Eq Utilizing the shallow ridge structure, zero birefringence is not obtainable, although it can be minimized to a negligible value. Simulations using the effective index technique reveal that the birefringence monotonically decreases with decreasing waveguide width and layer thickness t. It was found that the birefringence dependence on the core layer thickness is not monotonic. As the core layer thickness increases between 0.1 µm and 0.4µm, the birefringence increases. For a thickness beyond 0.4µm, the birefringence decreases. The results of these are shown in Fig. 2.8, Fig. 2.9 and Fig After extensive refractive index modeling, the birefringence in the fabricated waveguides can be reduced 64%, by decreasing the core layer thickness d from 0.3 µm to 0.2 µm.

28 Figure 2.6: Refractive indices of the TE and TM slab waveguide modes. 27

29 28 Figure 2.7: Typical waveguide structures which can be designed to have zero birefringence. This is ideal for AWGs to reduce polarization dependent loss. Figure 2.8: Birefringence decreases with waveguide width.

30 Figure 2.9: The birefringence quickly decreases as the waveguide core layer thickness is decreased below 0.4µm. 29

31 Figure 2.10: Waveguide birefringence decreases monotonically with layer thickness t. 30

32 Temperature Dependence The temperature dependence of the refractive index in InP has been measured experimentally using the Fabry-Perot technique [22] from room temperature to 600 K. This technique is explained in detail in chapter 5. In InP and its alloys, the refractive index increases with increasing temperature. The thermal change in refractive index was fit to a second order polynomial equation. dn dt (T ) = T 2 + K T + K 2 K (2.14) The semiconductor wafer consists of a very thin layer of InGaAsP, with the remaining material being InP. The effect of temperature can be well approximated by the effects of InP only. The change in refractive index with temperature of the InGaAsP material is assumed to mimic InP. This is important because the temperature dependence of the different compositions of InGaAsP has not been investigated. The change in refractive index with temperature for the mode of the waveguide profile in Fig. 2.4, is shown in Fig

33 Figure 2.11: The refractive index of InP changes roughly 0.5% over a temperature range of 70 K. This small shift has a much larger effect in the transmission spectrum of AWGs. 32

34 33 CHAPTER 3 ARRAYED WAVEGUIDE GRATING DESIGN AND OPERATION In this chapter, the theory of AWGs is discussed in detail, including the multiplexing properties, and the performance parameters, such as free spectral range, crosstalk, insertion loss, and uniformity. Bend loss in shallow ridge waveguides is also derived using a perturbation approach as a function of ridge height and radius. The chapter concludes by deriving the thermal and polarization dependence of AWGs and typical methods of designing insensitive AWGs to both temperature and birefringence. 3.1 Basic AWG Operation In this thesis, the AWGs consist of a single input waveguide, two symmetrical Rowland type star couplers [23], many phased array waveguides, and four or eight output waveguides. With reference to the AWG schematic in Fig. 3.2 and the expanded view of a star coupler in Fig. 3.3, the general operation is as follows. The mode traveling in the input waveguide is incident on the object side of the first star coupler. Once inside the star coupler, the mode is no longer laterally confined by the waveguide and expands or diffracts for the length of the star coupler. The surface shape of the image side of the first star coupler is circular and concave with the same radius as the expanding wavefront so all of the light entering the phased array has the same phase. The phased array consists of many waveguides which have a constant path length difference L between any two adjacent waveguides equal to an integer multiple of the central device wavelength in the material λ 0 /n eff. In other words, the phase of the wavefront incident on the phased

35 34 array waveguides is mapped to the object side of the second star coupler. Since the object surface of the second star coupler has a convex shape, the diverging wavefront on the image side of the first star coupler has been mapped to a converging wavefront as the object in the second star coupler. The second star coupler is a free-space region which allows the wavefront to continue to converge and focus on the image side of the second star coupler where the output waveguides are located. If the wavelength is desired for transmission, an output waveguide is positioned on the star coupler at the focal point of that wavelength to enable transmission. For wavelengths other than the central wavelength, the constant path length difference L produces a phase delay which causes a wavelength dependent wavefront tilt. For wavelengths shorter than the central wavelength, the phase tilt is counterclockwise whereas wavelengths larger than the central wavelength have a clockwise phase tilt. The magnitude of the tilt is proportional to the difference between the channel wavelength and the central wavelength λ-λ 0. Similar to geometrical optics, a wavefront tilt causes the focal position to shift in the direction of the tilt laterally on the image side of the second star coupler. As the wavelength increases, the focal position moves in the positive x direction. The position for each output waveguide coincides with the focal positions of the desired wavelengths for transmission. In essence, the AWG is a filter that transmits the desired wavelengths by placing an output waveguide in the proper position and attenuates the unwanted wavelengths by omitting an output waveguide. 3.2 Performance Characteristics Arrayed waveguide gratings are designed to meet certain performance criteria dependent on the application. Some of these performance criteria are crosstalk, uniformity, and insertion loss. Crosstalk is defined as the unwanted signal in a wavelength channel caused by the coupling of energy from another channel. The major possible sources of

