Loser
`Engineering
`
`Kelin Kuhn
`University of Washington
`
`ASML 1123
`
`AS1\/IL 1123
`
`1
`
`

`
`Library of Congress Cataloging-in-Publication Data
`Kuhn. Kelin 1.
`Laser engineering / Kelin J. Kuhn
`.
`cm.
`Includes index.
`ISBN 0-02-366921-7 (hardcover)
`
`I. Title.
`TAl675.K84
`
`1998
`
`97-5321 1
`CIP
`
`1.Lasers——Designandconstruction.2.Nonlinearoptics.
`
`Acquisition Editor: Eric Svendsen
`Editor-in-Chief: Marcia Horton
`Production Manager: Bayani Mendoza de Leon
`Editor-in-Chief: Jerome Grant
`Director of Production and Manufacturing: David W. Riccardi
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`Full Service Coordinator: Donna Sullivan
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`Cover Designer: Bruce Kenselaar
`
`© 1998 by Prentice-Hall, Inc.
`A Pearson Education Company
`Upper Saddle River, NJ 07458
`
`All rights reserved. No part of this book may be
`reproduced, in any form or by any means,
`without permission in writing from the publisher.
`
`‘These efforts
`The author and publisher of this book have used their best efforts in preparing this book.
`include the development, research. and testing of the theories and programs to determine their effectiveness.
`The author and publisher make no warranty of any kind, expressed or implied. with regard to these programs
`or the documentation contained in this book. The author and publisher shall not be liable in any event for
`incedental or consequential damages in connection with, or arising out of, the furnishing, performance, or
`use of these programs.
`
`Printed in the United States of America
`10
`9
`8
`7
`6
`5
`4
`3
`2
`
`ISBN D-DE-3!-.ul:"lE'l-7
`
`Prentice-Hall International (UK) Lirnited,London
`Prentice-Hall of Australia Pty. Limited, Sydney
`Prentice-Hall Canada Inc., Toronto
`Prentice-Hall I-Iispanoamericana, S.A., Mexico
`Prentice-Hall of India Private Limited, New Del.hi
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`Pearson Education Asia Pte. Ltd., Singapore
`Editora Prentice-Hall do Brasil, Ltda., Rio de Ianeiro
`
`'
`
`
`
`
`
`
`
`-‘Li:-'.:au_euaaraa._.-...::m._,.1'''.’.:''--=-»_
`
`
`
`.r:\;_-‘_:,sE-E,-.':'.-"'—'.
`
`
`
`2
`
`

`
`
`
`PHEFA CE
`
`xi
`
`Organization
`
`xi
`
`Technical Background
`
`xii
`
`Pedagogy xii
`
`Scheduling xiii
`
`Acknowledgments
`
`xiv
`
`Part I Laser Fundamentals
`
`1
`
`1
`
`INTRODUCTION TO LASERS
`
`2
`
`1.1
`
`1.2
`
`1.3
`
`1.4
`
`1.5
`1.6
`
`A Brief History
`
`2
`
`The Laser Market
`
`5
`
`Energy States in Atoms
`
`9
`
`10
`Basic Stimulated Emission
`1.4.1
`Transitions Between Laser States, 10
`1.4.2
`Population Inversion, 13
`
`Power and Energy
`
`14
`
`Monochromaticity, Coherency, and Linewidth
`
`15
`
`
`
`3
`
`

`
`
`
`., A.
`
`5F.:\
`F
`
`
`
`
`
`Contents
`
`1.7
`
`1.8
`
`1.9
`
`1.10
`
`1.11
`
`Spatial Coherence and Laser Speckle
`
`18
`
`The Generic Laser
`
`19
`
`Transverse and Longitudinal Modes
`
`20
`
`The Gain Profile
`
`22
`
`Laser Safety
`
`24
`
`Symbols Used in the Chapter
`
`25
`
`Exercises
`
`26
`
`2 ENERGY STATES AND GAIN
`
`34
`
`2.1
`
`35
`Energy States
`2.1.1
`Laser States, 35
`2.1.2 Multiple-State Laser Systems, 36
`2.1.3
`Linewidth and the Uncertainty Principle, 39
`2.1.4 Broadening of Fundamental Linewidths, 41
`
`2.2
`
`Gain
`
`43
`
`Basics of Gain, 43
`2.2.1
`2.2.2 Blackbody Radiation, 47
`2.2.3 Gain. 55
`
`Symbols Used in the Chapter
`
`58
`
`Exercises
`
`59
`
`3 THE FABHY-PEHOT ETALON
`
`62
`
`3.1
`
`3.2
`
`3.3
`
`62
`Longitudinal Modes in the Laser Resonant Cavity
`3.1.1
`Using an Etalon for Single Longitudinal Mode Operation, 64
`
`65
`Quantitative Analysis of a Fabry-Perot Etalon
`3.2.1
`Optical Path Relations in a Fabry-Perot Etalon, 65
`3.2.2 Reflection and Transmission Coefficients in a Fabry-Perot Etalon, 67
`3.2.3
`Calculating the Reflected and Transmitted Intensities for a Fabry-Perot
`Etalon with the Same Reflectances, 70
`Calculating the Reflected and Transmitted Intensities for a Fabry-Perot
`Etalon with Different Reflectances, 72
`Calculating the Q and the Finesse of a Fabry-Perot Etalon, 73
`
`3.2.4
`
`3.2.5
`
`Illustrative Fabry-Perot Etalon Calculations
`
`73
`
`Symbols Used in the Chapter
`
`78
`
`Exercises
`
`79
`
`4
`
`

