Modification of the Optical Performance of Fiber Bragg Gratings Using Femtosecond Laser Micromachining

Similar documents
CHIRPED FIBER BRAGG GRATING (CFBG) BY ETCHING TECHNIQUE FOR SIMULTANEOUS TEMPERATURE AND REFRACTIVE INDEX SENSING

Mode selective fiber Bragg gratings

Optical RI sensor based on an in-fiber Bragg grating. Fabry-Perot cavity embedded with a micro-channel

Femtosecond fiber laser direct writing of optical waveguide in glasses

Femtosecond laser microfabrication in. Prof. Dr. Cleber R. Mendonca

Title: Laser marking with graded contrast micro crack inside transparent material using UV ns pulse

Femtosecond Pulsed Laser Direct Writing System for Photomask Fabrication

Spectral Characteristics of Mechanically Induced of Ultralong Period Fiber Gratings (UPFG) as a Pressure Sensor.

Structural Modification in Borosilicate Glass by Use of Femtosecond Fiber Laser at 1.56 µm

Bragg and fiber gratings. Mikko Saarinen

Optical signal processing for fiber Bragg grating based wear sensors

Realization of Polarization-Insensitive Optical Polymer Waveguide Devices

Review Article Induced Bragg Gratings in Optical Fibers and Waveguides Using an Ultrafast Infrared Laser and a Phase Mask

An Optical Characteristic Testing System for the Infrared Fiber in a Transmission Bandwidth 9-11μm

High-speed Fabrication of Micro-channels using Line-based Laser Induced Plasma Micromachining (L-LIPMM)

3550 Aberdeen Ave SE, Kirtland AFB, NM 87117, USA ABSTRACT 1. INTRODUCTION

Romania and High Power Lasers Towards Extreme Light Infrastructure in Romania

High Power Femtosecond Fiber Chirped Pulse Amplification System for High Speed Micromachining

Optically switched erbium fibre laser using a tunable fibre-bragg grating

The absorption of the light may be intrinsic or extrinsic

Electronically switchable Bragg gratings provide versatility

Wavelength Division Multiplexing of a Fibre Bragg Grating Sensor using Transmit-Reflect Detection System

Effects of spherical aberrations on micro welding of glass using ultra short laser pulses

Optimization of Uniform Fiber Bragg Grating Reflection Spectra for Maximum Reflectivity and Narrow Bandwidth

Simultaneous measurement of two different-color ultrashort pulses on a single shot

Lasers à fibres ns et ps de forte puissance. Francois SALIN EOLITE systems

Examination Optoelectronic Communication Technology. April 11, Name: Student ID number: OCT1 1: OCT 2: OCT 3: OCT 4: Total: Grade:

Bragg gratings in multimode optical fibres and their applications

High Power and Energy Femtosecond Lasers

High-Power Femtosecond Lasers

Fabrication of microstructures on photosensitive glass using a femtosecond laser process and chemical etching

Laser Speckle Reducer LSR-3000 Series

Stable dual-wavelength oscillation of an erbium-doped fiber ring laser at room temperature

Optical fiber Fabry-Perot interferometer cavity fabricated by femtosecond laser micromachining and fusion splicing for refractive index sensing

Fiber lasers and their advanced optical technologies of Fujikura

Copyright 2000 by the Society of Photo-Optical Instrumentation Engineers.

New Lasers Improve Glass Cutting Methods

Femtosecond Laser Direct Writing of Optical Waveguides in Silicone Film

Fiber-optic Michelson Interferometer Sensor Fabricated by Femtosecond Lasers

Spectral Characteristics of Uniform Fiber Bragg Grating With Different Grating Length and Refractive Index Variation

Ultra-short distributed Bragg reflector fiber laser for sensing applications

Fiber Laser Chirped Pulse Amplifier

Continuum White Light Generation. WhiteLase: High Power Ultrabroadband

Novel fiber Bragg grating fabrication system for long gratings with independent apodization and with local phase and wavelength control

