DIRECTED ENERGY PROFESSIONAL SOCIETY Larger Image Back Cover       Introduction to High Power Fiber Lasers Second Edition R. Andrew Motes Sami A. Shakir Richard W. Berdine Hardback Textbook 436 Pages 2013, Directed Energy Professional Society Product Details       Table of Contents       Foreword This book, as well as other books on Directed Energy, are available from the DEPS online store. List of Figures .................................................................................................... ix List of Tables ..................................................................................................... xx Foreword ........................................................................................................... xxi   Chapter 1: Introduction.................................................................................. 1 Why High-Power Fiber Lasers?......................................................................... 2 History of Fiber Lasers (1840 to 1985).............................................................. 2 Recent Events and Programs (1985 to Present)................................................. 4 Current State of the Art of High-Power Fiber Lasers ........................................ 9 Summary.......................................................................................................... 10 References........................................................................................................ 10   Chapter 2: Introduction to Optical Waveguides............................................ 13 Light Confinement in Optical Waveguides by Total Internal Reflection .............. 13 Transverse Modes in Optical Waveguides....................................................... 18 Planar Waveguide Mode Derivation Using Ray Optics ..................................... 18 Planar Waveguide Mode Derivation Using Maxwell's Equations........................ 21 Cylindrical Waveguide Mode Derivation Using Maxwell's Equation.................. 28 Summary.......................................................................................................... 35 Practice Problems............................................................................................. 37 References........................................................................................................ 38   Chapter 3: Beam Propagation Modeling for Optical Waveguides .............. 39 Fast Fourier Transform Beam Propagation Method .......................................... 40 Two-Dimensional, Finite-Difference Beam Propagation Method..................... 42 Thomas Algorithm for Solving Tridiagonal Systems of Equations..................... 43 Slab Waveguide Model.................................................................................. 44 Three-Dimensional FD-BPM Using Cartesian coordinates............................ 48 Beam Propagation Modeling Using Cylindrical Coordinates ......................... 54 Optical Waveguide Eigenmodes ...................................................................... 64 Summary......................................................................................................... 66 Practice Problems............................................................................................. 67 References........................................................................................................ 69   Chapter 4: High-Power Optical Fiber Design and Fabrication .................... 71 Dual-Clad Fibers.............................................................................................. 71 Large Mode Area Fibers .................................................................................. 73 Large Mode Area Fibers and Bend Loss ....................................................... 73 Bend-Resistant, Large Mode Area Fibers...................................................... 76 Polarization-Maintaining Fibers ...................................................................... 78 Microstructure or Holey Fibers........................................................................ 80 Solid-Core Photonic Crystal Fibers .............................................................. 81 Other Novel Fiber Designs .............................................................................. 86 Hollow-Core Photonic Crystal Fibers........................................................... 86 Fiber Rod Lasers ........................................................................................... 87 Multicore Fibers ............................................................................................ 87 Fibers with Large Flattened Modes............................................................... 90 Helical Core Fibers ....................................................................................... 92 Optical Fiber Taxonomy .................................................................................. 95 Non–Silica-Based Glass Fibers........................................................................ 96 Phosphate Glass Fibers................................................................................. 96 Chalcogenide Glass Fibers............................................................................ 97 Fluorozirconate Glass (ZBLAN) Fibers ........................................................ 97 Glass Fiber Fabrication.................................................................................... 99 Summary.......................................................................................................... 99 Practice Problems........................................................................................... 101 References...................................................................................................... 102   Chapter 5: Fiber Lasers.............................................................................. 105 Fiber Laser Oscillator .................................................................................... 105 Fiber Cavity, Gain Medium, and Resonator .................................................. 106 Longitudinal Cavity Modes ........................................................................... 107 Fiber Laser and Amplifier Pumping Techniques ........................................... 109 Fiber End Pumping ........................................................................................ 112 Fiber Side Pumping........................................................................................ 114 Mode/Core Overlap Factor ............................................................................ 115 Quantum, Slope, and Wall-Plug efficiencies................................................. 116 Rate Equations ............................................................................................... 117 Optical Gain................................................................................................... 121 Fiber Laser Output Power Calculations......................................................... 125 Rare-earth, Ion-doped Fiber Lasers and Amplifiers..................................... 129 Neodymium.................................................................................................... 