`
`vi
`
`Contents
`
`4 TRANSVERSE MODE PROPERTIES
`
`83
`
`4.1
`
`4.2
`
`4.3
`
`4.4
`
`4.5
`
`Introduction
`
`84
`
`84
`TEM,_, Transverse Modes
`4.2.1
`The Paraxial Approximation, 84
`4.2.2 Mathematical Treatment of the Transverse Modes, 86
`
`88
`TEMo‘o Gaussian Beam Propagation
`4.3.1
`The TEMM or Gaussian Transverse Mode, 88
`4.3.2
`Properties of the TEMM Mode of the Laser, 94
`
`Ray Matrices to Analyze Paraxial Lens Systems
`4.4.1
`Ray Matrix for a Distance d, 103
`4.4.2
`Ray Matrix for a Lens, 104
`4.4.3 ABCD Law Applied to Simple Lens Systems, 108
`
`101
`
`110
`Gaussian Beams in Resonant Cavities
`4.5.1 Modeling the Stability of the Laser Resonator, 113
`4.5.2 ABCD Law Applied to Resonators, 117
`
`Symbols Used in the Chapter
`
`122
`
`Exercises
`
`124
`
`GAIN
`
`SATURATION
`
`131
`
`5.1
`
`5.2
`
`5.3
`
`131
`Saturation of the Exponential Gain Process
`5.1.1
`Gain Saturation for the Homogeneous Line, 134
`5.1.2 Gain Saturation for the Inhomogeneous Line, 134
`5.1.3
`The Importance of Rate Equations, 134
`
`135
`Setting Up Rate Equations
`5.2.1
`Rate Equations for Four-State Lasers, 137
`
`142
`Laser Output Power Characteristics
`5.3.1
`Optimal Coupling, a Simple Approach, 142
`5.3.2
`Pom versus Pin, an Engineering Approach, 147
`5.3.3
`Pom versus Pin, the Rig-rod Approach, 152
`
`Symbols Used in the Chapter
`
`159
`
`Exercises
`
`161
`
`6 TRANSIENT PROCESSES
`
`163
`
`6.1
`
`6.2
`
`164
`Relaxation Oscillations
`6.1.1
`A Qualitative Description of Relaxation Oscillations, 164
`6.1.2 Numerical Modeling of Relaxation Oscillations, 165
`6.1.3 Analytical Treatment of Relaxation Oscillations, 171
`
`177
`Q—Switching
`6.2.1
`A Qualitative Description of Q-Switching, 177
`
`~
`
`
`
`5
`
`

`
`
`
`
`
`
`
`_.-r....._.I....-.-.----~._--.w-gt-u
`
`
`
`vii
`
`Contents
`
`6.3
`
`6.4
`
`6.2.2 Numerical Modeling of Q-Switching. 177
`6.2.3 Analytical Treatment of Q-Switching, 178
`
`182
`The Design of Q-Switches
`6.3.] Mechanical Q-Switches, 183
`6.3.2
`Electrooptic Q-Switches, 184
`6.3.3 Acousto-Optic Q-Switches, 190
`6.3.4
`Saturable Absorber Dyes for Q-Switching, 191
`
`193
`Mode—Locking
`6.4.1
`A Qualitative Description of Mode-Locking, 193
`6.4.2 Analytical Description of Mode-Locking, 195
`6.4.3
`The Design of Mode—Locking Modulators, 198
`
`Symbols Used in the Chapter
`
`202
`
`6.5
`
`Exercises
`
`204
`
`7 INTRODUCTION TO NONLINEAR OPTICS
`
`207
`
`7.1
`
`7.2
`
`7.3
`
`7.4
`
`7.5
`
`7.6
`
`Nonlinear Polarizability
`
`208
`
`209
`Second Harmonic Generation
`7.2.1
`The Process of Conversion, 210
`7.2.2
`Phase Matching, 215
`7.2.3
`Design Techniques for Frequency-Doubling Laser Beams, 220
`
`Optical Parametric Oscillators
`
`221
`
`Stimulated Raman Scattering
`
`226
`
`Self-Focusing and Optical Damage
`
`231
`
`233
`Nonlinear Crystals
`7.6.1 Major Crystals, 233
`7.6.2 Other Crystals Used in Nonlinear Optics, 235
`
`Symbols Used in the Chapter
`
`236
`
`Exercises
`
`238
`
`8 SUPPOFITIVE TECHNOLOGIES
`
`241
`
`8.1
`
`8.2
`
`8.3
`
`Introduction
`
`242
`
`242
`~Multilayer Dielectric Films
`8.2.1
`The Fundamentals of Multilayer Film Theory, 243
`8.2.2
`Anti—Reflection Coatings from Multilayer Films, 245
`8.2.3 High-Reflectance Coatings from Multilayer Films, 248
`
`252
`Birefringent Crystals
`8.3.1
`Positive and Negative Uniaxial Crystals, 252
`8.3.2 Wave Plates from Birefringent Crystals, 254
`
`6
`
`