Fabrication and Characterization of Photonic Devices Directly Written in Glass Using Femtosecond Laser Pulses

Rogério Nogueira Instituto de Telecomunicações Pólo de Aveiro Departamento de Física Universidade de Aveiro

JLMN-Journal of Laser Micro/Nanoengineering Vol. 12, No. 2, Akinao Nakamura 1, Masaaki Sakakura 1,2, Yasuhiko Shimotsuma 1, Kiyotaka Miura 1

Single frequency MOPA system with near diffraction limited beam


Lithography. 3 rd. lecture: introduction. Prof. Yosi Shacham-Diamand. Fall 2004

Structured Fiber Bragg Gratings for Sensing Applications

High Energy-High Repetition Rate Fiber Laser System for Precision Micromachining with Fundamental and Second Harmonic Wavelengths

Dicing of Thin Silicon Wafers with Ultra-Short Pulsed Lasers in the Range from 200 fs up to 10 ps

Single-photon excitation of morphology dependent resonance

Shaping ultrafast laser inscribed optical waveguides using a deformable mirror

Photonic Generation of Millimeter-Wave Signals With Tunable Phase Shift

Automated Photosensitivity Enhancement in Optical Fiber Tapers

Vertical External Cavity Surface Emitting Laser

Micron and sub-micron gratings on glass by UV laser ablation

Spectral Analysis of the LUND/DMI Earthshine Telescope and Filters

Section 2: Lithography. Jaeger Chapter 2. EE143 Ali Javey Slide 5-1

True Three-Dimensional Interconnections

Sensitivity enhancement of Faraday effect based heterodyning fiber laser magnetic field sensor by lowering linear birefringence

MULTI-STAGE YTTERBIUM FIBER-AMPLIFIER SEEDED BY A GAIN-SWITCHED LASER DIODE

Supplementary Figure 1. GO thin film thickness characterization. The thickness of the prepared GO thin

FemtoFAB. Femtosecond laser micromachining system. tel fax Konstitucijos ave. 23C LT Vilnius, Lithuania

Characterization of Chirped volume bragg grating (CVBG)

SUPPRESSION OF THE CLADDING MODE INTERFERENCE IN CASCADED LONG PERIOD FIBER GRATINGS WITH LIQUID CRYSTAL CLADDINGS

Beam Shaping in High-Power Laser Systems with Using Refractive Beam Shapers

Optical Fiber Technology. Photonic Network By Dr. M H Zaidi

A novel tunable diode laser using volume holographic gratings

HIGH POWER LASERS FOR 3 RD GENERATION GRAVITATIONAL WAVE DETECTORS

A CW seeded femtosecond optical parametric amplifier

Laser Induced Damage Threshold of Optical Coatings

Optical Fiber Devices and Their Applications

Simultaneous measurement of temperature and strain by three-section phase-shift long period fiber grating

Fang-Wen Sheu *, Yi-Syuan Lu Department of Electrophysics, National Chiayi University, Chiayi 60004, Taiwan ABSTRACT

Quantum-Well Semiconductor Saturable Absorber Mirror

Pulse Shaping Application Note

Optical waveguides in crystalline dielectric materials produced by femtosecond-laser micromachining

Analysis of Self Phase Modulation Fiber nonlinearity in Optical Transmission System with Dispersion

Multi-wavelength laser generation with Bismuthbased Erbium-doped fiber

On-chip interrogation of a silicon-on-insulator microring resonator based ethanol vapor sensor with an arrayed waveguide grating (AWG) spectrometer

Dr. Rüdiger Paschotta RP Photonics Consulting GmbH. Competence Area: Fiber Devices

X-CAN. A coherent amplification network of femtosecond fiber amplifiers

Basic concepts. Optical Sources (b) Optical Sources (a) Requirements for light sources (b) Requirements for light sources (a)