36 35 crosstalk in the AWGs of this thesis are evanescent coupling between adjacent output and phased array waveguides, background radiation due to the shallow etch waveguide structure, field truncation at the star coupler, and fabrication error. The first three sources can be minimized with design, while the last source requires better processing. The origin of these different sources of crosstalk will be discussed in the following paragraphs. Crosstalk due to evanescent coupling is caused from placing waveguides in close proximity. If the exponential decaying tail of a mode extends into the mode of an adjacent waveguide, coupling from waveguide to waveguide occurs. Typically there are only two places in an AWG geometry where this is of concern, the phased array waveguide spacing d p and the input and/or output waveguides spacing d o on the star couplers. Crosstalk can be reduced by enlarging the waveguide spacing. However, as the phased array waveguide spacing is increased, less of the mode incident on the phased array from the first star coupler will couple into the phased array, increasing insertion loss. Therefore, waveguide separation is a trade off between crosstalk and insertion loss. Shallow ridge waveguides support slab modes which can propagate through the substrate and cause background noise in the output and increase crosstalk. The slab mode originates from light on the input. Since the mode emanating from a fiber is much larger than the semiconductor waveguide profile, light can also be coupled into the slab mode. If the output waveguides are directly across the wafer from the input waveguides and since semiconductor devices are generally very short in length, the slab mode can cause a large amount of background noise. Fig. 3.1 shows the output of an AWG. The bright spots are the modes emanating from the output waveguides and the in between light is the slab mode. The most obvious way to eliminate the slab mode background noise is to offset the placements of the input and output waveguides. In fact, the best results were obtained from the AWGs which had this offset.

37 36 Figure 3.1: End on picture showing the light from two output waveguides of an AWG and the slab mode. A finite number of phased array waveguides captures a finite portion of the incident mode in the first star coupler. The captured field by the phased array is therefore truncated. The image on the output waveguides is the Fourier transform of the object field in the second star coupler. The Fourier transform of a truncated field produces side lobes in the output which contributes to crosstalk. Crosstalk due to truncation is minimized in design by reducing the amount of truncation by increasing the number of phased array waveguides. This is discussed more in the following section outlining star coupler design. In practice, the crosstalk in AWGs are not limited by design, but by fabrication errors. For strong constructive interference and small crosstalk, the light from all paths through the AWG has to arrive with the correct relative phase generated in the phased array. Fabrication inhomogeneities, including varying waveguide width or height, imperfect etching of waveguide surfaces in the phased array, and the filling in of the gaps between the waveguides near the star coupler are the major sources of phase error in AWGs. A varying waveguide width or height causes the effective index of the mode to vary while propagating. We will see in the next section that a varying effective index will

38 37 Figure 3.2: Schematic representation of a four channel AWG with an S-shape phased array geometry. reduce the amount of constructive interference and increase crosstalk. Processing errors in semiconductor devices are inherently higher than in silica or sol-gel waveguides but can still be kept small due to the small nature of semiconductor AWGs. The optical path length through the phased array should be kept as short as possible to minimize the magnitude of phase errors. Increasing the width between waveguides, or better photolithography and/or mask resolution prevents the filling in of the gaps between the waveguides at the star couplers. In this thesis, higher mask resolution and shallow ridge waveguides were used to reduce the filling in of the gaps. 3.3 Design Variable Declaration Before going into the derivation of AWGs, some discussion of the design parameters and their meaning are required. Fig. 3.2 and Fig. 3.3 are schematics of the AWG and star couplers used in this thesis. The Rowland type star couplers have a length R, which is also the radius of curvature for the surface of the star couplers adjacent to the phased array. The surface adjacent to the input and output waveguides have a radius R/2. The separation of the phased array waveguides d p connected to the

39 38 Figure 3.3: Expanded view of a star coupler highlighting the design parameters. star couplers are held constant. The numbering of the phased array waveguides begins with the waveguide of the shortest distance, which is the bottommost waveguide, and continues up the figure with increasing length. The separation of the output waveguides on the second star coupler d 0 is held constant in conventional AWG design. In chapter 6, a new design approach for correcting refractive index dispersion effects is proposed which allows d 0 to vary. The modal refractive indices in the phased array and in the star couplers are n p and n s respectively. The focal point x on the image side of the second star coupler is a rotational coordinate and increases in a clockwise fashion. The position of the input waveguide on the first star coupler is denoted as x 1. And lastly, m is a positive integer and represents the grating order. 3.4 AWG Design Focusing and Dispersion Arrayed waveguide gratings multiplex light using interference. Essentially, they are blazed gratings implemented using waveguides and the path length difference is the blaze

40 39 angle used to concentrate the light into a particular order. For constructive interference, the optical path length difference of a mode beginning with a single input waveguide and traversing the two star couplers and two adjacent waveguides in the phased array must equal an integer multiple of the wavelength at the focal position x [20], [24]. n s (λ)(r x 1d p 2R ) + n p(λ)[l + (i 1) L] + n s (λ)(r + xd p 2R ) n s (λ)(r + x 1d p 2R ) n p(λ)[l + i L] n s (λ)(r xd p ) = mλ (3.1) 2R The above expression can be simplified by canceling common terms. n s (λ)x 1 d p R + n p (λ) L n s(λ)xd p R = mλ (3.2) The wavelength that satisfies the condition λ 0 = n p(λ 0 ) L m (3.3) is called the center wavelength and is labeled λ 0. Using this equation and simplifying Eq. 3.1, we get the relation: x 1 = x (3.4) This means that a shift in the position of the input waveguide on the first star coupler will produce the same shift in the transmission spectrum. This result will be used in chapter 7 in the discussion of flattening the pass band of each channel. The AWGs of this thesis consist of a single input waveguide located in the center of the star coupler. Setting x 1 =0 in Eq. 3.2, the focal position of wavelength λ is obtained by solving for x. x(λ) = [mλ n p(λ) L]R n s (λ)d p (3.5) From Eq. 3.5, the central wavelength λ 0 focuses at position x equal to zero which is at the center of the star coupler.