`
`Contents
`
`vill
`
`8.4
`
`261
`Photodetectors
`8.4.1
`Thermal Detectors, 261
`8.4.2
`Photoelectric Detectors, 262
`8.4.3
`Photoconductors, 263
`8.4.4
`Junction Photodetectors, 265
`8.4.5 MOS Capacitor Devices, 268
`
`Symbols Used in the Chapter
`
`269
`
`Part II Design of Laser Systems
`
`273
`
`9 CONVENTIONAL GAS LASERS
`
`274
`
`9.1
`
`9.2
`
`274
`HeNe Lasers
`9.1.1 History of HeNe Lasers, 274
`9.1.2 Applications for HeNe Lasers, 276
`9.1.3
`The HeNe Energy States, 280
`9.1.4 Design of a Modern Commercial HeNe Laser, 283
`
`288
`Argon Lasers
`9.2.1
`History of Argon- and Krypton-Ion Lasers. 289
`9.2.2 Applications for Argon- and Krypton-Ion Lasers, 290
`9.2.3 Argon and Krypton Laser States, 292
`9.2.4 Design of a Modern Commercial Argon-Ion Laser. 294
`Exercises
`300
`
`10 CONVENTIONAL SOLID-STATE LASERS
`
`302
`
`10.1
`
`History
`
`303
`
`10.2
`
`10.3
`
`Applications
`
`307
`
`308
`Laser Materials
`10.3.1 Crystalline Laser Hosts, 309
`10.3.2 Glass Laser Hosts, 310
`10.3.3 The Shape of the Solid-State Laser Material, 311
`
`10.4
`
`The Laser Transition In Nd:YAG 312
`
`10.5
`
`315
`Pump Technology
`10.5.1 Noble Gas Discharge Lamps as Optical Pump Sources for Nd:YAG
`Lasers, 316
`
`10.5.2 Power Supplies for Noble Gas Discharge Lamps, 321
`10.5.3 Pump Cavities for Noble Gas Discharge Lamp—Pumped Lasers, 324
`10.5.4 Spectra-Physics Quanta-Ray GCR Family, 327
`10.5.5 Semiconductor Lasers as Solid-State Laser Pump Sources, 329
`10.5.6 Pump Cavities for Diode Laser Pumped Solid-State Lasers, 333
`10.5.7 Coherent DPSS 1064 Laser Family, 337
`Exercises
`338
`
`
`
`7
`
`

`
`
`
`Contents
`
`11 TRANSITION-METAL SOLID-STATE LASERS
`
`344
`
`11.1
`
`11.2
`
`11.3
`
`11.4
`
`11.5
`
`History
`
`345
`
`Applications
`
`348
`
`348
`Laser Materials
`11.3.1 Ruby—Primary Line at 694.3 nm, 349
`11.3.2 Alexandrite--Tunable from 700 nm to 818 nm, 351
`11.3.3 Ti:Sapphire—Tunab1e from 670 nm to 1090 nm, 353
`11.3.4 Comparison between Major Solid—State Laser Hosts. 355
`
`Ti:Sapphire Laser Design
`11.4.1 Ring Lasers. 356
`11.4.2 Birefringent Filters. 362
`11.4.3 Coherent Model 890 and 899 Ti:Sapphire Lasers, 365
`
`356
`
`370
`Femtosecond Pulse Laser Design
`11.5.1 Dispersion in Femtosecond Lasers, 370
`11.5.2 Nonlinearities Used to Create Femtosecond Pulses. 371
`11.5.3 Measuring Femtosecond Pulses, 373
`11.5.4 Colliding Pulse Mode-Locking, 373
`11.5.5 Grating Pulse Compression, 374
`11.5.6 Solitons, 375
`11.5.7 Kerr-Lens Mode-Locking (KLM) in Ti:Sapphire, 376
`11.5.8 Coherent Mira Femtosecond Lasers, 377
`
`Exercises
`
`380
`
`12 OTHER MAJOR COMMERCIAL LASERS
`
`384
`
`12.1
`
`12.2
`
`12.3
`
`385
`The Design of Carbon Dioxide Lasers
`12.1.1
`Introduction to CO2 Laser States, 386
`12.1.2 The Evolution of CO2 Lasers. 389
`12.1.3 Waveguide CO; Lasers. 393
`12.1.4 A Typical Modern CO2 Industrial Laser, 394
`12.1.5 Optical Components and Detectors for CO2 Lasers, 403
`
`404
`The Design of Excimer Lasers
`12.2.1
`Introduction to Excimer Laser States, 405
`12.2.2 The Evolution of Excimers, 408
`12.2.3 General Design Background, 409
`12.2.4 A Typical Modem Excimer Laser. 414
`12.2.5 Laser Beam 1-Iomogenizers, 417
`12.2.6 Application Highlight, 418
`
`421
`Overview of Semiconductor Diode Lasers
`12.3.1 History of Semiconductor Diode Lasers, 421
`12.3.2 The Basics of the Semiconductor Diode Laser, 424
`12.3.3 Confinement in the Semiconductor Diode Laser, 428
`12.3.4 The Quantum Well Semiconductor Diode Laser. 432
`12.3.5 Application Highlight: The CD Player, 435
`
`8
`
`

