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 |