Waveguiding in PMMA photonic crystals

High-Energy 6.2-fs Pulses for Attosecond Pulse Generation

LOS 1 LASER OPTICS SET

DESIGN AND CHARACTERIZATION OF HIGH PERFORMANCE C AND L BAND ERBIUM DOPED FIBER AMPLIFIERS (C,L-EDFAs)

FABRICATION AND SENSING CHARACTERISTICS OF THE CHEMICAL COMPOSITION GRATING SENSOR AT HIGH TEMPERATURES

Lecture 7. Lithography and Pattern Transfer. Reading: Chapter 7

Wavelength Tunable Random Laser E.Tikhonov 1, Vasil P.Yashchuk 2, O.Prygodjuk 2, V.Bezrodny 1

Synthesis of projection lithography for low k1 via interferometry

Lecture 22 Optical MEMS (4)

High peak power pulsed single-mode linearly polarized LMA fiber amplifier and Q-switch laser

Infrared broadband 50%-50% beam splitters for s- polarized light

Ultrafast Lasers with Radial and Azimuthal Polarizations for Highefficiency. Applications

sensors ISSN

Theoretical Approach. Why do we need ultra short technology?? INTRODUCTION:

Transcription:

Modification of the Optical Performance of Fiber Bragg Gratings Using Femtosecond Laser Micromachining Hamidreza Alemohammad *, Ehsan Toyserkani * * Rapid Prototyping Laboratory, Department of Mechanical and Mechatronics Engineering University of Waterloo, 2 University Ave. West, Waterloo, Ontario, Canada N2L 3G1 E-mail: shalemoh@uwaterloo.ca This paper describes the use of femtosecond laser pulses to selectively modify the optical performance of as-fabricated fiber Bragg gratings (FBG) written in single mode optical fibers. As a result of the irradiation of FBGs by femtosecond laser pulses generated from a Ti:Sapphire amplifier, the resonance Bragg wavelength is changed, or split into two separate individual wavelengths. In addition, the bandwidth of the reflection peak is increased. Further analyses show that a change of 6.9 1-4 in the refractive index is achieved in a single pass of the laser beam. Periodic microgrooves are also inscribed along the fiber using femtosecond pulses. In addition to the optical performance, the sensing performance of the FBGs is increased by inscription of periodic microgrooves in the cladding of the fiber. The micromachined fibers are used for simultaneous measurement of temperature and concentration of liquids. Keywords: Femtosecond laser micromachining, fiber Bragg grating, optical performance, simultaneous measurement of temperature and concentration 1. Introduction Fiber Bragg gratings (FBG), which are submicron periodic modulations of the index of refraction in optical fibers, are widely used in sensing and communication industries. Fiber Bragg gratings are usually inscribed in single mode optical fibers using Ultra Violet (UV) radiation using masks [1]. The gratings can be customized by changing the masks which is a time consuming and expensive process. With the advancements in the femtosecond laser micromachining of transparent materials, e.g., glass, the performance of the as-fabricated FBGs can be selectively modified. The interaction of femtosecond laser pulses with dielectric materials, such as glass, has been a research topic during the past years [2-5]. The optical fiber is made of silica, which is transparent to visible and near-infrared (NIR) spectra of electromagnetic radiation. However, ultrashort laser pulses, i.e., tenth of picoseconds or femtosecond, at 8 nm enable both bulk modification and surface micromachining of silica. Surface material ablation of silica, associated with femtosecond laser radiation involves some fundamental processes. When the material surface is irradiated by a laser pulse, the electrons in the conduction band are excited through multiphoton ionization. The density of the electrons increases through avalanche ionization until the frequency of the formed plasma reaches the frequency of the laser radiation. The high density plasma is strongly absorbent to the laser energy. This energy is transferred from the plasma to the lattice after the laser pulse is gone. This transfer of energy occurs in a time scale much smaller than the thermal diffusion time, and can result in material ablation [2,5,6]. In addition to surface micromachining, structural modifications like change in the refractive index and stress induction can be accomplished due to nonlinear phenomena such as photoionization that occur during the interaction of femtosecond laser pulses with silica [7-9]. Also, femtosecond lasers have been used for the induction of birefringence in optical fibers by exposing the cladding to the laser radiation [1] and for direct writing of Bragg gratings in the core of optical fibers for sensing and fiber laser applications [11-14]. The fabrication of intracore Bragg gratings by the lateral illumination of the optical fibers using phase mask scanning technique is presented in [13]; to enhance the sensing performance of FBGs, a femtosecond laser was used for the inscription of high-temperature stable Bragg gratings in polarization maintaining (PM) fibers. The photo-enhanced birefringence caused by the femtosecond pulses resulted in FBG sensors with dual-parameter sensing capability in a wide range [14]. Bragg gratings have also been inscribed in the core of the Yb-doped fibers used in fiber lasers [15]. With the great potentials of femtosecond laser pulses in micromachining of silica, they can be effectively incorporated for customizing as-fabricated FBGs. In this paper, we report the use of femtosecond laser pulses to selectively modify the performance of as-fabricated FBGs. In the experiments, an as-fabricated FBG is radiated by femtosecond laser pulses moving in a specified path relative to the fiber. The reflectivity spectra obtained after laser processing show that the femtosecond laser radiation can effectively modify the reflectivity characteristics of the FBGs. Shift in the Bragg wavelength, splitting the single FBG peak into two individual peaks, and a change in the bandwidth of the Bragg reflection are obtained. In addition, the sensitivity of the FBGs for simultaneous measurement of temperature and concentration of liquids is increased as a result of the inscription of periodic micro-grooves in the cladding of the fiber. 61

