Loser
`Engineering
`
`Kelin Kuhn
`University of Washington
`
`i
`
`(cid:36)(cid:54)(cid:48)(cid:47) (cid:20)(cid:19)(cid:21)(cid:21)
`
`AS1\/IL 1022
`
`

`
`Library of Congress Cataloging-in»-Publication Data
`Kuhn. Kelin J.
`Laser engineering.’ Kelin J. Kuhn
`.
`cm.
`Includes index.
`ISBN O-02-36692!-7 (hardcover)
`l. Lasers——Design and construction. 2. Nonlinear optics.
`I. Title.
`TAl6'}'5.K84
`I998
`97-53211
`C11’
`
`Acquisition Editor: Eric Svendsen
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`@ 1993 by Prentice-Hall. Inc.
`A Pearson Education Company
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`
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`
`use ofthese programs.
`
`Printed in the United States of America
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`
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`
`_
`
`{J
`
`,
`
`i
`
`
`
`ii
`ii
`
`

`
`PREFACE
`
`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
`
`Monochrornaticity, Coherency. and Linewidth
`
`15
`
`

`
`
`
`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 Linewidtits. 41
`
`2.2
`
`Gain
`
`43
`
`Basics of Gain. 43
`2.2.1
`Blackbody Radiation. 47
`2.2.2
`2.2.3 Gain. 55
`
`Symbols Used in the Chapter
`
`58
`
`Exercises
`
`59
`
`3 THE FABHY-PEROT 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 Fahry-Perot Etalon, 65
`3.2.2 Reflection and Transmission Coefficients in a Fabry—Perot Etslon. 6'.’
`3.2.3
`Calculating the Reflected and Transmitted Intensities for a Fabry-Perot
`Etalon with the Same Refiectances. 7'0
`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
`
`1'3
`
`Symbols Used in the Chapter
`
`78
`
`Exercises
`
`79
`
`

`
`vi
`
`Contents
`
`4 THANSVERSE MODE PROPEFITIES
`
`83
`
`4.1
`
`4.2
`
`4.3
`
`4.4
`
`4.5
`
`Introduction
`
`84
`
`84
`TEMM. Transverse Modes
`4.2.1
`The Paraxial Approximation, 84
`4.2.2 Mathematical Treatment of the Transverse Modes. 36
`
`88
`TE.Mo_g Gaussian Beam Propagation
`4.3.1
`The "I'EMa_g, 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 of, 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
`
`5 GAIN
`
`SA TURATJON
`
`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
`5.13
`The Importance of Rate Equations. 134
`
`135
`Setting Up Rate Equations
`5.2.1
`Rate Equations for Four-State Lasers. 13?
`
`142
`Laser Output Power Characteristics
`5.3.1
`Optima! Coupling. a Simple Approach. 142
`5.3.2
`PM versus Pm. an Engineering Approach. 14'!
`5.3.3
`Pout versus Pm. the Rigrod Approach, 152
`
`Symbols Used in the Chapter
`
`159
`
`Exercises
`
`161
`
`6 TRANSIENT PROCESSES
`
`153
`
`6.1
`
`6.2
`
`164
`Relaxation Oscillations
`6.1.1
`A Qualitative Description of Relaxation Oscillations. [64
`6.1.2 Nulnerical Modeling of Relaxation Oscillations. 165
`6.1.3
`Analytical Treatment of Relaxation Oscillations. 17]
`
`177
`Q-Switching
`6.2.1
`A Qualitative Description of Q-Switching, 177
`
`-
`
`
`
`