`
`x
`
`APPENDIX
`
`441
`
`Contents
`
`A.1
`
`A.2
`
`A.3
`
`A.4
`
`A.5
`
`A.6
`
`A.7
`
`A.8
`
`441
`Laser Safety
`A. 1 . 1
`Electrocution, 44 1
`A.1.2 Eye Damage, 444
`A.l.3 Chemical Hazards, 446
`A.l.4 Other Hazards, 447
`
`Significant Figures
`
`450
`
`450
`
`The Elecuomagnetic Wave Equation
`A.3.1 Maxwell's Equations, 450
`A.3.2 A General Wave Equation for Light Propagation in a Material, 452
`A.3.3 Light Propagation in a Vacuum, 453
`A.3.4 Light Propagation in a Simple Isotropic Material with No Net Static
`Charge, 454
`A.3.5 Light Propagation in a Simple Laser Material with No Net Static
`Charge, 454
`A.3.6 A One-Dimensional Wave Equation for a Less Simple Isotropic
`Material, 454
`
`Lenses and Telescopes
`A.4.l
`Lenses, 456
`A.4.2 Classical Lens Equations, 457
`A.4.3 Telescopes, 459
`
`456
`
`461
`
`Reflection and Refraction
`A.5.1 Nomenclature, 461
`A52 Snell's Law, 462
`A53 Total lntemal Reflection, 462
`A.5.4 Brewster’s Angle, 462
`
`Fresnel Equations
`
`463
`
`The Effective Value of the Nonlinear Tensor 465
`
`Projects and Design Activities
`A.8.l Gas Laser Activities, 466
`A.8.2 Nd:YAG Laser Activities, 472
`A.8.3 Transition Metal Laser Activities, 473
`A.8.4
`Successful Student Projects, 474
`
`466
`
`A.9
`
`Laser Alignment
`
`475
`
`A.10 Glossary of Basic Laser Terms
`
`477
`
`INDEX
`
`483
`
`CONSTANTS USED IN BOOK
`
`498
`
`
`
`
`
`_«_-_L..'n—.A.-m.D..__‘-.
`
`
`
`....- ,H_._
`
`
`
`9
`
`

`
`major laser properties for
`. alexandrite, Tizsapphirc.
`
`10
`
`10
`
`

`
`
`
`Sec. 11.1
`
`History
`
`345
`
`9
`
`phonon
`
`ll
`
`photon
`
`T
`
`The transition-metal solid-
`Figure 11.!
`state tunable lasers use metals in the founh
`row of the periodic table as the active
`ions. These metals can produce transitions
`that
`involve phonons as well as photons
`(often called vibronic or phonon-terminated
`transitions). Such transitions can create
`
`l3h°|'|0“
`
`tunable four-level laser behavior.
`
`11.1 HISTORY
`
`The history of transition-metal solid-state tunable lasers is exceptionally fascinating. For
`the l-leNe, argon-ion and Nd:YAG lasers (even the diode pumped Nd:YAG lasers) the
`majority of the laser science was in place by the mid-l960s and commercial development
`proceeded rapidly after that. Transition-metal tunable solid-state lasers are quite different.
`Transition-metal tunable solid-state lasers are barely mentioned in review papers on tunable
`laser technology as recently as 1982.‘
`Ti:sapphire lasers (the current stars of the solid-state tunable laser market) were discov-
`ered by Moulton in 1982.2 However, early results with Tizsapphire were not promising due
`to difficulties with material growth? It was only after the materials problems were solved
`that the true potential of the Tizsapphire laser was realized. As a consequence. much of
`the laser development (including the remarkable self-mode-locking properties of Tizsapphire
`discussed in Section 11.5) has occurred relatively recently.
`The transition-metal solid-state tunable lasers use metals in the fourth row of the
`periodic table as the active ions. The transition-metals have a partially filled 3d shell. and
`the various observed transitions occur near this shell. 3d electrons interact more strongly
`with the crystal field than the 4f electrons in conventional solid-state lasers such as Nd:YAG.
`This can produce transitions that involve phonons as well as photons (often called vibronic
`or phonon-tenninated transitions). Such transitions are rather peculiar, as they can create
`four-level laser behavior between two level transitions. A schematic of a vibronic transition
`is illustrated in Figure l1.l.
`In a vibronic transition an optical photon is used to make the transition from the ground
`state to the pump state. Then the electron decays to the upper laser state by releasing a
`phonon (an acoustical quanta similar to a photon). The laser action occurs between the upper
`and lower laser states. The lower laser state then decays to the ground state by releasing
`
`
`
`B. D. Guenther and R. G. Buscr, IEEE J. of Quantum Electron. QE-18:1 179 (I982).
`3P. F. Moulton. Solid State Research Report. D'l1C AD-Al24305I4 (19823) (Lexington: MIT Lincoln Lab .
`I982). pp. 15-21.
`‘P. Lacovara and L. Esterowitz. IEEE J. of Quantum Electron. QE-2l:l6l4 (1985).
`
`11
`
`11
`
`

