Springer Series in Optical Sciences Volume 1 Springer Series in Optical Sciences Editorial Board: D .L. MacAdam A.L. Schawlow K. Shimada A. E. Siegman T. Tamir

Managing Editor: H. K. V. Latsch

42 Principles of Phase Conjugation 51 1\mable Solid State for Remote Sensing By B. Ya. Zel'dovich, N.F. Pilipetsky, Editors: R. L. Byer, E. K. Gustafson, and V. V. Shkunov and R. Trebino 43 X-Ray Microscopy 52 Tunable Solid-State Lasers II Editors: G. Schmahl and D. Rudolph Editors: A.B. Budgor, L. Esterowitz, 44 Introduction to Physics and L. G. DeShazer By K. Shimoda 2nd Edition 53 The C02 Laser By W.J. Witteman 45 Scanning Electron Microscopy Physics of Image Formation and Microanalysis 54 Lasers, Spectroscopy and New Ideas By L. Reimer A Tribute to Arthur L. Schawlow Editors: W. M. Yen and M.D. Levenson 46 Holography and Deformation Analysis By W. Schumann. J.-P. Ziircher, and D. Cuche 55 Laser Spectroscopy VIII 47 Tunable Solid State Lasers Editors: W. Persson and S. Svanberg Editors: P. Hammerling, A.B. Budgor, and A. Pinto 56 X-Ray Microscopy II Editors: D. Sayre, M. Howells, J. Kirz, and 48 Integrated Optics H. Rarback Editors: H. P. Nolting and R. Ulrich 49 Laser Spectroscopy VII 57 Single-Mode Fibers Fundamentals By E.-G. Neumann Editors: T. W. Hansch and Y. R. Sherr

50 Laser-Induced Dynamic Gratings 58 Photoacoustic and Photothermal Phenomena By H.J. Eichler, P. Giinter, and D. W. Pohl Editors: P. Hess and J. Pelzl

Volumes 1-41 are listed on the back inside cover Walter Koechner

Solid-State Laser Engineering

Second Completely Revised and Updated Edition

With 371 Figures

Springer-Verlag Berlin Heidelberg GmbH Dr. WALTER KOECHNER Fibertek, Inc., 510-A Herndon Parkway, Herndorn, VA 22070, USA

Editorial Board Professor Korcm SHIMODA, Ph. D. Faculty of Science and Technology Keio University, 3-14-1 Hiyoshi, Kohoku-ku Yokohama 223, Japan

DAVID L. MACADAM, Ph. D. Professor ANTHONY E. SIEGMAN, Ph. D. 68 Hammond Street Electrical Engineering Rochester, NY 14615, USA E. L. Ginzton Laboratory, Stanford University Stanford, CA 94305, USA

ARTHUR L. ScHAwLow, Ph. D. THEODOR TAMIR, Ph. D. Department of Physics, Stanford University Polytechnic University Stanford, CA 94305, USA 333 Jay Street, Brooklyn, NY 11201, USA

Managing Editor: Dr. HELMUT K. V. LaTSCH Springer-Verlag, Tiergartenstrasse 17, D-6900 Heidelberg, Fed. Rep. of Germany

ISBN 978-3-662-15145-7 ISBN 978-3-662-15143-3 (eBook) DOI 10.1007/978-3-662-15143-3

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. ©Springer-Verlag Berlin Heidelberg 1976 and 1988 Originally published by Springer-Verlag Berlin Heidelberg New York in 1988 Softcover reprint of the hardcover 2nd edition 1988

The use of registered names. trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

2154/3150-543210- Printed on acid-free paper Preface to the Second Edition

This monograph, written from an industrial vantage point, provides a detailed discussion of solid-state lasers, their characteristics, design and construction, and practical problems. The title Solid-State Laser Engineering is chosen so as to convey the emphasis which is placed on engineering and practical consider• ations. The author has tried to enhance the description of the engineering aspects of laser construction and operation by including numerical and technical data, tables, and curves. The book is mainly intended for the practicing scientist or engineer who is interested in the design or use of solid-state lasers, but it is hoped that the comprehensive treatment of the subject makes the work useful also to students of laser physics who want to supplement their theoretical knowledge with the engineering aspects of lasers. Although not written in the form of a college textbook, the book might be used in an advanced college course on laser technology. The aim was to present the subject as clearly as possible. Phenomeno• logical descriptions using models were preferred to an abstract mathematical presentation, even though many simplifications had then to be accepted. Re• sults are given in most cases without proof since the author tried to stress the application of the results rather than the derivation of the formulas. An exten• sive list of references is cited for each chapter to permit the interested reader to learn more about some particular subject. This new edition has been updated and revised to include important new developments, concepts and technologies which have emerged during the last ten years. Through a combination of new discoveries, successful implementation of well-known ideas, and new applications, research, development and engineer• ing of solid-state lasers has greatly intensified during the last decade. Rather dramatic possibilities have appeared on the horizon which could bring about a revolutionary change in solid-state laser technology. We are just on the verge of seeing these technologies emerge into the commercial and military market• place. The most exciting prospect is that of solid-state laser materials pumped by laser-diode arrays and including high-efficiency converters. Efficient, com• pact, frequency agile solid-state lasers with average power levels of up to a few