2. FBG Theory In FBGs, the coupling between the forward and backward propagating modes results in a resonance condition. The resonance condition occurs at the Bragg wavelength ( λ B ) which is a function of the effective mode index of refraction ( n ) and the grating pitch ( Λ eff ), as follows [16]: λ B = 2neffΛ (1) Any permanent change in the indices of refraction of the core or cladding of optical fiber, induced by external sources such as femtosecond laser radiation, can modify n eff and the spectral response. 3. Experimental Setup Fig. 1(a) shows a schematic diagram of the femtosecond laser setup and the position of the optical fiber relative to the laser beam. The FBGs were installed on a high precision 3-dimentional motion system manufactured by Aerotech Inc., and were moved across the laser beam to inscribe periodic grooves along the fiber. An NIR integrated, diodepumped, ultrafast Ti:Sapphire regenerative amplifier (Libra) manufactured by Coherent Inc. was used for the experiments. The laser produced light of 8 nm wavelength in 1 fs pulses with a repetition rate of 1 khz. The maximum pulse energy was 1 mj which was attenuated to 2-4 μj for the experiments. A 15 lens (NA=.28) was used to focus the beam to the processing zone. The laser spot diameter was ~8 μm, and the depth of focus (DOF) was ~21 μm. The beam focal point parameters are small relative to the cladding diameter of the fiber (125 μm), but in the experiments the laser beam was defocused on the fiber cladding surface to create larger features. The circular shape of the fiber gave non-circular intensity distribution at the process zone. In this case, the beam diameter along the fiber axis (z axis) was smaller than that in the direction perpendicular to the fiber axis (x axis) [17]. Fiber Bragg gratings with a central wavelength of around 155 nm were used for the experiments. The FBGs were outsourced from a supplier (O/E Land Inc.), and according to the data sheets they were fabricated by UV radiation with appodized grating. The optical fibers were coated with a protective polymeric layer to protect them during shipping and handling. Since the layer could modify the laser beam characteristics during the beam exposure, the layer was removed by a chemical stripping process before the laser micromachining. To do that, the FBGs were immersed in acetone for 1-15 minutes to dissolve the polymer. In the experiments, the fiber was moved continuously at a constant speed with a pre-specified pitch to periodically irradiate the fiber, as shown in Fig. 1(b). (a) (b) Fig. 1 (a) Femtosecond laser workstation setup, (b) laser path relative to the fiber 4. Experimental Results and Discussions: Optical Response 4.1 Shift of Bragg Wavelength In the first experiment, the laser beam was attenuated to an average power of 4 mw (equal to 4 μj pulse energy), and the fiber was moved continuously with a pitch of 5 μm and speed of 1 μm/s. Laser micromaching was performed on the full length of the grating (1 mm). The laserfiber distance was set in such a way that the exposure area on the fiber was 22 μm. This was obtained by measuring the trace width of the irradiated regions. As a result, the pulse intensity was 1.3 1 14 W/cm 2. The original and final reflection spectra of the FBG are shown in Fig. 2. As seen, the central wavelength of the fiber is shifted by 465 pm. The red shift in the Bragg wavelength is attributed to the change in the fiber index of refraction. As the index of refraction at the locations exposed to the femtosecond laser pulses increases, the effective mode index of refraction increases affecting the reflection spectrum. Using (1), the change in the core index of refraction at the points of laser 4 exposure is Δn 4.33 1. 62

