Loser
`Engineering
`
`Kelin Kuhn
`University of Washington
`
`i
`
`ASML 1122
`ASML 1122
`
`

`
`Library of Congress Cataloging-in-Publication Dal:
`Kuhn. Kelin J.
`Laser engineering I Kelio J. Kuhn
`.
`crn.
`Includes index.
`ISBN 0-02-36692!-7 (hardcover)
`
`I. Title.
`TA16'}'S.K84
`
`I 993
`
`97-5321 1
`CH’
`
`l.Lasers——Designandconstruction.2.Nonlinearoptics.
`
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`
`Printed in the United States of America
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`ISBN D-EIE-Ell.-aE‘|E1.-7
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`Prentice-Hail International (UK) Limited,l'..ondon
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`p
`
`''---
`
`"—::; k1!*——
`'.::_.'.'.'.1.-.un-t:u;_
`
`
`
`ii
`ii
`
`

`
`PREFACE
`
`xi
`
`Organization
`
`xi
`
`Technical Background xii
`
`Pedagogy
`
`xii
`
`Scheduling
`
`xiii
`
`Acknowledgments
`
`xiv
`
`Part I Laser Fundamentals
`
`1
`
`1
`
`JNTHODUCTION 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
`
`

`
`
`
`Contents
`
`1.".-'
`
`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
`
`Syrnbols Used in the Chapter
`
`25
`
`Exercises
`
`26
`
`2 ENERGY STATES AND GAIN
`
`34
`
`2.1
`
`2.2
`
`35
`Energy States
`2.1.1
`Laser States, 35
`2.1.2
`Multiple-State Laser Systems. 36
`2.1.3
`Line-width and the Uncertainty Principle. 39
`2.1.4
`Broadening of Fundamental Linewidths, 41
`
`Gain 43
`2.2.1
`2.2.2
`2.2.3
`
`Basics of Gain. 43
`Blackbody Radiation, 47
`Gain. 55
`
`Symbols Used in the Chapter
`
`53
`
`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, 6?
`3.2.3
`Calculating the Reflected and Transmitted Intensifies for a Fabry-Perot
`Etalon with the Same Reflectances. 70
`Calculating the Reflected and Transmitted Intensities for a Fabry-Perot
`Etalon with Dilferent Refleclances. 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
`
`

`
`vi
`
`Contents
`
`4 TFIANSVEHSE MODE PROPERTIES
`
`83
`
`4.1
`
`4.2
`
`4.3
`
`4.4
`
`4.5
`
`Introduction
`
`34
`
`84
`TEM,.,,. Transverse Modes
`4.2.1
`The Pa:-axial Approximation. 84
`4.2.2 Mathematical Treatment of the Transverse Modes. 86
`
`88
`TEMQQ Gaussian Beam Propagation
`4.3.1
`The TEM.;_., or Gaussian Transverse Mode. 88
`4.3.2
`Properties of the TEM¢_.;. Mode of the Laser. 94
`
`Ray Matrices to Analyze Paraxial Lens Systems
`4.4.1
`Ray Matrix for a Distance :1, 103
`4.4.2
`Ray Matrix for a Lens. 104
`4.4.3 ABCD Law Applied to Simple Lens Systems, 103
`
`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. 11'.-'
`
`Symbols Used in the Chapter
`
`122
`
`Exercises
`
`124
`
`5 GAIN
`
`SA TURATION
`
`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. I34
`
`135
`Setting Up Rate Equations
`5.2.1
`Rate Equations for Four-State Lasers, 13?
`
`142
`Laser Output Power Characteristics
`5.3.1
`Optimal Coupling. a Simple Approach, 142
`5.3.2
`P,“ versus Pg... an Engineering Approach. 14?
`5.3.3
`Pam versus Pin. the Rigrod 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. I71
`
`1'.-'7
`Q-Switching
`6.2.1
`A Qualitative Description of Q-Switching. 177
`
`-
`
`
`
`