v hundred watts and covering most of the visible, near- and mid-infrared regime could become a reality. The major new developments in solid-state laser engineering which are described in this new edition are briefly summarized here. Wavelength tunability: With the discovery of the alexandrite laser, followed by a number of other tunable lasers such as Ti : , great progress has been made, providing a tunable output from solid-state lasers for atmospheric and spectroscopic studies and for certain military applications. Improved efficiency: Co-doped laser crystals, such as Cr: Nd: GSGG, which are highly efficient absorbers of fl.ashlamp radiation have significantly improved overall system efficiency of flashlamp-pumped lasers. The introduction of Nd: phosphate glasses which have twice the gain of silicate glasses has helped to im• prove the efficiency of these lasers. The most dramatic impact on efficiency has come from laser-diode arrays employed as pump sources for solid-state lasers. Laser-diode pumping always looked attractive but was not practical due to such technological barriers as low efficiency, low power and short lifetime. The significant progress made in diode-laser technology, coupled with the emerg• ing technology of linear and planar diode arrays, has removed these former technological barriers. Diode pumping is now being widely investigated and is considered by many researchers to be potentially practical even for high-power lasers. Increased average power: Old concepts, such as the slab-laser design, have been revisited and engineering improvements have resulted in systems pro• ducing high average power with good beam quality. In particular, slab lasers pumped with laser-diode arrays look potentially very attractive. Improved beam quality: The use of unstable resonators for solid-state lasers has increased the power extraction at low order modes. Also, optical phase con• jugation employed to correct thermal distortions introduced by laser amplifiers has been shown to improve beam quality in high average power systems. Frequency agility: Improved nonlinear materials such as KTP, BBO and several organic crystals as well as scaling of KDP to very large apertures have made harmonic processes more attractive as a means of extending the wave• length coverage of solid-state lasers. Also, stimulated Raman scattering is now being frequently used to shift the wavelength from a laser into a spectral region not covered by any other system. Highly coherent systems: Excellent frequency stability and single axial mode operation of diode-pumped unidirectional ring lasers make it possible to design coherent Doppler systems in the near-infrared wavelength regime. Laser Superstructures: The last 10 years have seen the emergence of Nd: glass laser systems employed for inertial-confinement fusion research with beam diameters of close to 1 m and unprecedented power and energy levels. Although this edition has been expanded and updated, the organisation of the material has not changed compared to the first edition. The topics cov• ered include the optical amplification process, properties of laser materials, laser oscillators and amplifiers, resonators, pump systems and heat removal, Q-switches and mode-lockers, nonlinear devices and optical damage.

VI Omitted from this second edition is the chapter on lasers designed for specific applications, since many publications are available which deal with the various uses of lasers in research, industry, medicine and the military. This book would not have been possible without the many contributions to the field of laser engineering that have appeared in the open literature and which have been used here as the basic source material. I apologize to any of my colleagues whose work has not been acknowledged or adequately represented in this book. My special thanks are due to the editor, Dr. H. Lotsch, for his support and assistance in preparing the new edition for printing. Neither edition of this book could have been written without the encour• agement, patience and support of my wife Renate.