`
`
`
`Contents
`
`6.3
`
`6.4
`
`Numerical Modeling of Q-Switching. 177
`6.2.2
`6.2.3 Analytical Treatment of Q-Switching. 178
`
`182
`The Design of Q-Switches
`6.3.1 Mechanical Q-Switches. 183
`6.3.2
`Electrooptjc Q-Switches. 134
`6.3.3 Acousto-Optic Q-Switches. 190
`6.3.4
`Sarurable Absorber Dyes for Q-Switching. 191
`
`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
`
`'I.5
`
`7.6
`
`Nonlinear Polarizability
`
`208
`
`209
`Second Harmonic Generation
`7.2.1
`The Process of Conversion. 210
`?.2.2
`Phase Matching. 215
`1.2.3 Design Techniques for Frequency-Doubling Laser Beams. 220
`
`Optical Parametric Oscillators
`
`221
`
`Stimulated Rarnan 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
`
`233
`
`SUPPORTIVE TEOHNOLOGIES
`
`24 I
`
`8.1
`
`3.2
`
`8.3
`
`Introduction
`
`242
`
`242
`vMnltilayer Dielectric Films
`3.2.1
`The Fundamentals of Multilayer Film Theory. 243
`3.2.2 Anti-Reflection Coatings from Multilayer Films. 245
`3.2.3 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
`
`

`
`Contents
`
`vill
`
`8.4
`
`261
`Photodetectors
`8.4.1
`Thermal Detectors. 261
`8.4.2
`Photoelecu-ic Detectors. 262
`3.4.3
`Photoconductors. 263
`3.4.4
`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 3 Modern Commercial I-IeNe Laser. 283
`
`288
`Argon Lasers
`9.2.1
`History of ArgoI1- 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
`
`1'0 CONVENTIONAL SOLID-STATE LASERS
`
`302
`
`10.1
`
`History
`
`303
`
`10.2
`10.3
`
`307
`Applications
`Laser Materials
`308
`10.3.] Crystalline Laser Hosts, 309
`10.3.2 Glass Laser Hosts. 310
`10.3.3 The Shape of the Solid—State Laser Malerial. 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. 32?
`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
`
`'
`
`I
`I
`
`'
`
`i
`
`|
`
`
`
`

`
`
`
`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-«Primary Line at 694.3 nm, 349
`11.3.2 Alexandrite—Tunab1e from 700 nm to 818 nm. 351
`11.3.3 Ti:Sapphire—Tunable from 670 nm to 1090 run. 353
`11.3.4 Comparison between Major Solid-State Laser Hosts. 355
`
`Ti:Sa.pphire Laser Design
`11.4.1 Ring Lasers. 356
`11.4.2 Birefringenl Filters. 362
`11.4.3 Coherent Model 890 and 399 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 Ferntosecond Pulses. 371
`
`11.5.3 Measuring Femtosecond Pulses. 373
`11.5.4 Coiliding Pulse Mode-Locking. 373
`11.5.5 Grating Poise 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
`
`1'2 OTHER MAJOR COMMERCIAL LASERS
`
`384
`
`12.1
`
`12.2
`
`12.3
`
`385
`The Design of Carbon Dioxide Lasers
`12.1.1
`Introduction to CO; 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 C0; Industrial Laser. 394
`12.1.5 Optical Components and Detectors for CO: Lasers. 403
`
`404
`The Design of Excimer Lasers
`12.2.1 Introduction to Eatcimer Laser States. 405
`12.2.2 The Evolution of Excimers. 408
`12.2.3 General Design Background. 409
`12.2.4 A Typieai Modern Excimer Laser. 414
`12.2.5 Laser Beam Homogenizers. 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. 423
`12.3.4 The Quantum Well Semiconductor Diode Laser. 432
`12.3.5 Application Highlight: The CD Player, 435
`
`