`
` _
`
`Contents
`
`6.2.2 Numerical Modeling of Q-Switching. 177
`6.2.3 Analytical Treatment of Q-Switching, I78
`
`6.3
`
`182
`The Design of Q-Switches
`6.3.1 Mechanical Q-Switches, 133
`6.3.2
`Electrooptic Q-Switches. 184
`6.3.3 Acousto-Optic Q-Switches. I90
`6.3.4
`Saturable Absorber Dyes for Q-Switching. 191
`
`6.4
`
`193
`Mode-Locking
`6.4.]
`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
`
`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
`
`Se1f~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
`
`SUPPORTIVE TECHNOLOGIES
`
`241
`
`8.1
`
`3.2
`
`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 Uniaxiai Crystals. 252
`8.3.2 Wave Plates from Birefringent Crystals. 254
`
`.4....
`
`
`
`iI
`
`I il
`
`

`
`Contents
`
`vill
`
`8.4
`
`261
`Photodetectors
`8.4.1
`Thennal Detectors. 261
`8.4.2
`Photoelectric Detectors. 262
`8.4.3
`Photoconductors, 263
`8.4.4
`Junction Photodetectors. 265
`8.4.5
`M08 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
`I-ieNe Lasers
`9.1.1
`History of HeNe Lasers. 274
`9.1.2
`Applications for I-1eNe Lasers. 276
`9.1.3
`The HeNe Energy States. 280
`9.1.4
`Design of a Modern Commercial HeNe Laser. 233
`
`283
`Argon Lasers
`9.2.1
`History of Argoa- 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
`
`History
`
`303
`
`Applications
`
`307
`
`308
`
`Laser Materials
`10.3.1
`10.3.2
`10.3.3
`
`Crystalline Laser Hosts. 309
`Glass Laser Hosts. 310
`The Shape of the Solid-State Laser Material. 311
`The Laser Transition In Nd:YAG 312
`
`5-.
`5
`;
`
`10.1
`
`10.2
`
`10.3
`
`10.4
`
`10.5
`
`
`
`315
`Pump Technology
`10.5.1
`Noble Gas Discharge Lamps as Optical Pump Sources for Nd:YAG
`Lasers. 316
`Power Supplies for Noble Gas Discharge Lamps. 321
`Pump Cavities for Noble Gas Discharge Lamp—Pumped Lasers. 324
`Spectra-Physics Quanta—Ray GCR Family, 327
`Semiconductor Lasers as Solid-State Laser Pump Sources, 329
`Pump Cavities for Diode Laser Pumped Solid-State Lasers. 333
`Coherent DPSS 1064 Laser Family. 33'?
`
`10.5.2
`10.5.3
`10.5.4
`10.5.5
`10.5.6
`10.5.7
`
`Exercises
`
`338
`
`

`
`
`
`Contents
`
`'11 TRANSITION-METAL SOLID-STATE LASERS
`
`344
`
`11.1
`
`11.2
`
`11.3
`
`11.4
`
`11.5
`
`History
`
`345
`
`348
`Applications
`Laser Materials
`343
`11.3.1 Ruby——Prirnar_y Line at 694.3 nm, 349
`11.3.2 Alexandrite—Tunable from 700 nm to 818 nm. 351
`11.3.3 '1"i:SappI1i.re—Tunab1e from 670 nm to 1090 nm. 353
`11.3.4 Comparison between Major Solid-State Laser Hosts. 355
`
`Ti:Sapph'1re Laser Design
`11.4.1 Ring Lasers. 356
`11.4.2 Birefringent Filters. 362
`11.4.3 Coherent Model 890 and 899 Tirsapphire Lasers, 365
`
`356
`
`370
`Ferntosecond Pulse Laser Design
`11.5.1 Dispersion in Femtosecond Lasers, 370
`11.5.2 Noniinearities Used to Create Ferntosecond Pulses. 371
`
`11.5.3 Measuring Femtosecond Pulses. 373
`11.5.4 Coiliding 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 '1'i:Sapph.ire. 376
`11.5.3 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 C02 Laser States. 386
`12.1.2 The Evolution of C0; Lasers. 389
`12.1.3 Waveguide CO; Lasers. 393
`12.1.4 A Typical Modem C03 Industrial Laser. 394
`12.1.5 Optical Components and Detectors for CO2 Lasers, 403
`
`404
`The Design of Excirner Lasers
`12.2.1 Introduction to Excimer Laser States. 405
`12.2.2 The Evolution of Excirners. 408
`12.2.3 General Design Background. 4-09
`12.2.4 A Typical Modern Excimer Laser. 414
`12.2.5 Laser Beam Hornogenizers. 41?
`12.2.6 Application 1-Iighlight, 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 P1-ayer, 435
`
`