Herndon, VA Walter Koechner January 1988

VII From the Preface to the First Edition

The first decade of solid-state laser technology has seen the development of an enormous number of lasing materials and a large variety of interesting design concepts. However, in recent years the technology has matured to a point where solid-state lasers have reached a plateau in their development. To a major extent, the growth in importance of solid-state lasers for in• dustrial and military applications and as a general research tool is due to the improvement in reliability and maintainability of these systems. The practical advances of these devices had several major consequences: A wealth of appli• cations for solid-state lasers has emerged in materials processing, holography, rangefinding, target illumination and designation, satellite and lunar ranging, thermonuclear fusion, plasma experiments, and in general for scientific work requiring high power densities. Emphasis has shifted from research and innova• tion to cost reduction and system improvement. As a result, a standardization of the system designs has occurred. [... ]

The author is indebted to Dr. M. Stitch and D. Smart who have carefully read the manuscript and suggested many corrections. A special note of grati• tude for typing the manuscript on a tight schedule goes to Renate Koechner and Margaret Lochart. Thanks are due to the editor, Dr. H. Lotsch, for his assistance in preparing the work for printing. The book is dedicated to my wife Renate, whose encouragement and un• derstanding were a decisive factor in its timely completion. Without her en• couragement and patience the final goal would not have been achieved.

Santa Monica, CA, 1976 Walter Koechner

VIII Contents

1. Introduction ...... 1 1.1 Optical Amplification ...... 1 1.2 Interaction of Radiation with Matter ...... 2 1.2.1 Blackbody Radiation ...... 2 1.2.2 Boltzmann Statistics ...... 3 1.2.3 Einstein Coefficients ...... 4 1.2.4 Phase Coherence of ...... 7 1.3 Absorption and Optical Gain ...... 8 1.3.1 Atomic Lineshapes ...... 8 1.3.2 Absorption by Stimulated Transitions ...... 13 1.3.3 ...... 15 1.4 Creation of a Population Inversion ...... 17 1.4.1 The Three-Level System ...... 17 1.4.2 The Four-Level System ...... 19 1.4.3 The Metastable Level ...... 20 1.5 Laser Rate Equations ...... 22 .

2. Properties of Solid-State Laser Materials ...... 28 2.1 Overview ...... 28. . . 2.1.1 Host Materials ...... 29 . 2.1.2 Active ...... 34 . 2.2 ...... 38 . . . 2.3 Nd: Lasers ...... 47. . . 2.3.1 Nd:YAG ...... 48 2.3.2 Nd: Glass ...... 54. . 2.3.3 Nd: Cr: GSGG ...... 57 . 2.3.4 Nd: YLF ...... 60 . . 2.4 _Er: Lasers ...... 62 . . 2.4.1 Er:YAG ...... 63 2.4.2 Er: Glass ...... 64 . . 2.5 Tunable Lasers ...... 66. . 2.5.1 Alexandrite Laser ...... 71. 2.5.2 Ti : Sapphire ...... 76 .

IX 3. Laser Oscillator ...... 79 3.1 Operation at Threshold ...... 80 3.2 Gain Saturation ...... 84 3.3 Circulating Power ...... 87 3.4 Output versus Input Calculations ...... 88 3.4.1 Flashlamp-Pumped Lasers ...... 89 3.4.2 Laser-Diode-Pumped Oscillators ...... 94 3.5 Output Fluctuations ...... 97 3.5.1 Relaxation Oscillations ...... 98 3.5.2 Quantum Noise ...... 102 3.6 Examples of Regenerative Oscillators ...... 103 3.6.1 Ruby ...... 103 3.6.2 Nd: Glass ...... 111 3.6.3 Nd:YAG ...... 114 3.6.4 Laser-Diode-Pumped Regenerative Oscillator ...... 119 3.6.5 Alexandrite ...... 124 3. 7 Travelling-Wave Oscillator ...... 126

4. Laser Amplifier ...... 129 4.1 Pulse Amplification ...... 131 4.1.1 Ruby Amplifiers ...... 135 4.1.2 Nd: Glass Amplifiers ...... 141 4.1.3 Nd: YAG Amplifiers ...... 147 4.2 Steady-State Amplification ...... 150 4.2.1 Ruby Amplifier ...... 152 4.2.2 Nd: Glass Amplifier ...... , ...... 154 4.3 Signal Distortion ...... 155 4.3.1 Spatial Distortions ...... 155 4.3.2 Temporal Distortion ...... · 160 4.4 Gain Limitation and Amplifier Stability ...... 161 4.4.1 Spontaneous Decay, Superradiance, and Lateral Depumping ...... 162 4.4.2 Prelasing and Parasitic Modes ...... 165