`
`3;
`
`Contents
`
`APPENDIX
`
`44 1'
`
`Al
`
`441
`Laser Safety
`A.l.1
`Electrocution. 44!
`
`A.2
`
`A3
`
`AA
`
`A5
`
`A6
`
`AT!
`
`A.8
`
`A.l.2 Eye Damage. 444
`A.l.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
`£5.32 A General Wave Equation for Light Propagation in a Material. 452
`A33 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.4.1
`Lenses. 456
`A42 Classical Lens Equations. 457
`A.4.3 Telescopes. 459
`
`456
`
`Refiection and Refraction
`A.5.l Nomenclature. 461
`A.S.2
`Snell's Law. 462
`
`461
`
`13.5.3 Total Internal Reflection. 462
`A.5.4 Brewster’s Angie. 462
`
`Fresnel Equations
`
`463
`
`The Effective Value of the Nonlinear Tensor 465
`
`Projects and Design Activities
`A.8.1 Gas Laser Activities. 466
`A.B.2 Nd:YAG Laser Activities. 472
`A.8.3 Transition Metal Laser Activities. 473
`
`466
`
`A.8.4
`
`Successful Student Projects. 474
`
`A9
`
`Laser Alignment
`
`4'75
`
`A.10 Glossary of Basic Laser Temis
`
`477
`
`INDEX
`
`483
`
`CONSTANTS USED IN BOOK
`
`498
`
`I
`
`[
`
`
`
`

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

`
`Sec. 11.1
`
`History
`
`345
`
`25
`9
`
`photon
`
`2T
`
`29
`
`11.1 HISTORY
`
`phonon
`
`how“
`
`p
`
`by ?——j‘-—:
`
`Pl"|0fl0fl
`
`The transition-metal solid-
`Figure ll.l
`1
`[~ .
`..
`.l.-
`1.1,
`--
`-bi
`slate ttlua e users use meta s In [re ourti
`row of the periodic table as the active
`ions. These metals can produce transitions
`that involve phonons as well as photons
`
`[often called vibronit: or phonon-tc1‘1ninatcd
`
`transitions}. Such tlansitions can rsrcate
`tunable l'uLlr—ieve| laser hellavior.
`
`The history of transition-metal solid-state tunable lasers is exceptionally fascinating. For
`
`the He-Ne, 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-l96Us and commercial development
`proceeded rapidly after that. Transition-n'tetal 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 I982.‘
`Ti:sapphire lasers (the current stars of the solid—state tunable laser market) were discov-
`c1'cd by Mottlton in 1982.2 However. early results with Ti:sappl1ire were not promising due
`to difficulties with material g_rowth.3 It was only after the materials problems were solved
`that the true. potential of the Tizsappliire laser was realized. As a consequence. much of
`the laser development {including the remarkable self-mode-locking properties of Ti:sapphire
`discussed in Section 1 1.5) 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 t1'ansitions 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-terlninated 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
`
`'B. D. Gucnther and R. G. Buscr. lfflfff J. tJfQtmirlrri1: E."eclrun. QE-lS:l 17‘) {I982}.
`
`3P. F. Moulton. SOIidSrr:!e Re.rcam't Report. DTIC AD-Al24305;’=l ([9313) (I_exington: MIT Lincoln Lab..
`I932}. pp. 15-21.
`
`3P. Lacovara and L. I-lsterowitz. H:.'EE..~'. o_f'Qtmmum Elec-ti'u.u. Q!"-L-2l:l6l-4 {[985}.
`
`