`
`3;
`
`APPENDIX
`
`441
`
`Contents
`
`A.1
`
`A2
`
`A3
`
`A.4
`
`A.5
`
`A.6
`
`A}?
`
`A.3
`
`A.9
`
`441
`Laser Safety
`All
`Electrocution. 441
`24.1.2
`Eye Damage, 444
`A.1.3 Chemical Hazards. 446
`A.l.4 Other Hazards. 447
`
`Significant Figures 450
`
`450
`
`The Electromagnetic Wave Equation
`A.3.1 Maxwell's Equations, 450
`A32 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
`24.4.3 Telescopes. 459
`
`456
`
`Reflection and Refraction
`A.5.l Nomenclature. 46!
`A.5.2
`Snell's Law, 462
`
`461
`
`A.5.4 Brewster’s Angle. 462
`
`A.5.3 Total Internal Reflection. 462
`Fresnel Equations
`463
`
`The Effective Value of the Nonlinear Tensor 465
`
`466
`
`Projects and Design Activities
`A.B.l Gas Laser Activities, 466
`A.B.2 Nd:YAG Laser Activities, 472
`)\.8.3 Transition Metal Laser Activities. 473
`A.8.4
`Successful Student Projects. 474
`Laser Alignment
`4'75
`
`!
`
`{
`l
`
`"
`-
`
`A.l0 Glossary of Basic Laser Terms 4??
`
`INDEX
`
`483
`
`CONSTANTS USED IN BOOK
`
`498
`
`
`
`

`
`This material may be protected by Copyright law (Title 17 U.S. Code)
`
`

`
`Sec. 11.1
`
`History
`
`345
`
`phonon
`
`7/;
`
`photon
`
`The transition-metal solid-
`Figure IL!
`state tunable lasers use metals in the fourth
`
`row of the periodic table as the active
`ions. These metals can produce transitions
`
`2T
`
`29'
`
`11.1 HISTORY
`
`by —*-‘T-—*
`
`phonon
`
`that
`
`involve phonons as well as photons
`
`(often called vibronic or phonon—termina1ed
`
`transitions). Such transitions can create
`tunable four-level laser behavior.
`
`The history of transition-metal solid-state tunable lasers is exceptionally fascinating. For
`the HeNe, 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-1960s 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 !ase1's {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 Ti:sapphire laser was realized. As a consequence, much of
`the laser development (including the remarkable self-mode-locking properties of Tizsapphire
`discussed in Section 1 l.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 lase1's such as Nd:YAG.
`This can produce transitions that involve phonons as well as photons (often called vibronic
`or phonorI—terrninated 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 ll.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
`
`'13. D. Guenther and R. G. Buser. IEEE J. ry'Qmtrt.'m.u E.’e(:r:'tm, QE—l8:l I79 (I982).
`2P. F. Moulton. Solid Stare Rese-air}: Report. DTIC AD—A]2:l3l'lS!4 (19823) (Lexington: MIT Lincoln Lab.
`I982). pp.
`l5—2|.
`3?. Lacovara and L. Eslcrowilz. IEEE J. ofQnmimm Electron. QE-2l:l6l4 (I985).
`
`

