DIRECTED ENERGY PROFESSIONAL SOCIETY

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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

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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

 
Copyright 2013 Directed Energy Professional Society   Last updated: 6 May 2013