41 40 Focal dispersion in AWGs is defined as the unit change of focal position per unit wavelength. The focal position in geometrical optics is a longitudinal change along the optics axis. In AWGs however, the path length difference L causes the focal length position to shift laterally along x. In designing AWGs, the dispersion of the focal position dx with respect to the wavelength dλ is found by differentiating Eq. 3.5 with respect to λ. x λ dx dλ = LR n g (λ) R (mλ Ln λ 0 d p n s dn 2 p ) dn s s dλ x (λ)( λ) x (λ)( λ) (3.6) in which n g closely resembles the group refractive index of the mode in the phased array. n g (λ) = n p (λ 0 ) λ 0 dn p dλ (3.7) The first two terms in Eq. 3.6 correspond to the first term in the Taylor series expansion, the third and fourth terms correspond to the second and third Taylor series term and so forth. The standard model for designing AWGs is to keep only the first term in the Taylor series and evaluate the expression at the center wavelength λ 0, which sets the second term in Eq. 3.6 equal to zero. These approximations are valid for small bandwidth devices. All of the terms except the first are proportional to λ. For wavelengths near the center wavelength λ 0, the above expressions are small and can be neglected. After these approximations, the equation that remains represents the first order dispersion of the AWG as a function of geometrical parameters. The validity of the approximations made above, including the neglect of higher order Taylor series terms, will be calculated and discussed later in chapter 6. The proper path length difference required to satisfy the interference condition in Eq. 3.1 is obtained by setting the differentials x and λ equal to the output waveguide spacing d 0 and the wavelength channel spacing λ in Eq. 3.6 respectively. L = n sd p d 0 λ 0 n g R λ (3.8)

42 41 For waveguides with strong confinement with little refractive index dispersion, n s n g and Eq. 3.8 can be simplified to the following. L = d pd 0 λ 0 R λ (3.9) Errors in making this approximation can result in the channel spacing λ and the central wavelength λ 0 deviating from their designed values. This approximation was encountered in the commercially available AWG design software package WDM PHASAR and will be discussed further in chapter 5. The free spatial range of the m th and (m+1) th orders for the central wavelength of the AWG device is obtained from Eq. 3.5 as X fsr = x m+1 x m = λ 0R n s d p (3.10) The number of available wavelength channels is found by dividing the free spatial range by the waveguide channel spacing. N chan = X fsr d o = λ 0R n s d p d o (3.11) The free spectral range is of the m th and (m+1) th order is found using the dispersion of the AWG. λ fsr = X fsr dx/dλ = λ 0 m (3.12) which is consistent with standard grating theory when the grating order is defined as m =n g m/n p. In addition to defining the required path length difference L, the design parameters in Eq. 3.8 affect the amount of crosstalk, insertion loss, and uniformity of AWGs. The following paragraphs will illustrate each of these design parameters and how to use them to design an AWG with the correct dispersion and performance.

43 42 InP 2.5 of 3.5 m 1.45 m 0.11 m 0.3 m In 0.85 Ga 0.15 As 0.33 P 0.67 InP Figure 3.4: Shallow ridge waveguide used in AWG fabrication. The eight channel and four channel AWG were fabricated using a waveguide width of 3.5 µm and 2.5 µm respectively with the mode of the 2.5 µm being shown in the figure Waveguide Separation The first parameter to consider in AWG design is the waveguide separations on the star couplers for the phased array and output waveguides. Due to evanescent coupling between adjacent waveguides, the separation needs to be large enough to avoid crosstalk between channels but small enough to avoid excess coupling loss when passing from the star coupler to the phased array. A profile of the waveguide structure with a contour map of the mode superimposed on top is shown in Fig From Fig. 3.4 and Fig. 3.5, the modal field profile extends beyond the physical width of the waveguides. To avoid excessive crosstalk, the exponential decay of the mode outside the physical boundaries of the waveguide requires adjacent waveguides to have a few microns minimum of separation. The crosstalk is calculated via an overlap integral of the modes positioned in adjacent waveguides. Assuming the modes in adjacent

44 43 Figure 3.5: Slad waveguide with the mode superimposed. In shallow ridge waveguides, the exponentially decaying tail extends beyond the physical ridge. waveguides are identical, the overlap integral becomes the autocorrelation. E = η (x)η(x d)dx (3.13) in which η is the normalized mode of adjacent waveguides separated by a distance d. Fig. 3.6 shows a simulation of crosstalk as a function of waveguide separation d. For a theoretical crosstalk of -40 db, a waveguide separation of 5 µm is required Star coupler Length Modeling of the effective modal refractive indices of InGaAsP was done in chapter 2, which leaves the length of the star coupler R as the only parameter left to design. The length of the star coupler affects the uniformity and crosstalk of the device. Channel uniformity is defined as the power difference between the outer channels and the central

45 44 Figure 3.6: The crosstalk as a function of waveguide separation. For a crosstalk level of -40 db, a waveguide separation of 5 µm is required. channel. A schematic representation is displayed in Fig. 3.7, which depicts the channel uniformity, insertion loss, and free spectral range. The far field envelope is a Gaussian profile and can be explained as follows. The modal field entering the first star coupler can be approximated by a Gaussian field. The mode traversing the first star coupler and the phased array remains a Gaussian upon entering the second star coupler. The field on the output plane of the second star coupler is the Fourier transform of the object field. That is, the image field is the summation of the spatial Fourier transform of each of the phased array waveguides. Since the Fourier transform and summation can be switched in a linear system, the image field is the Fourier transform of the summation of the fields emanating from the phased array