`
`346
`
`-
`
`Transition-Metal Solid-State Lasers
`
`Chap. 11
`
`another phonon. Thus, four-state laser behavior is obtained from a system that is effectively
`two-state. More importantly, since a wide variety of phonon transitions are possible, the
`upper and lower laser states consist of large manifolds of states. Therefore, highly tunable
`laser action is possible.
`The first vibronic laser was reported by Johnson et al. at Bell Laboratories in 1963.4
`It was a divalent transition-metal laser using Ni“ in MgFg.
`It stimulated some early work
`by McCumber in the theory of vibronic lasers.-l 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
`MgFg and V“ in MgF2.6
`A major advancement occurred in 1976 when Morris and Cline? observed that a1exan-
`drite (BeA1;04:Cr3"” or chromium doped chrysoberyl,
`tunable from 700 nm to 8l8 nm)
`would lase on a vibronic transition. Walling et al. confirmed these results and demonstrated
`Q-switching behaviorf‘ Alexandrite was particularly interesting at the time of its discov-
`ery because it lased at t'oom temperature and increased in output power as the temperature
`increased.”
`
`in a beryl crystal led to several other interesting vibronic
`The successful use of Cr3"'
`lasers.
`In particular,
`in 1932 Shand and Walling,” and independently Buchert et £11.,”
`showed that emeraid [BB3AI2{Si03)IC1‘3+, another type of chromium-doped chrysoberyl and
`tunable from roughly 700 nm to 800 nm) would lase as a vibronic laser at room temperature.
`Chromium was also found to generate vibronic laser performance in gadolinium scandium
`gallium garnet (GSGG}.'3
`These encouraging results in chromium—doped materials led to a rebirth in tunable
`so1id—state laser research. Ti:sapphire (the crown jewel of modern tunable solid-state lasers}
`
`"'L. F. Johnson, R. E. Dietz, and H. J. Guggenheiin, Phys. Rev. Lett. 1I:318 (1963).
`5D. E. McCumber, Pity.-r. Rev. 134:A299 (1964); D. E. McCumber. J. Matti. Pt't_\'.v. 5:508 (1964): and D. E.
`McCumber. Pttrs. Rev. 136:A954 (1964).
`
`6L. F. Johnson, R. E. Dietz, and H. J. Guggenheim, Appt. Phys. Lett. 5:21 (1964): L. F. Johnson and H. J.
`Guggenheim, J. App}. Phys. 38:483':' (196?-'); L. F. Johnson and H. J. Guggenheim. J. Appt. PJl_\‘.!'. 38:4B3't' (I961):
`and L. F. Johnson, H. J. Guggenheim and R. A. Tltontas, Pttys. Rev.
`I49:l79 (1966).
`7R. C. Morris and C. F. Cline, “Chromium—Doped Beryllium Aluminate Lasers," U.S. Patent #3,99't'.853,
`Dec, 14. 1976.
`
`SJ. C. Walling. H. P. Jcnssen, R. C. Morris, E. W. O'De|], and O. G. Peterson. Annual meeting Opt. Sci.
`Amer.. San Francisco. CA, 1978: J. C. Walling, H. 1-’. Benson. R. C. Monis, E. W. O'De|i. and G. Peterson, Opt.
`Lett. 4:182 (19Tr'9): J. C. Walling. O. G. Peterson, H. P. Jenssen. R. C. Morris. and E. W. O‘Dell. JEEEJ. Qttrmtmtt
`Et"ectt'on. QE-lfi:l302 (1980): and C. L. Sara, J. C. Walling. H. P. Jenssen, R. C. Morris. and E. W. 0‘Dc1l. Proc.
`Soc. Pltoto~0pt. first. Eng. {.S'PtEJ24'i':13{J{198t'J}.
`
`9M. L. Shad and H. Jenscen, JEEL" J. of Qttt.1‘l't.I'ttttI Electron. QE—l9:480 (I933).
`'°M. Shand and J. Walling, JEEE J. of Qttottttt.-it Electron. QE— 18: 1829 (1932).
`"J. Bucherl, A. Katz, and R. R. Alfano, IEEE J. of Qttantttm Etectt'ott. QE—|9:|4Tl' (1983).
`“E. V. Zharikov, N. N. l1'ichev. S. P. Kaitin, V. V. Laptev. A. A. Ma1yu1in,V. V. Osiko. V. G. Ostroumov.
`P. P. Pashinin, A. M. Prokltorov. V. A. Smirnov, A. F. Umyskov. and I. A. Shcltcrbakov. Sov. J. Qttotttmtt Electrott.
`1311274 (1983).
`
`