`
`346
`
`laser action is possible.
`The first vibronic laser was reported by Johnson et al. at B
`ell Laboratories in 1963.‘
`It was a divalent transitiomnetal laser using Ni“ in MgF2.
`It stimulated some early work
`by McCumber in the theory of vibronic lasers.’ However,
`it was cryogenically cooled and
`did not excite much commercial interest.
`Further efforts by Johnson and his colleagues during the mid to late 1960s resulted in
`several more cryogenically cooled divalent transition-metal lasers. These included Co“ in
`MgF2 and V24’ in MgF-2.‘
`A major advancement occurred in 1976 when M
`drite (BeAl;O4:Cr-3+ or chromium doped chrysoberyl
`would lase on a vibronic tran '
`'
`Q-switching behavior.‘ Ale
`
`'
`
`The successful use of Cr-""' in a beryl crystal led to several other interesting vibronic
`lasers.
`In particular.
`in 1982 Shand and Walling,” and independently Buchert et al.."
`showed that emerald (Be3Al2(SiO3):Cr-"*, another type of chromium-doped chrysoberyl and
`tunable from roughly 700 nm to 800 nm)
`'
`'
`Chromium was also found to g
`gallium garnet (GSGG).”
`These encouraging results in chromium
`solid-state laser research. Ti:sapphire (the cm
`
`—doped materials led to a rebirth in tunable
`wn jewel of modern tunable solid-state lasers)
`
`.________._____
`
`‘L. F. Johnson. R. E. Dletz. and H. J. Guggenheim.
`‘D. E. McCurnber. Phys. Rev.
`l34:A299 (I964);
`Mr:Cumber, Phys. Rev.
`l36:A954 (1964).
`‘L. F. Johnson. R. E. Dietz. and H. J.
`Guggenheim. Appl. Phys. Lert. 5:2l (I964); L. F. Johnson and H. J.
`and H. J. Guggenheirrnl. Appl. Phys. 38:483'l' (1967):
`Guggenheim.J. Appl. Phys. 38:-1837 (1967):
`L. F. Johnson
`and L. F. Johnson. H. J. Guggenheim and R. A. Thomas. Phys. Rev.
`l49:I79 (I966).
`7R. C. Morris and C. F. Cline. "Chromium-Doped Beryllium Aluminate Lasers.
`Dec. 14. I916.
`
`Phys. Rev. Lett. Il:3l8 (I963).
`D. E. McCumber. J. Math. Phys. 5:508 (I964): and D. E.
`
`" U.S. Patent #3.997.853,
`
`Lert. 4:182 (I979); J. C. Walling. 0. G. Peterson. H. P. Jenssen.
`Electron. QE-l6:l3D2 (I980): and C. L. Sam. J.
`Soc. Photo-Opt. Inst. Eng. (SPIE) 247:l30 (198
`“M. r.. Shad and H. Jenseen. IEEEJ. of
`Quantum Electron. QE-l9:48Cl (I983).
`"M. Shand and J. Walling.
`IEEE J. afQuar:rtmr Electron. QE-I8: I829 (1982).
`"J. Buclrert. A. Katz. and
`R. R. Alfano. IEEE J. of Quantum Electron. QE-
`
`
`
`12
`
`12
`
`

`
`
`
`Sec. 11.2
`
`Applications
`
`347
`
`was discovered in I982 by Moulton at MIT Lincoln Labs.” Although sapphire is the oldest
`laser material (ruby is Cr“ in sapphire) the discovery of the broadly tunable nature of Ti“
`in sapphire was quite unexpected. A review report on tunable solid-state lasers published in
`I982” and a review paper on alexandrite lasers in 1985” do not even mention Tizsapphire.
`Part of the delay in Ti:sapphire emerging as a viable commercial tunable solid-state
`laser was materials-based. Early Ti:sapphire crystals showed an absorption at the lasing
`wavelengths that was approximately an order of magnitude higher than the absorption in
`high-quality sapphire. A number of possible defects were proposed” and after much inves-
`tigation the residual absorption in vertical-gradient-freeze (VGF) crystals was shown to be
`due to quadruply ionized titanium (Ti“) substituting for the aluminum in the sapphire.”'“’
`Growth and annealing methods have significantly reduced this problem in modem commer-
`cial Ti:sapphire material.
`In spite of its many advantages. Ttsapphire does suffer from a few disadvantages. In
`particular. its short upper state lifetime (3.2 us) makes it quite difficult to pump with a lamp.
`Although lamp-pumped Titsapphire lasers have been built.” most commercial Tizsapphire
`lasers are pumped with argon-ion or doubled Nd:YAG lasers.
`Several other materials have seen some commercial interest as possible lamp pumped
`laser materials. In particular LiCaAlF5:Cr3+ and LiSrAlF5:Cr3"' have seen some interest as
`possible tunable commercial laser sources.” A number of other chromium-doped materials
`including Crzforsterite and Cr:YAG are also showing strong potential.“
`Transition-metal solid-state tunable lasers are still being actively developed. Bamesn
`and Budgor et at.” provide good overview treatments of this developing field. In addition.
`there are three special issues in IEEE journals on tunable lasers?“
`
`"P. F. Moulton. Solid State Research Report. DTIC AD-A124305I4 (l982:3) (MIT Lincoln Lab.. Lexington.
`I982). pp.
`I5-2!. reported by P. F. Moulton. "Recent Advances in Solid-State Lasers." Proc. Con. Lasers
`Electra-opr.. Anaheim. CA. 1984. paper WA2.
`"B. D. Guenther and R. G. Buser. IEEE J. of Quantum Electron. QE-18: I 179 (I932).
`'51. C. Walling. D. F. Heller. H. Sarnelson. D. J. I-larter. J. A. Pete. and R. C. Morris. IEEE J. of Quantum
`Eh-crran. QB-2 1 : I568 ( 1985).
`"P. Lacovara and L. Esterowitz. IEEE J. of Quantum Electron QE—2l:l614 (I985).
`"A. Sanchez. A. J. Strauss. R. L. Aggarwal. and R. E. Fahey. IEEE J. of Quantum Electron. 24:995 (1988).
`“R. Aggarwal. A. Sanchez. M. Stuppi. R. Fahey. A. Strauss. W. Rapoport. and C. Khattak. IEEE J. of
`Quantum Electron. 24:l003 U938).
`l0:2'I3 (I985).
`'91’. Lacovara. L. Esterowitz and R. Allen. Opt. Leu.
`2°S. A. Payne. L. L. Chase. H. W. Newkirk. L. K. Smith. and W. F. Krupke. IEEE J. of Quantum Electron.
`24:2243 (1938): and S. A. Payne. L. L. Chase. L. K. Smith. W. L. Kway. and H. W. Newldrk. J. Appl. Phys.
`66:I05I (I989).
`
`“C. Pollock. D. Barber. J. Mass. and s. Markgraf. 151:5 J. ofSel. Topics in Quantum Electron. 1:52 (I995).
`32Norrnan P. Barnes. "Transition Metal Solid State Lasers." in Tunable Losers Handbook. ed F. .l. Duane
`(San Diego: Academic Press. 1995).
`
`“A. Budgor. L. Estcrowtiz. and L. G. DeShazer. eds. Tunable Solid State Laser: 1! (Berlin: Springer Verlag.
`1936).
`
`141555 J. of Quantum Electron. QE-18 (I982); QE-2| uses); and IEEE J. of Sci. Topics in Quantum
`Electron. (I995).
`
`13
`
`13
`
`