46 45 Figure 3.7: Schematic representation of the image field highlighting the insertion loss, uniformity, and free spectral range. waveguides. Since the Gaussian function is a Fourier transform pair with itself, it can be concluded that the far field intensity should also be Gaussian. Using the Gaussian approximation, the far field intensity profile follows ( ) 2θ 2 I(θ) = I 0 exp θ 2 0 (3.14) where θ equals the mode diffraction angle and θ 0 is the angular width of the Gaussian far field amplitude and equals θ 0 = λ n s w (3.15) where w is the width of the waveguide. The uniformity L u or power difference between the center channel and the outside channel is found from Eq ( ) 2θ 2 L u = 10 log max θ 2 0 (3.16) where θ max equals the subtended angle of the outside phased array waveguide. The maximum acceptable uniformity is found by solving Eq for θ max. The minimal

47 46 star coupler length is then found using R = N chand p θ max (3.17) which is approximately 272 µm and 529 µm for the four and eight channel AWGs respectively. The only remaining item left to calculate is the number of waveguides in the phased array. The number of phased array waveguides determines the amount of field truncation at the first star coupler/phased array interface. As stated above, the field truncation is also a source of crosstalk originating from the side lobes produced during the Fourier transform. A representative plot of the response of a single wavelength channel is shown in Fig. 3.8 for an AWG consisting of nine phased array waveguides with a star coupler length of 272 µm. More waveguides would increase the sampling number of the first star coupler s field and suppress the side lobes and lower crosstalk while increasing array transmission. More waveguides, however, require a longer star coupler to maintain the same uniformity and a wider star coupler to make room for the extra waveguides. A longer star coupler increases propagation loss, so a trade off exists in designing the lengths of star couplers. The four and eight channel AWGs consisted of 9 and 21 phased array waveguides which will give a theoretical crosstalk of -20 db. For the same crosstalk and uniformity values, the larger channel AWG requires longer star couplers and more waveguides. The width of the transmission peak is determined by the grating order and the number of waveguides in the phased array. As the channel number increases, the grating order decreases and the FWHM of each channel increases as shown in Fig If the channel width extends into an adjacent channel, an increase in crosstalk will result. The channel width is inversely proportional to the number of phased array waveguides [11]. Therefore, the eight channel AWG requires

48 47 Figure 3.8: A single channel response of an AWG with a star coupler of length 272 µm and nine waveguides with a separation of 5 µm. The side lobes are a result of the truncated field produced by the finite number of phased array waveguides. The AWG will have approximately -20 db of crosstalk. longer star couplers and more phased array waveguides to maintain the same crosstalk and uniformity relative to the four channel AWG. The path length difference L can now be obtained using Eq. 3.8 since all of the parameters are known. L in the four and eight channel AWGs is µm and 4.42 µm which means they will operate in the 22nd and 9th grating order respectively.

49 48 Figure 3.9: Typical phased array layouts used in narrowband AWGs. 3.5 Phased Array Waveguide Layout There are many phased array geometries used in AWG design. The only requirements of the array is to introduce the relative phase difference in each waveguide to satisfy the interference condition and operate using the correct grating order. A phased array geometry should, however, consist of waveguides with a separation large enough to restrict evanescent coupling and should have a minimum total path length to limit the amount of phase errors introduced from fabrication errors. By far the most common geometry in use today is the horseshoe or Ω shaped phased array as shown in Fig From a design aspect, the horseshoe layout is the most simple. Each arm in the phased array has a waveguide with a constant radius and is symmetrical around a vertical center line. This layout has a minimum number of waveguide junctions minimizing loss as well. Another common layout is similar to the horseshoe but has square edges. Both of the layouts above are symmetrical about a vertical center line. On semiconductor, these designs are ideally suited for higher order narrowband AWGs with a free

50 49 Figure 3.10: If a horseshoe geometry is used for AWGs with a free spectral range exceeding 30nm, the waveguides will cross and/or intersect destroying the AWG. spectral range less than 30 nm. These AWGs have a large path length difference L, typically hundreds of wavelengths. Path length difference L and the FSR are inversely proportional to each other. If an AWG has a large FSR, than a small L is required. In broadband AWGs, where the free spectral range can be extremely large, up to 360 nm for CWDM, L is on the order of a few wavelengths. Conventional symmetrical type AWG geometries will not work for broadband AWGs since they cannot produce a small path length difference L without creating a phased array consisting of intersecting or crossing waveguides as shown in Fig S-shape phased array geometries use an antisymmetric design which allows broadband AWGs with an arbitrarily small path length difference L [11]. S-shape AWGs have a phased array consisting of three sections which are shown in the schematic of Fig Sections I and III, consist of two straight waveguides on each side of a curved waveguide

51 50 section. The purpose of the straight waveguides adjacent to the star couplers is to separate out the waveguides and prevent evanescent coupling within the array. The path length difference L is generated in section II. It consists of a series of concentric arcs, which all subtend the same angle but have different radii of curvature. The generated path length difference is L = θ R (3.18) in which θ is the subtended angle and R is the difference in radius of curvature of two adjacent waveguides. Sections I and III are designed such that the differential phase accrued between waveguides in section I is exactly canceled in section III. Therefore, the net relative phase from each waveguide exiting the phased array is generated entirely in section II. The optical path length within an S-shape geometry is typically longer than the path length of a horseshoe layout which renders them slightly more sensitive to fabrication errors. This is evident in the fact that sections I and III in Fig. 3.2 are a flipped version of the horseshoe style AWG. The overall length of the phased array in an S-shape AWG is longer than a horseshoe AWG by the amount contained in section II which is the path length difference. 3.6 Waveguide Profile Deep ridge waveguides have been the focus recently in AWG design. Deep ridge structures support highly confined modes which enable small bend radii of 100µm or less. AWGs utilizing deep ridge waveguides have been fabricated with a total device footprint of 2 mm x 2 mm. The high confinement, however, results in a higher insertion loss compared to waveguides having less confinement. The mode from a fiber is much larger than a deep ridge single mode waveguide and suffers high coupling loss. Less light

52 51 Figure 3.11: Excess transmission loss in deep ridge waveguides due to the waveguide separation d p. is also coupled from the star coupler to the phased array. The excess coupling loss into the phased array for deep ridge waveguides was calculated in [15]. The loss is minimized by positioning the separation of the phased array waveguides in very close proximity requiring very high photolithographic resolution. Extremely smooth processing is also required because of high modal contact with etched surfaces. Fig shows that even when the waveguides are very close to each other, the AWG still suffers high loss. AWGs fabricated using shallow ridge waveguides have several advantages over deep ridge waveguides. They suffer less loss and ease photolithographic and processing requirements. Shallow ridge waveguides support modes which are larger than the physical boundaries of the waveguide (3.4) and better match a fiber mode reducing insertion loss. Photolithography tolerances are relaxed since the waveguide spacing d p is much larger.

