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Transverse Mode Selection and Brightness Enhancement in Laser Resonators by Means of Volume Bragg Gratings

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Transverse Mode Selection and Brightness Enhancement in Laser Resonators by Means of Volume Bragg Gratings TRANSVERSE MODE SELECTION AND BRIGHTNESS ENHANCEMENT IN LASER RESONATORS BY MEANS OF VOLUME BRAGG GRATINGS by BRIAN MATTHEW ANDERSON B.S. UNIVERSITY OF WASHINGTON, 2009 A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the College of Optics and Photonics at the University of Central Florida Orlando, Florida Summer Term 2015 Major Professor: Leonid Glebov © 2015 Brian Anderson ii ABSTRACT The design of high power lasers requires large mode areas to overcome various intensity driven nonlinear effects. Increasing the aperture size within the laser can overcome these effects, but typically result in multi-transverse mode output and reduced beam quality, limiting the brightness of the system. As one possible solution, the angular selectivity of a diffractive optical element is proposed as a spatial filter, allowing for the design of compact high brightness sources not possible with conventional methods of transverse mode selection. This thesis explores the angular selectivity of volume Bragg gratings (VBGs) and their use as spatial transverse mode filters in a laser resonator. Selection of the fundamental mode of a resonator is explored using transmission Bragg gratings (TBGs) as the spatial filter. Simulations and experimental measurements are made for a planar, 1 cm long resonator demonstrating near diffraction limited output (M2 < 1.4) for aperture sizes as large as 2.0 mm. Applications to novel fiber laser designs are explored. Single mode operation of a multi-mode Yb3+ doped ribbon fiber laser (core dimensions of 107.8 μm x 8.3 μm) is obtained using a single transmission VBG as the filter in an external cavity resonator. Finally, a novel method of selecting a pure higher order mode to oscillate within the gain medium while simultaneously converting this higher order mode to a fundamental mode at an output coupler is proposed and demonstrated. A multiplexed transmission VBG is used as the mode converting element, selecting the 12th higher order mode for amplifications in an Yb3+ doped ribbon fiber laser, while converting the higher order mode of a laser resonator to a single lobed output beam with diffraction limited divergence. iii ACKNOWLEDGMENTS I would like to acknowledge the love and support of Heidi Jones that has helped me to complete my PhD. I’d like to thank past and present members of the PPL group. I’d like to thank my advisor Dr. Leonid Glebov and the head of the laser group Dr. George Venus: I’d also like to thank Boris Zeldovich, Ivan Divliansky, Derrek Drachenberg, Apurva Jain, Daniel Ott, Evan Hale, Marc Segall, Julien Lumeau, Sergiy Kaim, and Sergiy Mokhov. I would like to thank the funding agencies and external groups who have provided material support for this project. I’d like to acknowledge Derrek Drachenberg and his colleagues at Lawrence Livermore National Laboratory for providing the ribbon fiber used in these experiments. Key results would not have been possible without their support. I’d also like to thank all colleagues at Lawrence Livermore National Laboratory involved with the design and construction of the ribbon fiber, including: Jay W. Dawson, Derrek R. Drachenberg, Mike J. Messerly, Paul H. Pax, and John B. Tassano. I’d also like to acknowledge the ARO-JTO for providing the funding support for this work. Finally I’d like to acknowledge the DEPS HEL Graduate Scholarship for their support during my graduate career. iv TABLE OF CONTENTS LIST OF FIGURES ..................................................................................................................... viii LIST OF TABLES ....................................................................................................................... xvi CHAPTER ONE: INTRODUCTION ............................................................................................. 1 CHAPTER TWO: MOTIVATION AND METHODS OF TRANSVERSE MODE SELECTION ......................................................................................................................................................... 4 2.1. Diode Pumped Solid State Lasers ........................................................................................ 5 2.1.1. Transverse modes .......................................................................................................... 7 2.1.2. Methods of mode selection ........................................................................................... 9 2.2. Fiber lasers ......................................................................................................................... 12 2.2.1. Transverse modes ........................................................................................................ 14 2.2.2. Methods of mode selection ......................................................................................... 16 2.3. Figures of Merit ................................................................................................................. 18 2.4. Summary ............................................................................................................................ 21 CHAPTER THREE: VOLUME BRAGG GRATINGS ............................................................... 22 3.1. Types of diffraction gratings .............................................................................................. 22 3.2. Plane-wave theory of volume Bragg gratings .................................................................... 23 3.2.1. Reflecting Bragg gratings ........................................................................................... 27 3.2.2. Transmission Bragg gratings ...................................................................................... 29 v 3.3. Interaction of finite beams with VBGs .............................................................................. 31 3.4. Photosensitive materials for volume Bragg gratings ......................................................... 35 3.5. Volume Bragg gratings recorded in PTR glass ................................................................. 37 3.6. Applications for VBGs recorded in PTR ........................................................................... 38 3.6.1. Spectral locking of lasers ............................................................................................ 38 3.6.2. Spectral beam combining (SBC)................................................................................. 39 3.6.3. Coherent beam combining (CBC) .............................................................................. 41 3.6.4. Transverse mode selection .......................................................................................... 41 CHAPTER FOUR: MODELING ................................................................................................. 43 4.1. Introduction ........................................................................................................................ 43 4.2. Solid state resonators ......................................................................................................... 43 4.2.1. Interaction of Hermite-Gaussian modes with TBG .................................................... 44 4.2.2. Fox-Li analysis of mode selection in a laser resonator ............................................... 47 4.2.3. Summary ..................................................................................................................... 60 4.3. Fiber lasers ......................................................................................................................... 61 4.3.1. Laser gain and mode competition ............................................................................... 61 4.3.2. Guided modes and interaction with VBG ................................................................... 64 4.3.3. Cavity design .............................................................................................................. 68 4.4. Discussion .......................................................................................................................... 72 vi CHAPTER FIVE: BRIGHTNESS ENHANCEMENT OF A SOLID STATE LASER .............. 74 5.1. Introduction ........................................................................................................................ 74 5.2. Experimental Results ......................................................................................................... 74 5.3. Discussion .......................................................................................................................... 81 CHAPTER SIX: BRIGHTNESS ENHANCEMENT OF A RIBBON FIBER ............................ 83 6.1. Introduction ........................................................................................................................ 83 6.2. Experimental Results ......................................................................................................... 85 6.3. Analysis of losses ............................................................................................................... 90 6.4. Discussion .......................................................................................................................... 95 CHAPTER SEVEN: MODE CONVERSION BY MULTIPLEXED TBG ................................. 97 7.1. Introduction ........................................................................................................................ 97 7.2. Multiplexed VBGs ............................................................................................................
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