`
`348
`11.2 APPLICATIONS
`
`Transition-Metal Solid-State Lasers
`
`Chap. 11
`
`extremely short pulses.
`The tunability feature means that these lasers are ideal for spectroscopic applications.
`This not only includes traditional scientific spectroscopy. but also medical diagnostic spec-
`troscopy. For example, Ti:sapphire lasers have been used to perform an optical version of
`conventional mammography.” There are also potential applications for absorption, Raman.
`and fluorescence spectroscopy in medical imaging.”
`
`telangiectasia. warts. stretch marks. acne scars, removing tattoos, and psoriasis.” Tunable
`solid-state lasers also compete with dye lasers for medical applications such as shattering
`kidney stones.“
`In addition.
`the extremely short pulses possible with tunable solid-state lasers are
`finding application in micromachining. Ferntosecond-pulsed T'i:sapphire lasers can be used
`for micromachining holes in metal and polymer substrates as well as for ablating pho-
`toresist films and cutting traces on semiconductor materials.” Tizsapphire lasers compete
`with Nd:YAG. diode-pumped Nd:YACi. and excirner lasers for this extremely important
`
`market.
`
`11.3 LASER MATERIALS
`
`A number of publications can provide additional information for the interested reader.
`Overview treatments are given by Weber.” Koechner.“ and Duane.” while more specific
`
`__________.__..
`
`25b:rser Focus World. Feb.: 33 (1996).
`3°I41ser Focus World. Feb.: 72 (I996).
`”La:er Focus World. May: 66-7 (I996).
`:3Laser Focus World. May: 66-7 (1996).
`“Laser Focus Worid. January: 22 (I996).
`“Marvin I. Weber. ed. Handbook oflaser Science and Tecltnology. Vol. 1. laser: andMaser: (Boca Raton.
`FL: CRC Press. lnc.. I982): and more recently. Marvin J. Weber. ed, Handbook afLaserScience and Technology.
`Supplement I. Lasers (Boca Raton. FL: CRC Press. Inc.. I991).
`3' Walter Koechner. SolidStare Laser Engineering. 4th ed. (Berlin: Springer-Verlng. I996).
`
`
`
`14
`
`14
`
`

`
`
`
`Sec. 11.3
`
`Laser Materials
`
`349
`
`ruby.
`
`Figure 11.2
`
`The energy band diagram for
`
`information can be obtained from the wide variety of review papers on alexandrite” and
`Ti:sapphire.34'35 Manufacturer data sheets and application notes are also very useful.“
`
`11.3.1 FIuby—Pr|mary Line at 594.3 nm
`
`Ruby (chromium-doped A1203) is a red or pink hexagonal crystal whose most familiar appli-
`cation is jewelry. Ruby is an optically uniaxial crystal” that is hard (Moh's hardness of 9).
`of good optical quality. and extremely thenrially conductive (0.42 Wlem-K at 300K). Ruby is
`nonhygroscopic. refractory. and is generally considered the most durable of the common laser
`crystals (with the possible exception of Tizsapphire). Ruby crystals are typically grown by the
`Czochralski method (the same method as used for the growth of silicon). Ruby can be grown
`at 0. 60. or 90 degrees to the optic axis. and laser material is usually grown at 60 degrees.
`Sapphire is doped with Cr” to obtain ruby. The Cr“ substitutes for the Al“ in the
`crystal. Typical dopings are 0.05 weight percent of CF20}. However. excess chromium can
`distort the crystal structure and concentrations are sometimes reduced to 0.03 weight percent
`to enhance the optical beam quality.
`The energy diagram for ruby is given in Figure 11.2. Ruby is three-state and is the
`only commercially viable three-state laser system. The laser pump bands are principally
`the ‘F; and the ‘F; bands. The ground state is the ‘A; band. The two pump bands form
`manifolds centered around the blue (400 nm) and green (555 nm). The pump bands are
`
`315.1. Duarte ed, Tumble Laser: Handbook (San Diego: Academic Press I995).
`33:. c. Walling. o. F. Heller. H. Sarnelson. o. l. Harter. r. A. Pete. and R. c. Morris. IEEE J. of Quantum
`Electron. QE-21:l568 (1985).
`“A. Sanchez. A. J. Strauss, R. L. Aggarwal. and R. E. Fahey. IEEE J. ofguanrum Electron. 24:99!) (1938).
`
`35R. Aggarwal. A. Sanchez. M. Stuppi. R. Fahey, A. Strauss. W. Rapoport, and C. Khattak. IEEE J. of
`Quantum Electron. 2421003 ([988).
`
`“Major crystal suppliers are Union Carbide (ruby. alexandrite and Tizsapphire) and Litton Airtron
`(alexandrite).
`
`37A uniaxial crystal is one where two of the Cartesian directions have one index of refraction ii. and the third
`has a different index of reI'rai:tiori in. See Section 8.3 for a discussion of uniaxial and biaxial crystals.
`
`15
`
`15
`
`