53 52 Modal contact with etched surfaces is also reduced as seen in Fig. 3.4, which lowers propagation losses and the overall sensitivity to processing errors. 3.7 Bend Loss Before calculating the bend loss, it is instructive to discuss the methods used in the calculation. Two methods were used and checked against each other for consistency. The first method involved a commercial software package titled BeamProp by RSoft. Beam propagation methods typically apply the paraxial approximation to the wave equation for easier simulation of the wave equation, which limits how small of an angle or radius a waveguide can have to retain simulation accuracy. BeamProp contains a built-in wideangle package which can calculate bend loss with a small radius of curvature. BeamProp determines the optical power in a waveguide by calculating the overlap integral of the propagating mode with the waveguide eigenmode as it propagates down the waveguide. For this example, the power would be found by calculating the correlation of the propagating mode and the curved waveguide eigenmode. The bend loss is the correlation rate of decay. The results were then verified with an analytic approach. When a mode enters a curved section of a waveguide, the mode center shifts laterally to the outside of the waveguide as discussed in the previous paragraph. Using a perturbation approach [21], bend loss is calculated by using the unperturbed mode in the perturbed or curved waveguide. In this model, the unperturbed mode is assumed to stay in the middle of the waveguide as it enters the curve as shown in Fig As the mode propagates around the bend, the phase front velocity is small near the center of the waveguide and increases with radius. At a certain radius, the velocity of the exponentially decaying tail of the mode must travel faster than the speed of light in the material to keep up with the rest of the mode. Since this is unphysical, the mode must radiate away in the form of bend loss. The problem then is to calculate in terms of

54 53 Figure 3.12: Using a first order perturbation approach, bend loss is the radiation which must travel faster than light to keep up with the mode around a bend. d p. the bend loss α, how much of the mode exists past the critical distance of being physical. α x η 2 dx (3.19) in which η is the normalized eigenmode of the waveguide. The integral was evaluated and simplified in [21] to the following. α = γ2 x e k γx 3 k 2 2 r (3.20) In shallow ridge waveguides, the confinement is strongly dependent on the thickness t, as displayed in Fig. 3.4, of the thin InP layer directly above of the InGaAsP layer. Bend loss as a function of layer thickness t was simulated using the perturbation approach for the waveguide design pictured in Fig. 3.4 with the width w equal to 2.5 µm and 3.5 µm. The radius of curvature of the waveguide used in the calculation is 1000 m which coincides with the smallest radius of any segment used in the AWG designs.

55 54 Figure 3.13: The bend loss in a shallow ridge waveguide quickly increases as the thickness of the thin InGaAsP layer is increased beyond 0.2 µm. d p. Fig demonstrates how bend loss quickly increases for a waveguide as the thickness t of the layer is increased beyond 0.25 µm for a width of 2.5 µm and 3.5 µm. This is due to the decreasing lateral confinement of the mode as the layer thickness increases. In waveguides, the confinement increases with width, which is why narrower waveguides have higher bend loss. Etching to within 0.2 µm of the InGaAsP layer was necessary to create a strong enough confinement so that bend loss would remain small in the curved waveguides of the AWG. A shallow ridge was etched 1.45 µm high resulting in a layer thickness t equal to 0.11 µm. A depth greater than 0.2 µm was used to ensure negligible bend loss in the AWGs.

56 55 Figure 3.14: Bend loss as a function of radius for waveguides of different widths. The concern in designing small AWGs is the increasing amount of bend loss that exists as the radius decreases. This is especially apparent in shallow ridge waveguides where the lateral confinement is small. The bend loss as a function of radius is displayed in Fig for the fundamental mode and the second order mode. The maximum bend radius used in the AWG design was 1000 µm to minimize bend loss for both waveguide widths. Conventional AWG design uses single mode waveguides because higher order modes have different effective indices which causes modal dispersion in the phased array waveguides. Modal dispersion can lead to increased crosstalk due to ghost images appearing in the transmission spectrum caused from the higher order modes. A ghost image is the single mode transmission spectrum replicated but slightly shifted in wavelength. It will be shown in chapter 7, that the AWGs of this thesis are

57 56 modal dispersion insensitive and that wider waveguide widths can be used to decrease insertion loss throughout the device.

58 Final AWG Designs The final AWG design parameters are located in Table 3.1. number of channels 4 8 channel spacing 20 nm 20 nm center wavelength λ nm 1550 nm number of phased array waveguides 9 21 L µm 4.42 µm FPR Length (R) 227 µm 529 µm waveguide separation (d p and d o ) 5 µm 5 µm FWHM 11 nm 11 nm minimum bend radius 1000 µm 1000 µm maximum crosstalk -20 db -20 db non-uniformity 2 db 2 db Table 3.1: Final AWG design parameters 5. The differences between the designed and the measured values are discussed in chapter 3.9 Thermal and Polarization Dependence Broadband interference filters are less susceptible to temperature and polarization due to their inherent wide pass band of each channel. As the grating order within a filter increases, the channel width decreases as shown in Fig DWDM networks consist of filters which operate with a grating order of around 100. CWDM networks are much lower and operate with grating orders less than ten.

