| 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 |
Editor's Comments
This book provides a comprehensive review of current high-power fiber laser (HPFL) technology. It is intended as an introduction to this rapidly developing field but can also be used by researchers and technology managers as a handy and comprehensive reference. It contains a broad review ranging from a history of HPFLs to an introduction of the science and engineering required for full HPFL systems, plus the authors' predictions of future applications and research directions. Readers will also find detailed information that will help them to understand and model optical waveguides, fiber amplifiers and lasers, beam combining techniques, beam quality, and free-space beam propagation. This book describes a rapidly developing field of laser technology, and fills the very important role of providing students, researchers, and technology managers with valuable, timely, and unbiased information on the subject.
This second edition contains information on recent research to achieve increased output powers by increasing the power of individual beams and by combining multiple beams. It also features new chapters on fast beam propagation modeling and simulation for optical waveguides and free space.
About the Authors
In the last 40 years R. Andrew Motes has been (in chronological order) a sharecropper, electronic technician, electronic engineer, and theoretical scientist. He received his B.S. degree in electrical engineering from the University of Arkansas in 1978, M.S. degree in electrical engineering from the Air Force Institute of Technology in 1979 with a specialty in navigation, guidance and control theory, and Ph.D. in electrical engineering in 1987 from the University of New Mexico with a specialty in laser physics and electro-optics. All degrees were earned while serving on active duty in the U.S. Air Force. Dr. Motes is licensed to practice engineering in multiple states including New Mexico. He has written three books, seven commercial educational software packages, and many scientific journal and magazine articles. He taught astronautical engineering and control theory at the U.S. Air Force Academy; physics and electronic design at John Brown University; and retired from the U.S. Air Force Reserves in 2007 at the rank of colonel. He can be contacted via e-mail at: andymotes@msn.com.
Sami A. Shakir is a senior scientist with Tau Technologies. Before that, he was a technical fellow with Northrop Grumman and later with TASC. Dr. Shakir earned an MSc. and Ph.D., both in optical sciences from the Optical Sciences Center in Tucson, Arizona, in 1978 and 1980, respectively. He has been involved with design, analysis, and experimentation involving high-power gas lasers, semiconductor lasers, solid-state lasers, and fiber lasers. Dr. Shakir's research interests include optical filter design, coherent laser interaction with matter, femto-second laser effects, and fiber laser array phasing and beam control. He has published extensively in these fields and has eight patents to his name.
Richard W. Berdine received a B.S. degree in 1975 from Iowa State University in engineering science, and an M.S. degree in 1981 from the Air Force Institute of Technology in engineering physics. While on active duty in the Air Force, he served as branch chief of the Experimental Resonator Branch and Directed Energy Branch at the Air Force Weapons Laboratory and the Foreign Technology Division, respectively. He also served as assistant professor of physics at the U.S. Air Force Academy, teaching courses in physics, optics, and laboratory methods, and as a technical director at the Field Command Defense Nuclear Agency on several international programs. Berdine is currently a senior physicist at the Air Force Research Laboratory's Directed Energy Directorate in Albuquerque, New Mexico.
Lasers have become pervasive in our daily lives. They are used at checkout counters in supermarkets and department stores to scan barcodes; in home and office copiers, printers, and DVD players; in industrial applications and materials processing involving marking, drilling, cutting, and welding; in science and engineering for precise measurements of distance, temperature, density, fluid velocity, and specie concentrations; in high-speed, high-bandwidth communications; and in imaging and remote-sensing applications. These lasers come in many varieties. Most lasers built into consumer products are small diode lasers, while lasers for industrial applications are typically high-power gas or bulk solid-state lasers (SSLs). On the other hand, fiber lasers—a relatively new technology that is a subclass of solid-state lasers—are growing in popularity for communications and industrial applications. Undoubtedly lasers will find additional applications and become more ubiquitous in the future.