5. Optical Resonator ...... :...... 168 5.1 Transverse Modes...... 168 5.1.1 Intensity Distribution of Transverse Modes...... 169 5.1.2 Characteristics of a ...... 172 5.1.3 Resonator Configurations...... 174 5.1.4 Stability of Laser Resonators...... 178 5.1.5 Diffraction Losses...... 180 5.1.6 Higher-Order Modes...... 182 5.1.7 Active Resonator...... 183 5.1.8 Resonator Sensitivity...... 185 5.1.9 Mode-Selecting Techniques...... 189 5.1.10 Examples of Advanced Stable Resonator Designs...... 196

X 5.2 Longitudinal Modes...... 203 5.2.1 Fabry-Perot Resonators...... 203 5.2.2 Spectral Characteristics of the Laser Output ...... 211 5.2.3 Axial Mode Control...... 215 . . 5.3 Temporal and Spectral Stability ...... 226. 5.3.1 Amplitude Fluctuations...... 226 5.3.2 Frequency Changes...... 229 5.4 Hardware Design ...... 232. . . 5.5 Unstable Resonators...... 236 5.5.1 Confocal Positive-Branch Unstable Resonator...... 240 5.5.2 Negative-Branch Unstable Resonators...... 242 5.6 Wavelength Selection...... 244

6. Optical Pump System ...... 24 . .7 6.1 Pump Sources...... 247 6.1.1 Noble Gas Flashlamps...... 251 6.1.2 Continuous Arc Lamps...... 265 6.1.3 Tungsten-Filament Lamps...... 272 6.1.4 Laser Diodes...... 274 6.1.5 Nonelectric Pump Sources...... 289 6.2 Power Supplies ...... 290 . . . 6.2.1 Operation of cw Pump Sources...... 290 6.2.2 Operation of Flashlamps ...... 292 . 6.3 Pump Cavities...... 309. . . . 6.3.1 Pump Cavity Configurations...... 309 6.3.2 Energy Transfer Characteristics ...... 321 6.3.3 Mechanical Design...... 335. .

7. Heat Removal ...... 350. . . . 7.1 Thermal Effects in Laser Rods...... 350 7.1.1 cw Operation...... 351 7.1.2 Single-Shot Operation...... 369 7.1.3 Repetitively Pulsed Lasers...... 372 7.2 Cooling Techniques...... 382 7.2.1 Liquid Cooling...... 382. . 7.2.2 Air or Gas Cooling...... 385 7.2.3 Conductive Cooling...... 386 . 7.3 Noncylindrical Laser Elements...... 388

8. Q-Switches and External Switching Devices ...... 402 8.1 Pulse-Reflection Mode Q-Switches...... 402 8.1.1 Q-Switch Theory...... 403 8.1.2 Mechanical Devices...... 412 8.1.3 Electrooptical Q-Switches...... 414 8.1.4 Acoustooptic Q-Switches...... 431 . 8.1.5 Dye Q-Switch...... 437

XI 8.2 Pulse-Transmission Mode Q-Switches ...... 442 8.3 Optical Gates External to Resonator...... 446

9. Mode Locking...... 451 9.1 Passive Mode Locking...... 455 9.1.1 Design and Performance Characteristics of Passively Mode-Locked Solid-State Lasers...... 460 9.2 Active Mode Locking ...... 466 9.2.1 Design of Actively Mode-Locked Laser Systems...... 469 9.3 Active-Passive Mode Locking...... 476

10. Nonlinear Devices...... 477 10.1 Harmonic Generation...... 479 10.1.1 Basic Equations of Second-Harmonic Generation..... 479 10.1.2 Parameters Affecting the Doubling Efficiency...... 487 10.1.3 Properties of Nonlinear Crystals...... 492 10.1.4 Intracavity Frequency Doubling...... 504 10.1.5 Third-Harmonic Generation ...... 511 10.1.6 Examples of Harmonic Generation...... 514 10.2 Parametric Oscillators ...... 518 10.3 Raman Laser...... 526 10.4 Optical Phase Conjugation ...... 535

11. Damage of Optical Elements...... 540 11.1 Surface Damage...... 541 11.2 Inclusion Damage...... 542 11.3 Self-focusing...... 543 11.4 Damage Threshold of Optical Materials ...... 549 11.4.1 Scaling Laws ...... 550 11.4.2 LaserMaterials ...... 551 11.4.3 Damage in Optical Glass ...... 552 11.4.4 Damage Levels for Nonlinear Materials...... 553 11.4.5 Laser Induced Damage in Dielectric Thin Films...... 554 11.5 System Design Considerations ...... 556

Appendix A 559 Appendix B 564

References ...... 567 Subject Index ...... 601

XII