129 Ytterbium ....................................................................................................... 129 Erbium-Ytterbium Co-Doping....................................................................... 132 Directly Pumped Erbium ............................................................................... 133 Thulium.......................................................................................................... 133 Summary........................................................................................................ 136 Practice Problems........................................................................................... 138 References...................................................................................................... 139   Chapter 6: Mechanisms That Limit Fiber Laser and Amplifier Power ........ 141 Fiber Damage Mechanisms............................................................................ 142 Fiber Nonlinear effects.................................................................................. 144 Stimulated Brillouin Scattering ................................................................... 145 Stimulated Raman Scattering ...................................................................... 155 Limitations Due to Photo Darkening ............................................................. 156 Summary........................................................................................................ 156 Practice Problems........................................................................................... 157 References...................................................................................................... 158   Chapter 7: Pulsed Fiber Lasers .................................................................. 161 Methods for Producing Pulses on Laser Outputs........................................... 162 Q-Switching ................................................................................................. 162 Mode Locking................................................................................................ 164 Amplified Seed Pulse ................................................................................... 166 Nonlinear Effects in Pulsed Fiber Lasers....................................................... 167 Stimulated Brillouin Scattering and Stimulated Raman Scattering ............ 167 Four-Wave Mixing ....................................................................................... 168 Self-Phase Modulation................................................................................. 168 Self-Focusing ............................................................................................... 170 Group Velocity Dispersion............................................................................. 171 Pulse Compression......................................................................................... 177 Pulse Compression with External Gratings................................................. 177 Pulse Compression in All-Fiber Ring Lasers .............................................. 177 Some Pulse Energy Limitations and Solutions.............................................. 179 ASE Self-Saturation ..................................................................................... 179 Glass Damage.............................................................................................. 180 Summary........................................................................................................ 181 Practice Problems............................................................................................. 183 References........................................................................................................... 184   Chapter 8: Overview of Fourier Optics ........................................................ 185 Wave Propagation, Diffraction, and Interference .......................................... 185 Fourier Series................................................................................................. 189 Selected Fourier Transform Theorems and Transform Pairs............................ 190 The Fraunhofer Far-Field Approximation ..................................................... 191 Far-Field Irradiance Patterns Produced by Rectangular Apertures with Uniform Field Distributions................................................................................. 195 Far-Field Irradiance Patterns Produced by Circular Apertures with Uniform Field Distributions................................................................................................ 197 Far-Field Irradiance Produced by a Gaussian Field Distribution ..................... 199 Far-Field Irradiance Pattern for Truncated Gaussian Beams............................ 201 Far-Field Irradiance Patterns Produced by Multiple Apertures........................ 203 Observation of Fraunhofer Diffraction at Lens Focal Plane.......................... 206 Summary........................................................................................................ 207 Practice Problems........................................................................................... 209 References...................................................................................................... 210   Chapter 9: Beam Quality and Brightness..................................................... 211 Beam Divergence and Far-Field Beam Size .................................................. 211 Gaussian Beams and Their Far-Field Spots ....................................................... 212 Uniformly Illuminated Circular Aperture and Its Far-Field Spot (Airy Pattern) ... 216 Measures of Beam Quality............................................................................. 217 Beam Parameter Product and M2 ................................................................ 217 Power in the Bucket ..................................................................................... 222 Brightness .................................................................................................... 225 Strehl Ratio .................................................................................................. 227 Beam Quality of Truncated Gaussian Beams ................................................ 229 Summary........................................................................................................ 231 Practice Problems........................................................................................... 233 References...................................................................................................... 234   Chapter 10: Beam Combination .................................................................... 235 Beam-Combining Architectures..................................................................... 236 Incoherent Beam Combining ......................................................................... 236 Coherent Beam Combining............................................................................ 237 Active Coherent Beam Combining................................................................ 238 Passive Coherent Beam Combining ............................................................. 