Because of the widespread use of lasers, it is now even more important that engineers, scientists, and technical managers understand all forms of this technology. Several excellent textbooks1–4 are available that describe the theory and operation of lasers in general, but this book specializes in high-power fiber laser (HPFL) technology, beam combination and HPFL systems. Because the technology is relatively new, there is limited HPFL information available in a single place for use in universities for teaching and conducting research and in industry for making technical and managerial decisions. Here we have collected information from literally hundreds of research publications and arranged it in what we hope is a logical format. We have tried to make it useful for students, scientists, engineers, and technical managers. However, it is difficult, if not impossible, to please everyone. Students and scientists typically want to see the derivations while engineers and technical managers usually just want the bottom line. In certain places we show derivations and in others we simply refer the reader to the relevant scientific publication for derivation details. At the end of each chapter we provide a summary of the most important information, so readers interested only in the bottom line can find it there. We hope our approach is a useful compromise of information content that allows for the widest possible dissemination of information about this rapidly maturing technology.
We begin this book with a general introduction to HPFLs. In this introduction, we first discuss the history of these devices and illustrate the recent rapid rate of maturation. Then we answer the question, "Why high-power fiber lasers?" There are other high-power bulk SSLs that are vying for position in industry and defense, so we believe the reader will be interested in learning the advantages of fiber lasers over bulk SSLs. We conclude the general introductory chapter with a discussion of the current state of the art in fiber lasers.
Next we provide a detailed, technical overview of HPFLs, first providing an introduction to optical waveguides in silica glass fibers and then a technical review of fiber amplifiers and lasers. Since no laser is perfect, we also include a chapter on fiber laser limitations. And speaking of limitations, because single-fiber lasers are limited in output power, we also provide chapters on Fourier optics, beam quality, and beam combining. An understanding of these fundamental concepts will hopefully aid in the development and scaling of fiber laser systems past 10 kW with good beam quality.
Because fiber lasers can also be used in pulse mode, this second edition contains a chapter that describes this mode of operation. These pulsed fiber lasers are now becoming widely available for industrial marking and cutting applications.
The second edition also includes two chapters on beam propagation modeling—one for optical waveguides such as optical fiber, and one for free-space or atmospheric beam propagation. Modeling for beam propagation in fiber waveguides and lasers is very useful in the design of microstructured fibers such as those with multiple cores. The free-space beam-propagation simulations are useful in determining the propagation characteristics of fiber array outputs. These fiber array outputs must also be focused for short-range applications, so we have included a chapter on laser beam focusing. Beam-propagation simulations can then be used to predict target irradiance patterns produced by focused array outputs.
We conclude with a chapter on system design considerations and a chapter on applications and future directions. These are important issues when the overall effectiveness of HPFLs is considered. Systems engineers and technical managers will be especially interested in the systems discussion where we consider issues such as performance trades, weight, thermal management, and efficiency. Technical planners may be more interested in the information provided on applications and future directions. Naturally, these last chapters will be less mathematically rigorous.
In summary, we first provide a general introduction to fiber lasers, followed by a detailed technical introduction and top-level information on system design considerations, and then finally a discussion of applications and future directions of HPFLs. We believe this to be a logical approach to understanding HPFLs.
We offer special thanks to two people who have made significant contributions to this edition. Jim Griggs's careful reading of the first edition was very helpful in identifying errors so that we could correct them in this edition. Next, Gabe Mounce was kind enough to review several chapters of the current edition and provided numerous useful recommendations. We also note that our primary reviewer for the first edition of this book, Sami Shakir, has been promoted to author for the second edition due to his significant contribution. Finally, there are contributions from many scientists noted throughout the text that have not only added significantly to the state of the art of fiber laser research today, but who have also generously contributed to this book.
References
- Siegman, A.E., Lasers, University Science Books (1986).
- Verdeyen, J.T., Laser Electronics, 2nd ed., Prentice Hall Series in Solid State Physical Electronics (1989).
- Yariv, A., Optical Electronics, 3rd ed., Holt, Rinehart and Winston (1985).
- Milonni, P.W., Eberly, J.E., Lasers, Wiley & Sons (1988).