.45.4.25.35.2.3.25.15.2.15.1.1.5.5 1548 1548.5 1549 1549.5 155 155.5 1551 1551.5 1552 1552.5 1553 Fig. 2 Initial and micromachined FBGs reflection spectra at a pulse intensity of 1.3 1 14 W/cm 2 4.2 Dual Peak Reflectivity In another experiment, the laser beam was attenuated to a power of 17.5 mw (equal to 17.5 μj pulse energy). The exposure area in the fiber was 1 μm resulting in a pulse intensity of 1.45 1 14 W/cm 2. The fiber was moved continuously with a pitch of 1 μm and speed of 1 μm/s to radiate half of the length of the grating (5 mm). The reflectivity spectra are shown in Fig. 4. As seen, two resonance wavelengths are generated in FBG at 155.33 nm and 155.99 nm. Accordingly, the change in the index of refraction is Δn 6.9 1 4. 4.3 Bandwidth Increase Fig. 4 shows the results of an experiment in which the fiber was moved periodically with a pitch of 5 μm, so half of the length of the grating (5 mm) was micromachined with a laser power of 4 mw and continuous laser scanning speed of 1 μm/s. The exposure area was 24 μm resulting in a pulse intensity of 9.6 1 13 W/cm 2. As seen, the bandwidth of the reflectivity signal was increased. The Full-width-athalf-maximum (FWHM) for the initial and final spectra are 33 pm and 56 pm, respectively..45.4.35.3.25.2.15.1.5 1548 1548.5 1549 1549.5 155 155.5 1551 1551.5 1552 1552.5 1553 Fig. 3 Initial and micromachined FBGs reflection spectra at a pulse intensity of 1.45 1 14 W/cm 2 1548 1548.5 1549 1549.5 155 155.5 1551 1551.5 1552 1552.5 1553 Fig. 4 Initial and micromachined FBGs reflection spectra at a pulse intensity of 9.6 1 13 W/cm 2 4.4 Discussions: Optical Response According to the experimental results in Fig. 2, 3 and 4, three different scenarios occurred in the interaction of femtosecond laser pulses with FBGs. The modifications are directly attributed to the change in the index of refraction of the FBGs. In the interaction of femtosecond pulses with silica the index of refraction is increased in the exposed areas [9]. The change in the index refraction is a function of pulse intensity; higher pulse intensities result in larger index changes. In Fig. 2, the Bragg wavelength has permanently shifted to a higher wavelength, as the whole length of grating is exposed to laser pulses. However, in Fig. 3, the micromaching was conducted on half of the length of grating, so the initial Bragg wavelength is preserved and another one was generated at a higher wavelength. In Fig. 4, two wavelengths are available. Due to the lower laser pulse intensity, the Bragg peaks spacing is small and are seen as one peak with a larger bandwidth. In addition to the above-mentioned modifications of the spectral response, the reduction of the sharpness (in Fig. 2, Fig. 3, and Fig. 4), increase of the out-of-band background level (in Fig. 3 and Fig. 4), and grating strength reduction (in Fig. 2) are observed. These are attributed to the phase shifts resulted from the induced perturbations [18]. The modifications of the index of refraction obtained in these experiments are comparable to the results reported in literature [19]. By tuning the laser parameters and characterizing the process, the optical performance of the FBGs can be selectively customized. 5. Sensing Performance In addition to the changes in the optical performance of the FBGs, the femtosecond laser pulses caused the cladding surface to ablate forming periodic micro-grooves. Fig. 5 shows the structures fabricated on a fiber with the pitch of 5 μm at a laser average power of 4 mw and laser speed of 1 μm/s. The width (w) and the depth (h) of the structures are 22 μm and 32 μm, corresponding to 22 pulses per spot on the center line at a laser speed of 1 μm. 63