`
`Chap. 11
`Transition-Metal Solid-State Lasers
`350
`each quite wide. with the blue band about 0.05 microns wide and the green band about 0.07
`microns wide.
`The lifetime in the pump bands is extremely short, with the ions cascading almost
`immediately to the metastable IE states. The upper 2E state is termed the 2?? state and the
`lower is termed the E state. The 23 and 2'' states are separated by 29 cm", which gives
`a population ratio at thenrtal equilibrium of 87%. Thus. while fluorescence in ruby occurs
`from both the 23- state to the ‘A2 (termed the R; transition at 692.9 nm) and from the E
`state to the ‘A2 (termed the R. transition at 694.3 nm), laser action first occurion the R_1
`
`line by special dielectric coated minors or internal
`on the R; line is to suppress the R;
`cavity absorbers.
`(Interesting enough. even though lasing occurs primarily on the R; and
`R; lines, sidebands have been observed on the long wavelength side, in particular at 767
`
`21
`
`.5
`1.0
`0'7
`0.5
`0.4
`9;,
`0.2
`
`0.15 -°
`
`=9;
`0
`$
`'9
`.3
`0.
`£3
`E
`§
`
`w 2
`
`0.1
`
`0.07
`
`0.4
`
`0.3
`_ 0.2
`—.
`5
`? 01
`E 07
`.3 °-
`§ 0.05
`5 0.04
`E1003
`Q 0.02
`
`Pink ruby
`laser rod
`
`
`
`am
`0.007
`
`6860
`
`6850
`
`6900
`
`0.05
`
` 0.04
`6920
`6940
`6960
`6980
`7000
`7020
`Wavelength A [A]
`
`
`
`Figure 11.3 Since ruby is uniaxial. its absorption coefficient is a very strong function
`of the polarization direction of the light.
`(From D. C. Cronerneyer. J. Opt. Soc. Am.
`56:l703 (I966). Reprinted with the pennission of the Optical Society of America.)
`
`
`
`16
`
`16
`
`

`
`
`
`i
`
`-."I\.'___
`
`Sec. 11.3
`
`Laser Materials
`
`351
`
`Yellow
`
`Laser 1
`
`5: V"’'°''''°
`E
`
`Figure 11.4 The energy band diagram for
`alexandrite.
`
`11.3.2 Alexandrlte—Tunable from 700 nm to 318 nm
`
`Alexandrite (BeAlgO4:Cr3"‘ or chromium-doped chrysoberyl) is a hard orthorhombic mate-
`rial. Chrysoberyl itself is considered a semiprecious jewelry material and is commonly called
`oriental topaz. It ranges in color from yellow through green to brown. When chrysoberyl is
`doped with chromium, the material turns emerald green and displays a secondary red color
`when viewed in artificial light. (As an aside. one variety of chrysoberyl occurs in a crystal
`form consisting of parallel arrangements of fibers. When out as a cabochon, it is called
`cat's-eye or tiger’s-eye.)
`Alexandrite is biaxial,” hard, of good optical quality. and quite thermally conductive
`(0.23 Wlcm-K as compared with 0.14 Wlcm-K for YAG and 0.42 W/cm-K for ruby).
`Alexandrite is nonhygroscopic. melts at l8'l0°C. and has a Moh’s hardness of 8.5 (which
`makes it harder and more durable than YAG. but somewhat less than ruby). Additionally.
`alexandrite has a very high thermal fracture limit (60% of ruby and five times that of YAG).
`Doping the yellowish chrysoberyl with chromium results in an emerald green alexan-
`drite crystal. Alexandrite is biaxial and the crystal appears green. red, or blue. depending on
`the angle and lighting conditions. The principle axes of the indicatrix are aligned with the
`crystallographic axes.” Lasers are usually operated with light parallel to the b-axis because
`the gain for polarization in this direction is roughly ten times that of any other direction.
`As with ruby. the C1“ occupies the aluminum sites in the crystal. However. there are
`two different aluminum sites in alexandrite. One site has mirror symmetry. the other has
`inversion symmetry. Most of the chromium substitutes for aluminum in the larger mirror
`site (about 78%). which (luckily!)
`is the dominant site for laser action. The doping in
`alexandrite can be a great deal higher than with ruby. Doping concentrations as high as 0.4
`weight percent still yield crystals of good optical quality (although 0.2 to 0.3 weight percent
`is somewhat more common).
`
`The energy diagram for alexartdrite is given in Figure 11.4. Aleigandrite can be
`operated as either a three-state system or as vibronic four-state system (note the similarity
`to rubyl). The laser pump bands are principally the ‘T; (higher) and the ‘T2 (lower) bands.
`The ground state is the ‘A; band. The two pump bands form manifolds centered around
`
`“A biartial crystal is one where all three of the Cartesian directions have different indices of refraction. See
`Section 8.3 for a discussion of uniarrial and biaxial crystals.
`“See Section 8.3 for more discussion on the indicatrirt.
`
`17
`
`17
`
`