59 58 Figure 3.15: The channel pass band width increases as grating order and channel separation decreases. The grating orders 10, 19, and 193 correspond to AWGs designed with channel spacings of 1 nm, 10 nm, and 20 nm Thermal Dependence When the temperature of an AWG is increased, the optical path difference between waveguides in the phased array is also increased. This has the effect of introducing a red shift into the AWG transmission spectrum. The optical path length difference n p L is dependent on the physical path length difference L and the refractive index in the phased array n p. The thermo-optic effect of the refractive index dn p /dt and thermal expansion of materials with varying temperature d L/dT causes the optical path length difference to vary with temperature. The temperature dependence of the star couplers

60 59 can be ignored since the typical length of the phased array is much greater than that of the star couplers. The temperature dependence is found by starting with Eqn. 3.3 and taking the derivative with respect to temperature. m dλ 0 dt = n d L a dt + Ldn a dt (3.21) The temperature dependence of the refractive index and linear expansion are and respectively. The thermal expansion is more than an order of magnitude less than the thermo-optic effect and can be ignored. Dividing through by lambda 0 and using Eq. 3.3, the above equation becomes dλ 0 dt = λ 0 dn a n a dt (3.22) Temperature insensitive AWGs have been fabricated on InP canceling out the effects of the thermo-optic effect. In this study, the phased array waveguides were divided into two sections each consisting of buried waveguides whose thermo-optic effect differs in magnitude. The basic principle behind their design is as the temperature begins to rise, the optical path length increase for one material will be compensated for by the second material such that the overall path length difference L will not change. The temperature dependent wavelength shift of the AWG transmission spectrum was reduced from 1 Å/degC to 0.1 Å/degC. This is an important result because AWGs no longer required a thermoelectric cooler for temperature stability. The other components, including the source laser, still requires temperature stabilization however. An alternative solution to prevent channel hopping, increasing the performance of AWGs, and lowering overall network cost is to increase the bandwidths of each channel such that the natural thermal laser wavelength variation will still fall within the pass band of a single AWG channel. As the grating order or path length difference is decreased, the spectral width of the channel pass bands in the AWG is increased. This can

61 60 be explained as follows: the output waveguides transmit the wavelengths whose mode has an overlap with the output waveguide mode. As the focal dispersion increases, more wavelengths will focus in the near vicinity of the output waveguide. Since broadband AWGs have a very large focal position dispersion, the wavelength pass band is also large. Eq reveals that the thermal spectral shift is grating order and path length difference independent. This means that AWGs of all grating orders and path length differences, given a material, will shift the same amount with temperature. It can be concluded that broadband AWGs are ideal for networks where lower cost networks are desired and thermal variation produces a wavelength shift of no more than 6 nm Polarization Dependence There is a need to control polarization in DWDM networks for the same reason that temperature is controlled. The transverse electric (TE) and transverse magnetic (TM) fields have different refractive index. The different refractive indices cause the two modes to see different optical path lengths in the phased array waveguides. Similar to temperature, this results in a spectral red shift in the transmission spectra between the TE and TM modes which introduces a polarization dependent loss (PDL) in the device. If the shift is large, then channel hopping and/or increase in crosstalk are also possible. This is a major concern for high density networks. The polarization dependence of AWGs is found by taking the derivative of Eq. 3.3 with respect to wavelength and allowing the refractive index to be wavelength dependent. Using Eq. 3.3 again, the equation can be simplified to dλ 0 = L m dn a (3.23) dλ 0 λ 0 = n T E n T M n T E (3.24)

62 61 The center wavelength shift is proportional to the birefringence in the refractive index of the TE and TM modes. The above equation is independent of the grating order m and the path length difference L. This means that AWGs of all grating orders and path length differences experience the same wavelength shift due to birefringence of the TE and TM modes. The TE spectrum is red shifted relative to the TM spectrum since the TE mode has a higher effective index. In conventional AWG design, the refractive index is assumed to be a constant. Over a large wavelength band, the refractive indices of the TE and TM mode changes considerably. It will be shown in Chapter 6, this error is a cause of excess transmission loss.

63 62 CHAPTER 4 PHOTOLITHOGRAPHY AND SEMICONDUCTOR PROCESSING AWG design is based on a very specific refractive index distribution derived from the waveguide profile. If the waveguide profile differs after fabrication from the intended design, the refractive indices n s and n p will be different from design and can have detrimental effects on the transmission spectrum and/or channel spacing. With this in mind, the requirements of processing are very specific to accurately model a waveguide profile. It is much easier to simulate waveguides with straight vertical walls, so a process which gives vertical walls is desired. The performance of AWGs is directly related to the quality of the processing for multiple reasons. For example, poor photolithography and/or processing can lead to decreased crosstalk and higher insertion loss. This chapter will discuss the processing and fabrication of waveguides and AWGs. 4.1 Preliminary Tests There are several different methods of etching semiconductor waveguides. Argon ion beam etching, wet chemical etching, and reactive ion etching were three different processing techniques investigated in this study. Reactive ion etching was chosen in the end for reasons that will be discussed in the next few paragraphs.