`
`Sec. 1 1 .2
`
`Applications
`
`347
`
`was discovered in 1982 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 lase1's published in
`1982” and a review paper on alexandrite lasers in 1985” do not even mention Tizsapphire.
`Part of the delay in Tissapphire 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 verticaI-gradicnt—freeze (VGF) crystals was shown to be
`due to quadruply ionized titanium ('I'i"‘*) substituting for the aluminum in the sapphire.” '3
`Growth and annealing methods have significantly reduced this problem in modern commer-
`cial Ti:sapphire material.
`In spite of its many advantages, Titsapphire does suffer from a few disadvantages. In
`particular. its short upper state lifetime (3.2 ,tLS) makes it quite difficult to pump with a lamp.
`Although lamp-pumped Ti:sapphire lasers have been built,” most commercial Ti:sapphire
`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 LiS1'AlF.5:Cr3+ have seen some interest as
`possible tunable commercial laser sources.” A number of other chromiun1—doped materials
`including Criforsterite and Cr:YAG are also showing strong potential.“
`Transition-metal solid-state tunable lasers are still being actively developed. Barnes”
`and Budgor et al.23 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 Re.s'mi'cli Report. DTIC AD-AI243[]5l4 (I982:3) (MIT Lincoln Lab.. Lexington.
`I982), pp.
`I5—2I, reported by P. F. Mouhon. “Recent Advances in So|id—Slale Lasers." P1-or. Crm. Lcrserx
`Elecn'o-a_m., Anaheim. CA, I984. paper WA2.
`“B. D. Guenther and R. G. Buser, 155.5 J.‘ of Qmnimm Eledrtm. QE—I 8:| 179 (I982).
`'51. C. Walling, D. F. Heller.
`I-l. Samelson, D. .l. Hatter. J. A. Pete, and R. C. Morris, lEE£ J. of Qimnrinn
`Elecwon. QB-2 1 : I568 (1985).
`“SP. Lacovara and L. Eslerowitz, lEEE J’. of Qnrmmm Elecnrrm. QE—2I:l6I4 ([985).
`“A. Sanchez, A. J. Strauss, R. L. Aggarwal. and R. E. Fahey, lEEE J’. of Qumim.-ii Ele’£‘.".!‘0.'l. 24:995 (I988).
`“R. Aggarwal, A. Sanchez, M. Sluppi. R. Fahey. A. Strauss, W. Rapoport. and C. Khaltak. IEEE J. of
`Qnnnttun Electron. 24:ll}03 (I988).
`
`I0:2?'3 (I935).
`WP. Lacovnra, L. Esterowitz and R. Allen, Opt. Len.
`308. A. Payne. L. L. Chase, H. W. Newkirk. L. K. Smith. and W. F. Krupke. IEEE J. of Qnrmmm Electron.
`242243 (1988): and S. A. Payne. L. L. Chase. L. K. Smith. W. L. Kway, and H. W. Neivkirk. J. Appl. Phys.
`66:|05l (1989).
`
`|:62 (1995).
`“C. Pollock. D. Barber, J. Mass. and S. Markgraf, lEEE J. af5el. Topics in Qmmmm Elecmm.
`33Nor|nan P. Barnes, "Transition Metal Solid State Lasers," in Tunable La.\'er.r Hmrrlbrmlt, ed F.
`.I. Duarle
`(San Diego: Academic Press, I995).
`33A. Budgor. L. ESl6I'D\\«'il‘£$. and L. G. DeShazer, eds. Tmmble SolldS1ate Lasers ll (Berlin: Springer Verlag.
`I986).
`
`“IEEE J. of Qlfrtrtlltlll Elec.'rau. QE-I8 (I982); QE-2] (I985): and IEEE J. of Sel.
`Electron. U995).
`
`Topi'c.i' In Qirmilimi
`
`