`
`Transition-Metal Solid-Stale Lasers
`352
`the blue (410 um) and yellow (590 nm). The pump bands are each quite wide. with widths
`
`approximately 1000 angstroms.
`In a fashion similar to rub
`
`
`
`18
`
`18
`
`

`
`
`
`sec. 11.3
`
`Laser Materials
`
`353
`
`Alexandrite
`0.063 atomic 79 Cr“
`
`For Polarization:
`
`Since alexandrite is biaxial.
`Figure 11.5
`its absorption coefficient is a very strong
`function of the polarization direction of the
`light. for all three directions.
`(Modified
`from J. C. Walling. H. P. Jenssen. R. C.
`Morris. E. W. O‘Dell. and O. 0. Peterson.
`Opt. Lett. 4:l82( 1979), Figure 3. Reprinted
`700 with the permission of the Optical Society
`at America).
`
`‘
`
`400
`
`500
`Wavelength [nm]
`
`600
`
`Since alexandrite is biaxial, its absorption coefficient is a very strong function of the
`polarization direction of the light. in all three directions!
`(See Figure ll.5.) This creates
`some of the same orientation and pumping inhomogeneities observed in mby.
`
`11.3.3 Tl:sapphlre—Tunab|e from 670 nm to 1090 I'll'l1
`
`Ti:sapphire was developed relatively late in laser evolution. However. since the discovery
`of laser action in Ti:sapphire in 1982. Tizsapphire has become one of the most widely used
`solid-state laser materials.
`
`Recall that ruby is chromium-doped M203. Ti:sapphire is titanium-doped Al-303.
`Thus. ruby and Tizsapphire have many of tlte same mechanical and optical properties.
`'I'i:sapphire is also an optically uniaxial crystal that is hard (Moh's hardness of 9). of good
`optical quality. and extremely thermally conductive (0.42 Wlcm-K). Ti:sapphire is nonI1y-
`groscopic. refractory and is even more durable than ruby due to a slight advantage obtained
`with the titanium doping.
`Sapphire is doped with Ti“ to obtain laser quality Tizsapphire. The Ti“ substitutes
`for the Al“ in the crystal. Typical dopings range from 0.03 to 0.15 weight percent of
`titanium (slightly higher than the chromium in ruby). However. the similarities between
`ruby and Tizsapphire do not include the spectroscopy. The energy diagram for Tizsapphire
`(Figure ll.6) possesses only two states, but the vibronic nature of the transitions makes it
`possible to absorb from the bottom of the ground state to the upper vibronic manifold and
`to lase from the bottom of the upper vibronic manifold down to the vibronic ground states.
`This peculiar spectroscopy is driven by the single (3d)‘ electron. The (3d)' state
`(which would be degenerate in a free transition-metal) is split by the cubic field when the
`metal is substitutionally doped into the aluminum site in the sapphire. The result is a doubly
`degenerate excited state 2E3 and a triply degenerate ground state 3T;g. These excited and
`ground states are further split by the ttigonal field and spin orbit coupling. The result is a
`bottom manifold of states 3755. and a top manifold 215,. One phonon of energy 172 cm"
`couples to the excited state 3E, state and two phonons with energies of 220 and 260 cm"
`couple to the ground state 2T1g.
`(In comparison. ruby has three Cl I=|=Cl|’0I'5 and 3 1'33""
`more conventional energy state diagram!)
`
`19
`
`19
`
`

`
`354
`
`Transition-Metal Solid-State Lasers
`
`Chap. 11
`
`E",
`Em
`
`
`
`-'35,
`35
`._____.___.
`
`2
`
`2A‘
`.’—" '
`E‘
`.__._j——¢' 25
`
`
`
`
`251:2
`
`u
`
`. "-—"—:
`
`“”“' Era
`
`Figure 11.6
`Tt':sapphire.
`
`The energy band diagmm for
`
`rr Polarization
`
`
`
`
`
`PA
`
`Absorbance
`
`0.2
`
`1.0
`Intensity[arb.units] 09chas
`
`
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`
`Fluorescence
`
`500
`
`600
`
`700
`
`800
`
`Wavelength [nm]
`
`Ti:sapphlre possesses very
`Figure 11.7
`large polarintion-dependent absorption
`bands in the blue-green (centered around
`490 nm with widths of roughly I50 nm).
`Similarly. Ti:sapphire possesses very large
`polarization dependent emission bands in
`the redIIR (centered amund 780 nm with
`widths of roughly 230 nm).
`(From P. F.
`Moulton. J. Opt. Soc. Am. B 3:125 (1986).
`Reprinted with the permission of