PECULIARITIES OF THE THERMO-OPTIC COEFFICIENT AT HIGH TEMPERATURES IN FIBERS CONTAINING BRAGG GRATINGS A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Igor Fedin August, 2011 PECULIARITIES OF THE THERMO-OPTIC COEFFICIENT AT HIGH TEMPERATURES IN FIBERS CONTAINING BRAGG GRATINGS Igor Fedin Thesis Approved: Accepted: ______________________________ ______________________________ Advisor Dean of the College Dr. Sergei F. Lyuksyutov Dr. Chand K. Midha ______________________________ ______________________________ Faculty Reader Dean of the Graduate School Dr. David S. Perry Dr. George R. Newkome ______________________________ ______________________________ Department Chair Date Dr. Robert R. Mallik ii ABSTRACT The temperature dependence of thermo-optic coefficient in silica-based fibers containing fiber Bragg gratings (FBGs) includes thermal instability of chemical composition gratings, non-linear temperature dependence of FBGs written in different fibers, quadratic behavior of FBGs, and long-term stability of silica-based FBGs. Experimental measurements of the thermo-optic coefficient for the temperature interval 50 – 7800C in fused silica fiber containing FBGs were conducted while the temperature shift of the Bragg’s peak was monitored between 1300 and 1311 nm with sub-Angstrom precision. Numerical computations were focused on the FBG’s diffraction efficiency calculations accounting for the temperature drift of the gratings and found to be in excellent agreement with obtained experimental data. It has been found that the thermo- optic coefficient changes between 0.79×10-5 and 1.45×10-5 K-1 and undergoes a minimum in the vicinity of 440°C. Additional observation indicates a negative sign of the second- order thermo-optic coefficient. The experiments reveal that the grating reflectivity decays at temperatures higher than 6600C which correlates with calculated decay of the refractive index modulation. It suggests that an FBG is erased at high temperatures. Based on the energy dispersive spectroscopy it has been determined that thermal erasing of the FBGs at a temperature around 780°C correlates well with germanium sublimation (apparently in the form of germanium monoxide) out of silica-based fiber cores. iii ACKNOWLEDGEMENTS I acknowledge the attention and valuable comments of Professor Robert R. Mallik and Professor David S. Perry related to this project. I would like to thank my co-workers that helped me during this project: Ujitha Abeywickrema, Dr. Ivan Dolog (UA), and Dr. Mindaugas Rackaitis (Bridgestone Americas) I am very thankful and grateful to my scientific advisor Dr. Sergei F. Lyuksyutov for his guidance during this project, help, and support throughout two years of my studies and research. Without him this project would never be possible. iv TABLE OF CONTENTS Page LIST OF TABLES ............................................................................................................ vii LIST OF FIGURES ......................................................................................................... viii CHAPTER I. INTRODUCTION ........................................................................................................1 II. BACKGROUND ..........................................................................................................3 2.1. Optical Fibers ........................................................................................................3 Geometrical Optics Prospectives ...........................................................................3 Wave Optics Prospectives......................................................................................4 Connection to Geometrical Model .........................................................................9 2.2. Fiber Grating: Historical Background .................................................................10 2.3. Photosensitivity in Fibers .....................................................................................12 Origins of Photosensitivity ..................................................................................12 Ways to Enhance Fiber Photosensitivity .............................................................17 Models for the Photoinduced Refractive Index Change ......................................19 2.4. Methods for External Grating Inscribing .............................................................21 Interferometric Fabrication Technique ................................................................21 Phase-Mask Technique ........................................................................................24 Other Methods of Grating Fabrication .................................................................25 v 2.5. Quantitative Description of Gratings .....................................................................26 Definition of Gratings and Resonance Conditions ..............................................26 Coupled Wave Equations .....................................................................................29 Bragg Gratings as Temperature Sensors ..............................................................32 2.6. Thermal Decay of FBGs ......................................................................................33 III. EXPERIMENTAL PROCEDURE ...........................................................................35 3.1. Fiber Optics Setup................................................................................................35 3.2. SEM and EDS of FBGs .......................................................................................36 IV. CALCULATION METHOD ....................................................................................38 4.1. Calculation of Thermo-optic Coefficient .............................................................38 4.2. Calculation of Other Fiber, Modal, and Grating Parameters ...............................40 V. RESULTS AND DISSCUSION ................................................................................42 5.1. Grating Response as a Function of Temperature .................................................42 5.2. Results for Thermo-Optic Coefficient .................................................................43 5.3. Results for Fiber and Mode Parameters ...............................................................47 5.4. Grating Decay at Elevated Temperatures ............................................................50 5.3. Suggested Mechanism of Grating Decay .............................................................51 VI. CONCLUSIONS ......................................................................................................55 REFERENCES .................................................................................................................57 vi LIST OF TABLES Table Page 5.1.1 The values of the fitting parameters, and the calculated parameters Bi΄.. ..........................................................................................43 5.3.1 The fiber and mode parameters for the two sustained modes: LP01 and LP11. ............................................................................................47 5.3.2 The resonant wavelengths for possible mode couplings ............................49 vii LIST OF FIGURES Figure Page 2.1.1 A schematic of optical fiber is shown. .........................................................3 2.1.2 A diagram for a ray launched into a fiber is shown. ....................................4 2.1.3 Cartesian (x, y, z) and cylindrical (r, φ, z) coordinates in optical fiber are introduced. .....................................................................4 2.1.4 Electric field patterns for several lowest LP modes are shown. ..................9 2.1.5 A vector model for the eigenvalue u and propagation constant β ................9 2.3.1 Absorption spectrum of germania-silica glasses in the UV .......................15 2.3.2 The diagram exhibits the way of GeE΄, Ge(1) and Ge(2) centers formation from the Ge-Si “wrong bonds” .....................................15 2.3.3 Schematic energy diagram showing relevant defect levels and UV– induced photochemical reactions in GeO2-SiO2 glasses. ..................16 2.3.4 Illustration of the dipole model ..................................................................20 2.4.1 A schematic of amplitude-splitting interferometer for grating formation ....................................................................................................22 2.4.2 Schematic of the prism interferometer for the grating fabrication ............23 2.4.3 Schematic of Lloyd interferometer for grating formation .........................23 2.4.4 Schematic of the phase-mask technique for grating fabrication ................24 2.4.5 Setup for point-by-point grating fabrication ..............................................26 2.5.1 A grating inscribed in the fiber core is shown ...........................................26 2.5.2 A schematic of the refractive index perturbation is shown........................27 viii 2.5.3 Diffraction of light by a grating is shown ..................................................28 2.6.1 Diagram for the proposed model for grating decay ...................................33 3.3.1 Schematic presentation of experimental setup ...........................................36 5.1.1 The variation of grating response with temperature ..................................42 5.2.1