`
`348
`
`Transition-Metal Solid-State Lasers
`
`Chap. 11
`
`11.2 APPLICATIONS
`
`Transition-metal solid-state tunable lasers provide two major features. First, they are tunable
`over a broad range of visible and near IR wavelengths. Second, they can be used to produce
`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 lase1's have been used to perform an optical version of
`conventional mammography.” There a1'e also potential applications for absorption, Raman,
`and fluorescence spectroscopy in medical imaging.2"
`Solid-state lasers compete with dye lase1's fo1' medical applications requiring both
`tunability and intensity. Primary among these are cosmetic surgery for port wine birthrnarks,
`telangiectasia, warts, stretch marks, acne scars, removing tattoos, and psoriasis.37 Tunable
`solid-state lasers also compete with dye lasers for medical applications such as shattering
`kidney stones.”
`the extremely sho1't pulses possible with tunable solid—state lasers a1'e
`In addition,
`finding application in micromachining. Femtosecond-pulsed Ttsapphire 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.” Ti:sapphire lase1's compete
`with Nd:YAG, diode-pumped Nd:YAG, and excimer lasers for this extremely important
`market.
`
`11.3 LASER MATERIALS
`
`Ruby, alexandrite, and Tizsapphire are the major transition-metal solid—state laser materials.
`Although ruby is not used commercially as a tunable laser, it does have a tunable vibronic
`transition.
`Interestingly enough, the band structure of alexandrite is quite similar to ruby;
`except in alexandrite the vibronic transition is the important one and the narrow line transition
`is not used.
`In contrast, Ti:sapphire has crystalline and mechanical properties virtually
`identical to ruby, but a dramatically different band structure.
`A number of publications can provide additional information for the interested reader.
`Overview treatments are given by Weber,-°‘° Koe-chne1‘,31 and Duarte,-‘Z while more specific
`
`35£.u.rer Factor World, F€l.‘I.E 38 (I996).
`1°Ix.r.rer' Focus World‘. Feb.: 72 (I996).
`
`27La.s'er' Focus World. May: 66-? (I996).
`2“L(J.re:' Focmr Worlrl. May: 66-? (I996).
`29l.'.ase:' I-‘oc'n.r WrmI'(1. January: 22 (I996).
`I‘. La.r(=r.r am! Maseru‘ (Boca Ralon.
`3‘’Marvin J. Weber, ed, Hmidbnok of Laser Sr.‘i'e'm_'e mm‘ Te'c.’mo.log.\‘, Vol.
`FL: CRC Press, lnc.. I982); and more recently. Marvin J. Weber, ed. Hmidbaok of Laser‘ Sciatica mm‘ Te:-liaising)’.
`Siippleiiiem I, Lasers (Bocu Ralon. FL: CRC Press, Inc. I991).
`“Walter Kocchner, Solid State l'..(fX£l‘EJlglJl£€I'iJ1g.
`-'-lth ed. (Berlin: Springer—Verlag, I996).
`
`

`
`Sec. 1 1 .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.3"'-35 Manufacturer data sheets and application notes are also very useful.“
`
`11.3.1 Fluby—Primary Line at 694.3 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 thermally conductive (0.42 Wicm-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 C13‘'‘ to obtain ruby. The Cr3+ substitutes for the Al“ in the
`crystal. Typical dopings are 0.05 weight percent of CrgO3. 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 4F] and the 4F; bands. The ground state is the ‘A; band. The two pump bands fo1'in
`manifolds centered around the blue (400 nm) and green (555 nm}. The pump bands are
`
`321-‘. J. Duarte ed, Tunable Lasers Handbook (San Diego: Academic Press 1995).
`33]. C. Walling, D. F. Heller. H. Sarnelson, D. J. Hatter. J. A. Pete, and R. C. Morris, IEEE J. of Quanrmrr
`Electron. QE-2l:lS68 (1985).
`
`“A. Sanchez, A. J. Strauss. R. L. Aggarwal, and R. E. Fahey, IEEE J’. of Qtm.-n'n.-n Electra.-i. 24:995 ([988).
`“R. Aggarwal, A. Sanchez. M. Stuppi. R. Fahey. A. Strauss, W. Rapoport. and C. Khattak. IEEE J. of
`Qumirrrm Electron. 24:i0O3 (1983).
`
`“Major crystal suppliers are Union Carbide (ruby. alexandrile and Ti:sapphirc) and Litton Ainron
`(alexandrile).
`'
`
`“A uniaxial crystal is one where two of the Cartesian directions have one index of refraction no and the third
`has a different index of refraction in. See Section 3.3 for a discussion of uniaxial and biaxia] crystais.
`
`