`
`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.5 However. it was cryogenically cooled and
`did not excite much commercial interest.
`
`Further efforts by Johnson and his colleagues during the mid to late l960s resulted in
`several more cryogenically cooled divalent transition-metal lasers. These included Co“ in
`MgFg and V” in MgFg.5
`A major advancement occurred in 1976 when Morris and Cline? observed that alexan—
`drite (BeAl304:Cr3+ or chromium doped ehrysoberyl,
`tunable from 700 nm to 818 nm)
`would Jase on a vibronic transition. Walling et al. confirmed these results and demonstrated
`Q—switChing behavions Alexandrite was particularly interesting at the time of its discov~
`ery because it Iased at room temperature and increased in output power as the temperature
`increased.9
`
`The successful use of Cr“ in a beryl crystal led to several other interesting vibronic
`lasers.
`In particular.
`in I982 Shand and Walling,” and independently Buchert et al.,"
`showed that emerald (Be3A|3(SiO3):C13"', 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 scanclium
`gallium garnet (GSGG_).'2
`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. Dielic, and 1-1. I. Guggenheim, Phys. Rev. Lett.
`
`ll:3 18 {I963}.
`
`l34:A299 (1964): D. E. M-::Cumber. J. Mmnlr. Ph_\'s. 5:508 (1964): and D. E.
`5D. E. MCC-amber. P.lt_‘l'.'u’. Rev.
`McCumber. Phys‘. Rev.
`l36:A954 (1964).
`
`6L. F. Johnson. R. E. Diets, and H. J. Guggenheim. Appl. F'I'r_vs. Len. 5:2] {I964}; L. F‘. Johnson and H. J.
`Guggenheim. J. Appl. Pltys. 383-1337 (1967); 1.. F. Johnson and H. J. Guggenheim. J. Appl. Phys. 3S:483? [|06?);
`and L. F. Johnson. H. J. Guggenheim and R. A. Thomas. Pltys. RE‘.-'. 149: N9 (1966).
`
`7R. C. Morris and C. F. Cline, "Cl11‘omium—Doped Beryllium Aluminate Lasers." U.S. Patent #3.99?.853.
`I4. 19?6.
`
`Dec.
`
`SJ. C. Walling. H. P. Jen.-tsen. R. C. Morris, E. W. O‘Dr:ll. and O. G. Peterson. Annual meeting Opt. Sci.
`AI'nt!I‘.. San Francisco. CA. 1978: J. C. Walling. H. P. Benson. R. C. Morris, E. W. O‘Dell, and G. Peterson. Opt.
`Lett. 4:182 (I979): .l. C. Walling, O. G. Peterson. H. P. Jenssen. R. C. Morris. and E. W. O‘Dell, IEEEJ. Qunmnrm
`Electron. QE—l6:l302 (I930): and C. L. Sam. J. C. Walling. H. P. Jenssen. R. C. Morris. and E. W. O’Dell, Proc.
`Soc. Phom—0pr. hm’. Eng. ISPIEJ 24'r':|30 (I930).
`
`9M. L. Shad and H. Jenscen. JEEE J. QfQt.{nn.'mn Etl(’L‘.'."0tt. QE-1*):-'-H50 ([983).
`NM. Shand and J. Walling. l'EEEJ. of Qiraimtnt Electron. QE—l8:l3?.9 (I982).
`
`“J. Buclterl, A. Katz. and R. R. Alfano. IEEE J. r1fQmrrmun Electron. QE- l9:l-177 [I983].
`“E. V. Zharikov. N. N. |l'ichev. S. P. Kaltin. V. V. Laptev. A. A. Malyutin. V. V. Osiko. V. G. Oslroumov.
`P. P. Pashinin. A. M. Prokhorov. V. A. Smirnov. A. F. Umyskov. and 1. A. Shcherbaltov. S01’. J. Qmutftuit E.-'er:n‘0n.
`l3:l274 (I983).
`
`