Fig. 5 Periodic microgrooves fabricated on the fiber with laser average power of 4 mw (pulse energy of 4 μj) and laser speed of 1 μm/s In optical fibers, the effective mode index of refraction ( n ) is a function of the indices of refraction of core ( n ), eff core cladding ( n clad ) and the surrounding medium [2]. Any change in these values may cause n eff to modify. If an FBG which has had the cladding selectively removed using the laser micromachining process is moved from one medium to another with different refractive index, the effective mode index of refraction and as a result the Bragg wavelength are changed. The effective parameter determining the refractive index of liquids is concentration. To investigate these effects, the micromachined FBG with double resonance wavelength was placed in liquid solutions of different concentrations and the optical responses were obtained. Fig. 6 shows the reflection spectra of the FBG at different temperatures in ethanol and 2.6 % solution of Polyvinyl Butyral (PVB) in ethanol. According to this figure, while the first resonance wavelength ( λ B 1 ) is dependent on both concentration and temperature, the second resonance wavelength ( ) is λ B 2 mainly a function of temperature and its sensitivity to the concentration of the surrounding liquid is much lower. Fig. 7 shows the change in the Bragg wavelengths spacing ( Φ= λb λ ), associated with the resonance 2 B1 wavelengths in Fig. 6, when the sensor is immersed in ethanol and PVB solutions in ethanol. According to this figure, the Bragg wavelengths spacing decreases with increasing the concentration. As seen in the experimental results, the sensitivity of the micromachined FBGs to liquid concentration was increased as a result of the fabrication of corrugated structures on the cladding. When the corrugated structures are fabricated, the cladding effective thickness is decreased and as a result the effects of the refractive index of the surrounding liquid become more significant in the coreconfined propagation modes of the optical fiber. The Bragg condition is a function of n eff and as a result, a Bragg wavelength shift occurs when a corrugated FBG is placed in a liquid with different refractive index. According to (1), in an FBG with two resonance wavelengths, e.g., Fig. 6, the wavelength spacing ( Φ ) is Φ= λb λ 2 2 B = Δn 1 effλ (2) In this case, increasing the concentration and hence the index of refraction of the surrounding medium causes Δ to decrease accordingly which reduces Φ. n eff 1.9 λ B1 λ B2.8.7.6.5.4.3.2.1 155.4 155.6 155.8 1551 1551.2 1551.4 1551.6 1551.8 1552 Ethanol at 5 o C Ethanol at 55 o C Ethanol at 6 o C 2.6 %, PVB in Ethanol at 5 o C 2.6 %, PVB in Ethanol at 55 o C 2.6 %, PVB in Ethanol at 6 o C Fig. 6 Reflection spectra of the micromachined FBG sample with dual resonance wavelengths at different temperatures in ethanol and PVB solution in ethanol Fig. 7-Average Bragg wavelengths spacing ( Φ ) for different liquid concentrations In addition, according to the experimental results, the FBGs are still sensitive to temperature which means that, in contrast to previous FBG sensors reported in the literature (e.g. [11-12]), a single sensor of the type developed here using selective laser micromachining can be used for simultaneous measurement of both temperature and concentration of liquids. 8. Conclusions In this paper we reported the femtosecond laser micromachining of fiber Bragg gratings to modify their performance. Different scenarios were investigated in terms of the laser processing parameters and laser pulse intensity. Permanent change of the Bragg wavelength, reflection peak splitting and bandwidth increase are among the effects that happened in the micromachined FBGs. In addition, the sensing performance of the micro-machined FBGs was increased by the inscription of periodic micro-grooves along the fiber axis. The micromachined fibers were successfully used in the simultaneous measurement of concentration and temperature of liquids. Acknowledgments The authors are pleased to express their appreciation for the cooperation of Dr. Andrew Pinkerton, Dr. Amin Abdol- 64