245 Spectral Beam Combining ............................................................................. 253 Spectral Beam Combining with Diffraction Gratings .................................. 254 Spectral Beam Combining with Volume Bragg Gratings ............................. 258 Simultaneous Passive Coherent and Spectral Beam Combining................... 264 Architecture Comparisons ............................................................................. 265 Summary........................................................................................................ 266 Practice Problems........................................................................................... 269 References...................................................................................................... 270   Chapter 11: Tiled-Aperture, Fiber Laser Array Modeling, Simulation, and Analysis............................................................................ 273 Seven-Element Fiber Laser Array.................................................................. 276 Nineteen-Element, Tiled-Aperture, Truncated Gaussian Fiber Arrays.......... 283 Far-Field Irradiance for the 19-Element, Truncated Gaussian Coherent Array.................................................................................................................. 284 Far-Field Irradiance for 19-Element, Truncated Gaussian Incoherent Array.................................................................................................................. 292 Degradation Comparisons of 19-Element, Truncated Gaussian, Tiled-Aperature Coherent and Incoherent Array............................................... 297 Thirty-Seven–Element, Tiled-Aperture Fiber Array............................................ 299 On-Target Phase Correction for Coherent Tiled-Aperture Arrays ..................... 303 Electronic Beam Steering with Coherent Tiled-Aperture Arrays........................ 311 Summary........................................................................................................ 315 Practice Problems........................................................................................... 317 References...................................................................................................... 319   Chapter 12: Focusing Laser Beams on Targets........................................... 321 Focusing Gaussian Beams ............................................................................. 321 Focusing Coherent, HcP Array Outputs........................................................ 326 Summary........................................................................................................ 332 Practice Problems........................................................................................... 334 References...................................................................................................... 334   Chapter 13: Atmospheric Beam Propagation............................................... 335 Beam Propagation Approximation Using Time-Averaged Spread Angle...... 335 FD-BPM for Atmospheric Beam Propagation............................................... 341 Finite-Difference Beam Propagation with Atmospheric Turbulence............. 347 Beam Distortion by Thermal Blooming ........................................................ 351 Summary........................................................................................................ 353 Practice Problems........................................................................................... 355 References...................................................................................................... 356   Chapter 14: Fiber Laser System Design Considerations ........................... 357 Continuous Wave (cW) or Pulsed ................................................................. 358 Wavelength .................................................................................................... 359 Bandwidth—Narrow Linewidth or Broadband ............................................. 363 Beam Quality and Spot Size/Shape on Target ............................................... 363 Beam Quality and Spot Size for Single-Beam Systems................................. 363 Beam Quality and Spot Size for Multiple-Beam Systems ............................. 367 Beam Control................................................................................................. 371 Thermal Management and Thermal Control.................................................. 372 Size, Weight, and Power ................................................................................ 378 Reliability....................................................................................................... 383 Ruggedness .................................................................................................... 384 Supportability/Maintainability ........................................................................... 384 Life-Cycle Cost.............................................................................................. 385 Summary........................................................................................................ 386 Practice Problems........................................................................................... 388 References...................................................................................................... 390   Chapter 15: Applications and Future Directions......................................... 391 Areas for Further Research ............................................................................ 391 Monolithic Fiber Components........................................................................ 391 Thermal Management..................................................................................... 393 Efficiency...................................................................................................... 393 Single-Fiber Power Scaling............................................................................ 394 Beam Combining ............................................................................................ 396 Eye-Safer Wavelengths................................................................................. 397 Concluding Remarks...................................................................................... 398 References...................................................................................................... 399   Appendix A: Physical Constants and Units....................................................... 401 Appendix B: Electromagnetic Wave Derivation................................................ 403 Appendix C: Beer's Law ................................................................................... 411 Appendix D: Fourier Transform of Gaussian Function..................................... 413 Appendix E: Bragg Diffraction/Reflection........................................................ 415 Appendix F: Engineering Economics Short Course (Life-cycle Cost Analysis)......................................................................................................... 417

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