64 63 Figure 4.1: Wet chemical etching will produce waveguides with oscillating overcut and undercut in curved waveguides due to the lattice orientation dependence Wet Chemical Etching Wet chemical etching is a well known technique in etching semiconductor waveguides. Typical etchants for InP include several acids like HCl, H 2 SO 4, HBr, and CH 3 COOH (otherwise known as acetic acid). Wet chemical etching is purely a chemical etch and produces smooth sidewalls and etched surfaces and causes little or no damage or defects to the surface lattice. Plain photoresist is typically used as a mask, which eases overall fabrication. The basic procedure for chemical etching starts with determining the etching solution which gives the desired etching. The chemicals are mixed together in a glass beaker, and the semiconductor wafer is placed in the mixture. Etch rates are typically 50 nm/min [25]. Once the etching is completed, the sample is quickly washed off with water. Fig. 4.1 shows some results from wet etching using HCl:H 3 PO 4 :H 2 O 2.

65 64 Figure 4.2: Wet chemical etching will produce waveguides with oscillating overcut and undercut in curved waveguides due to the lattice orientation dependence. The ridge suffers from severe undercut which is inherent to wet etching. Wet etching is an isotropic etch, which means that etching is independent of direction. In an isotropic etch, the chemicals will approximately etch as far in (under the photoresist mask) as down. Since two sides of the waveguide are being exposed to chemicals simultaneously, the etch will cut roughly 1.5 µm in on each side, if the waveguide is 1.5 µm high. If the waveguide width is less than two times the height, etch profiles similar to Fig. 4.1 will result. Wet chemical etching is also lattice orientation specific. If the device of interest consists of straight waveguides, this would not be an issue. But, for all AWGs which consist of a star coupler, as opposed to an MMI coupler, have waveguides which are bent. Depending on the lattice orientation and the chemical etchant being used, the etched waveguides will suffer from an oscillating overcut and undercut along the curve. A schematic of overcut and undercut waveguides are displayed in Fig The changing waveguide profile will cause some dispersion in the array which will affect the interference condition and increase crosstalk levels. With such severe undercut and a changing waveguide profile, it was concluded that wet chemical etching was not usable in fabrication of AWGs on InP.

66 65 Figure 4.3: With argon ion etching, walls had a shallow etch angle and were extremely rough. A trench was also observed in the etch profile. All of these characteristics are highly undesirable for AWGs Argon Ion Beam Etching Argon ion beam etching, also known as argon ion milling, is a purely physical etch. Argon ions blast the semiconductor and physically break off a piece of the surface not protected by a mask, in which photoresist is suitable. Etch rates are typically 45 nm/sec and is controlled by the acceleration voltage of the ions [26]. Argon etching is anisotropic which means that etching is directional. Results of etched InP waveguides using argon ion beam are displayed in Fig The walls are more vertical than wet etching but are still unacceptable. The etch angle, shown in Fig. 4.2, can be controlled by varying the angle of incidence of the argon ion beam. This, however, causes the leeward side of the ridge waveguide to not get etched, called shadowing. The etched surfaces are also very rough. A trench formed at the base of the waveguide ridge giving a difficult index

67 66 Figure 4.4: Vertical wall and smooth surfaces with high aspect ratios are possible with reactive ion etching. distribution to derive. Rough surfaces, trenches, and angled sidewalls all rendered argon ion etching un-useable Reactive Ion Etching Reactive ion etching is a cross between argon ion etching and wet chemical etching in that it is both a physical etch and a chemical etch. Reactive ion etching is an anisotropic etch and has the ability to produce vertical sidewalls and smooth surfaces. The quality of etch is extremely dependent on the recipe and varies from machine to machine. In other words, the optimum recipe derived for one RIE machine will be different for another RIE, but they are a good starting point. Some preliminary results, shown in Fig.??,revealed smooth structures with a vertical walls and a high aspect ratio. For these reasons, RIE was the only investigated approach possible for fabricating AWGs.

68 Photolithography With reactive ion etching, it was determined that photoresist was not suitable to be used as a mask, even after a 30 minute hardening post-bake. Spurs developed which extended beyond the ridge and prevented further etching under the spurs. These areas had extremely rough sidewalls. An SiO 2 mask was used instead which increases processing, photolithography and AWG design but required for reasons mentioned above. A 300 nm layer of SiO 2 was deposited on the InP wafer using an electron beam evaporator. A few different layer thickness were investigated but found that 300 nm was the minimum layer thickness that did not lift off of the InP wafer during the buffered oxide etching. The thickness of the SiO 2 layer was measured using the crystal oscillator inside the electron beam evaporator and verified with a surface profilometer. The wafer was then cleaned in acetone followed by isopropanol and rinsed with D.I. water. The excess water was blown off by compressed N 2 and dried in an oven at 100 degc for five minutes. To aid in photoresist adhesion to the SiO 2 surface, the wafer was further cleaned in a plasma asher for 3 minutes immediately before spinning an adhesion promoter onto the wafer. The plasma asher is a modified microwave oven which cleans the interior with an oxygen plasma under vacuum. The vacuum in addition to the plasma help in further drying the SiO 2 surface. The photoresist consistently separated from the SiO 2 during developing, if the plasma asher and adhesion promotor were not used. Shipley 1813 photoresist was spin coated at 5000 RPM for one minute which resulted in a 1.5 µm thick layer and then soft baked at 110 degc for two minutes. The photoresist was patterned using UV light with an irradiance of 276 mw/cm 2 for 10 seconds. AZ 352 for approximately 45 seconds was used for developing. The patterned photoresist was then hard baked at 110 degc for five minutes. The photoresist pattern was transferred to SiO 2 using HF acid buffered with NH 4 (ammonia) in a 7:1 ratio for seven seconds. Buffering the HF acid slows down the etch rate. Buffered oxide etching is an isotropic wet chemical etch. Since the SiO 2