vand and Dr. David Whitehead at the Laser Processing Research Centre (LPRC) of the University of Manchester, and the financial support from National Sciences and Engineering Research Council (NSERC) of Canada and Ministry of Research and Innovation of Ontario. References [1] A. Othonos and K. Kalli: Fiber Bragg Gratings (Artech House, Boston, 1999) p. 31. [2] C. B. Schaffer, A. Brodeur, and E. Mazur: J. Meas. Sci. Technol., 12, (21) 1784. [3] C. B. Schaffer, A. Brodeur, J. F. García, and E. Mazur: Optics Letters, 26, (21) 93. [4] J. Kruger and W. Kautek: Advances in Polymer Science ed. by Lippert T. (Springer, Berlin / Heidelberg, 24) 168 p. 247. [5] X. Liu, D. Du, and G. Mourou: IEEE J. Quantum Electronics, 33, (1997) 176. [6] M. Lenzner, J. Kruger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautek, and F. Krausz: Physical Review Letters, 8, (1998) 476. [7] Chan J W, Huser T, Risbud S and Krol D M 21 Structural changes in fused silica after exposure to focused femtosecond laser pulses Optics Letters 26 1726-1728. [8] B. Poumellec, L. Sudrie, M. Franco, B. Prade, and B. Mysyrowicz: Optics Express, 11, (23) 17. [9] R. R. Gattass and E. Mazur: Nature Photonics, 2, (28) 219. [1] D. Grobnic, S. J. Mihailov, and C. W. Smelser: J. Lightwave Technology, 25, (27) 1996. [11] S. J. Mihailov, C. W. Smelser, D. Grobnic, R. b. Walker, P. Lu, H. Ding, and J. Unruh: J. Lightwave Technology, 22, (24) 94. [12] A. Martinez, M. Dubov, I. Khrushchev, and I. Bennion: Electronics Letters, 4, (24) 117 [13] J. Thomas, E. Wikszak, T. Clausnitzer, U. Fuchs, U. Zeitner, S. Nolte, and A. Tunnermann: J. Applied Physics A, 86, (27) 153. [14] C. Zhan C, J. Lee, S. Yin, P. Ruffin, and J. Grant: J. Applied Physics, 11, (27) 5311. [15] E. Wikszak, J. Thomas, S. Klingebiel, B. Ortaç, J. Limpert, S. Nolte, and A. Tunnermann: Optics Letters, 32, (27) 2756. [16] T. Erdogan: J. Lightwave Technology, 15, (1997) 1277. [17] F. Durr, H. G. Limberger, R. P. Salathe, F. Hindle, M. Douay, E. Fertwin, and C. Przygodzki: Applied Physics Letters, 84, (24) 4983. [18] R. Feced, and M. N. Zervas: J. Lightwave Technol., 18, (2), 9. [19] D. M. Krol: J. of Noncrystalline Solids, 354, (28) 416. [2] J. A. Buck: Fundamentals of Optical Fibers (John Wiley & Sons, Hoboken, 24) Chapter 3. (Received: June 16, 28, Accepted: March 1, 29) 65