`
`350
`
`I
`
`Transition-Metal Solid-State Lasers
`
`Chap. 11
`
`each quite wide, with the blue band about 0.05 microns wide and the green band about 0.0”.-’
`microns wide.
`
`The lifetime in the pump bands is extremely short, with the ions cascading almost
`immediately to the metastable 2E states. The upper 2E state is termed the 23 state and the
`lower is termed the E state. The 2? and E states are separated by 29 cm"', which gives
`a population ratio at thermal equilibrium of 87%. Thus, while fluorescence in ruby occurs
`from both the 2:’: state to the “A; (termed the R; transition at 692.9 nm) and from the E
`state to the 4A; (termed the R]
`transition at 694.3 nm), laser action fi1'st occurs on the R.
`transition. Once laser action has begun.
`the rapid relaxation time from the 2; to the E
`transition prohibits laser action starting on the R2 line. The only way to statt laser action
`on the R; line is to suppress the R1 line by special dielectric coated mirrors or internal
`cavity absorbers.
`(Interesting enough, even though lasing occurs primarily on the R; and
`R3 lines, sidebands have been observed on the long wavelength side, in particular at 767
`nm, attributed to vibronic lasing.)
`Since ruby is uniaxial, its absorption coefficient is a very strong function of the po-
`larization direction of the light (see Figure 11.3). This property strongly affects the beam
`quality. The best optical quality ruby is grown with the crystal axis at 60 degrees to the
`boule axis. When such a ruby rod is pumped in a diffuse refiecting pump cavity, pump
`light parallel to the c-axis will be absorbed differently than pump light perpendicular to
`the c-axis. This will cause the pump distribution (and thus the laser output beam) to be
`elliptical.
`0.4
`0.3
`
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`J 15'
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`laser rod
`
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`
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`
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`
`5860
`
`Wavelength A [13]
`
`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. Cronemeyer. J. Opt‘. Soc. Am.
`56:1".-'03 (1966). Reprinted with the permission of the Optical Society of America.)
`
`0.05
`I||tI|||t:|ttI|1|I 0-04
`6330
`6900
`5920
`5940
`6960
`5980
`7000
`7020
`
`

`
`Sec. 11.3
`
`Laser Materials
`
`351
`
`1
`
`2
`
`4
`
`A2
`
`Blue
`
`6.6 :18
`
`
`
`Yellow
`
`Laser
`
`Vlbmmc
`
`Figure 11.4
`alexandrite.
`
`The energy band diagram for
`
`11.3.2 Alexandrlte--Tunable from 700 nm to 818 nm
`
`Alexandrite (BeAlgO4:Cr3+ or chromium-cloped 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 tums emerald green and displays a secondary red color
`when viewed in artificial light. (As an aside, one variety of chrysobe1'yl occurs in a crystal
`form consisting of parallel arrangements of fibers. When cut 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 Wi’cm—K as compared with 0.14 W.’cm—K. for YAG and 0.42 Wfcm-K for ruby).
`Alexandrite is nonhygroscopic, melts at 1870°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 Cr” 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 alexandrite is given in Figure ll.4. Alexandrite 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 41'"; (lower) bands.
`The ground state is the 4A3 band. The two pump bands form manifolds centered around
`
`33A biaxial crystal is one where all three of the Cartesian directions have different indices of refraction. See
`Section 8.3 for a discussion of Ltniaxial and biaxial crystals.
`39See Section 3.3 for more discussion on the indicatrix.
`
`

`
`352
`
`Transition-Metal Solid-State Lasers
`
`Chap. 11
`
`the blue (410 nm) and yellow (590 nm). The pump bands are each quite wide, with widths
`approximately l000 angstroms.
`In a fashion similar to ruby, there is a metastable 2E state. As with ruby, laser action
`can occur on the R lines of the 3E state and can generate three-state laser behavior at similar
`wavelengths (680.4 nm). The major difference between the R-state lasing in alexandrite and
`1'uby is that alexandrite possesses a higher threshold and lower efficiency. Thus, alexandrite
`is not used as a ruby replacement.
`The major value of alexandrite is in its four—state tunable laser energetics. When
`operated as a four—state laser, alexandrite