69 68 layer is 300 nm thick, 600 nm of undercutting was expected. The patterned wafer was cleaned in acetone, isopropanol, and D.I. water to remove any loose SiO 2 residue left on the surface. Fig. 4.5 is a process flow of the photolithography and buffered oxide etching. 4.3 Reactive Ion etching There are two common methods for the reactive ion etching of InP. Early studies into RIE of InP mostly included chlorine containing gas mixtures (Cl 2, BCl 3, CCl 4, and CCl 2 F 2 )[27],[28]. Fast etch rates and a smooth morphology are possible but require processing temperatures exceeding 150degC, which requires a heater to be located inside the etching chamber. Gas mixtures containing methane and hydrogen also produce smooth surfaces and processing is done at room temperatures. The waveguide ridge was fabricated using a dual Oxford Plasmalab 100 Reactive Ion Etcher (RIE) and Electron Cyclotron Resonance (ECR) unit. The next few paragraphs outline the basic operation of RIE and ECR and how they etch InP. The wafer to be etched is typically placed on an electrode plate with the opposite cathode directly above. The desired gases are injected into the etch chamber, under vacuum, where the atoms are subjected to an RF field and form a plasma of ionized gas. The voltage is applied across the plates where the ions feel the Lorentz force F = qe and are accelerated towards the lower cathode and etch the wafer both chemically and physically. A higher acceleration voltage increases the etch rate by increasing the amount of physical etching. As discussed above, physical etching leads to higher surface damage and rougher sidewalls. The ECR unit in the Plasmalab 100 adds an additional microwave source and current coil inside the chamber above the region where the RIE exists. The microwave source is tuned to the electron resonance frequency (2.45 GHz) which aids in creating a higher density of ions in the plasma. The current in the coil applies a Lorentz

70 Figure 4.5: Schematic representation of the process flow used in the fabrication of ridge waveguides. 69

71 70 force F = q( v B) which directs the plasma towards the wafer to assist in etching. The microwave forward power, and current coil were set at the values specified by the clean room technician of 500 W, and 16.4 Amps respectively. The RF power was determined by allowing it to vary between values of 75 to 150 W and measuring the surface roughness after a sample wafer was etched. The RF power which gave the smoothest surface, as measured with an optical profiler, was 150 W. In the case of InP, a combination of methane and hydrogen is used for etching [29]. As the gas is injected into the chamber, the RF field and/or microwave field form CH 3 and H + ions [30]. The chemical etch originates from the CH 3 ions reacting with the InP surface and forming (CH 3 )In x compounds. The H + ions created in the plasma are responsible for the sputtering or physical etch. It also preferentially reacts with phosphorous forming phosphine PH 3 which increases surface roughness. If the concentration of methane in the chamber is too high, a layer of organic debris forms on the surface of the wafer and gives localized areas of decreased etching and increasing surface roughness. Sidewall roughness is increased also if the organic material forms over the edge of the ridge inhibiting etching in its shadow. If the organic layer is too thick, etching is inhibited entirely. Sputtering by the H + ions is essential because it reduces the amount of organic build-up and enables continuous etching. Therefore, the proper concentrations of methane and hydrogen in the recipe is crucial for smooth surface morphologies. The proper gas flow rates were determined from the starting point suggested by [30] (10 sccm, cubic centimeter per second of CH 4 and 20 sccm of H 2 ) and allowed to vary while monitoring the surface roughness using an optical surface profilometer and visibly using an SEM. The recipe which gave the surface with the least amount of roughness was 10 sccm and 20 sccm of CH 4 and H 2 respectively. Waveguides of width 2.5 µm were fabricated from waveguides on the mask which were 3.5 µm wide. The one micron undercut is attributed mainly to the isotropic buffered HF

72 71 etching. Reactive ion etching is expected to have minimal undercutting. The potential for undercutting was accounted for by designing many AWGs with varying waveguide widths. AWGs of width 2.5 µm, 3.5 µm, 4.5 µm, and 5.5 µm were designed on the mask. Preparation of the etch chamber was crucial for a repeatable process. Previous users of the RIE leave residue on the chamber walls which can greatly alter the etching result. Before each run, the chamber was cleaned with oxygen plasma for two hours to ensure the chamber was rid of any gases or residue. This also helps in drying the chamber to help in achieving a good vacuum. The etching process was then run for 20 minutes, without the wafer, in a CH 4 /H 2 atmosphere to condition the walls of the chamber [31]. The ridges were etched in a CH 4 (10 sccm)/h 2 (20 sccm) atmosphere at a pressure of 60 mbar and had an average etch rate of 0.7 nm/s. Upon completion of the etching, the remaining SiO 2 was measured at 200 nm thick. The selectivity of InP to SiO 2 during RIE etching was greater than 15 to 1. The sample was then washed in straight HF acid to clean off the remaining silicon dioxide mask. An image of a sample waveguide taken with a high resolution scanning electron microscope is displayed in Fig The waveguide width is smaller than the waveguides utilized in the AWGs because a picture of a waveguide was desired that came from the same wafer as one of the tested AWGs; the waveguide most resembling one of the AWGs was used. As can be seen in the figure, the etched surfaces appear rougher than previous studies have achieved. The surface roughness was measured using an atomic force microscope. The image is shown in Fig The root mean square (rms) surface roughness was 8.5 nm Previous studies have achieved a surface roughness less than 2 nm rms, which is a factor of four or more less. 1 As discussed in chapter 3, rougher surfaces are tolerated with shallow ridge waveguides due to smaller modal contact with etched surfaces. 1 The RIE machine used in the fabrication had a leak inside the main chamber which caused contamination and limited the etch quality.

73 Figure 4.6: A scanning electron microscope image taken of a sample waveguide. 72

74 Figure 4.7: An atomic force microscope image of the etched surfaces of a waveguide. The rms surface roughness is less than 9 nm. 73