`
`Sec. 1 1.2
`
`Applications
`
`34?
`
`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 solicl—state lasers published in
`1982” and a review paper on alexandrite lasers in 1985” do not even mention Ti:sapphire.
`Part of the delay in Tizsapphire emerging as a viable commercial tunable solid-state
`laser was materials-based. Early Tizsapphire 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 (Ti4+) 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, Ti:sapphire does suffer from a few disadvantages. In
`particular. its short upper state lifetime (3.2 as") 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:C13+ and LiSrAlF(,:Cr3+ have seen some interest as
`possible tunable commercial laser sonrces.3° A number of other chromium-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 at.“ provide good overview treatments of this developing field.
`In addition.
`there a1'c three special issues in IEEB journals on tunable lasers.“
`
`”P. F. Moulton. Solid Smte Reseaifli Report. DTIC AD—Al24305.t'4 (198223) [MIT Lincoln Lab” Lexington.
`1982), pp.
`15-2], reported by P. F. Moulton. “Recent Advances in Solid-Slate Lasers." Pme. Con.
`Lfl'.$‘£‘I‘.\'
`Eler.'ri'o-opr.. Anaheim. CA. 1984. paper WA2.
`
`“B. D. Guenlher and R. G. Buser. IEEE J.‘ of Qumimm Et'eeu'oii. QE-l8:l I79 {I982}.
`
`'51. C. Walling, D. F. Heller. H. Samclsou. D.
`E."eL‘l'rt'm. QE-2 l I I568 (I935).
`
`.|. I-larter. J. A. Pete, and R. C. Morris. IEEE J. of Qmmmni
`
`'°P. Lacovara and L. Esterotvitz, IEEE J. ofQ:ionmm Electron. QE—?.l:l6l-‘l (1985).
`
`“A. Siltaeliez, A. J. Strauss, R. L. Aggarwal. and R. E. Fahey. IEEE J. of Qucmtmii Efervroii. 24:9‘)5 {I933}.
`
`HR. Aggarwal. A. Sanchez. M. Stuppi. R. Fahey. A. Strauss. W. Rapoport. and C. Khattak. IEEE J’. of
`Qtmilfurti Elr.’r:ri'on. 24:l0U3 (I933).
`
`"’P. Lacovara, L. Esterotviut and R. Allen. Opt. Len. 10:27} (1985).
`
`NS. A. Payne, L. L. (.‘hase, H. W. Newklrk. L. K. Smith, and W. F. Krupke. IEEE J. o{'Quou.'iim Eleciroii.
`2422243 {I988}; and S. A. Payne. L.
`l.. Chase. 1.. K. Smith, W. L. I-(way. and H. W. Newkirk. J’. Appl.
`P."l_f.‘.'.'.
`ti6:lt_l5l (1939).
`
`“C. Pollock. D. Barber. J. Mass. and S. Marltgraf. IEEE J. ofSe.-'. Top.I'r:.r in Qimiiiiuii Ei'ec'iroii. 1:62 (1995).
`
`33Norman P. Barnes. “Transition Metal Solid State Lasers." in Timuble Lo.rer.s Hriiirllaorrlr. ed F. J. Duarte
`
`(San Diego: Academic Press. 1995').
`“A. Budget. L. Estero\vti2, and L. C]. L)eSha?_er, eds, Timyib.-'9 So:'.r‘o'Sro1e I.ci.s'e.»-.s' H (Berlin: Springer Verlag,
`1986).
`
`'”l'l:’E[:' J. of Qiunmrm l?t'ectrr.vi. QB-I8 H982); QE-?.l
`E!er_‘.'i‘on. (1995).
`
`([935); and IEEE J. oj'Set'.
`
`?'opir.t' in Qurmtiim
`
`

`
`348
`
`Transition-Metal Solid-Stale 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 lasers have been used to perform an optical version of
`conventional mammography.35 There are also potential applications for absorption. Raman,
`and fluorescence spectroscopy in medical imagi11g.3“
`Solid-state lasers compete with dye lasers for medical applications requiring both
`tunabilily and intensity. Primary among these are cosmetic surgery for port wine birthmarlts,
`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.“
`
`In addition,
`the extremely short pulses possible with tunable solid-state lasers are
`finding application in micromachining. Femtoseconcl-pulsed Ti: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 scrniconduclor malerials.39 Ti:sappl1ire. lasers compete
`with Nd:YAG. diode-pumped Nd:YAG. and excirner lasers for this extremely important
`market.
`
`11.3 LASER MATERIALS
`
`Ruby. alexandrite, and Ti:sapphire are the major transition-nietal solid—state laser materials.
`Although ruby is not used commercial-ly 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.
`[11 contrast, Ti:sapphire has crystalline and mechanical properties virtually
`identical to ruby. but a dramatically different band strticttire.
`
`A number of publications can provide additional inforniation for the interested reader.
`Overview treatments are given by Weber,” l{oechner._3‘ and Duarte.33 while more specific
`
`35Ln.rer Form ll"or!r.’. Feb.: 38 (1996).
`
`3"‘tm.«.»r Foctr.\' ivm-M. Feb; 72 (1996).
`
`‘7‘?I_u.s'e:' Foc'n.\' l-Vnrld. May: 66-? ( I996}.
`
`1‘*tam I-‘ocris ll/min‘. May: 66-‘? (I996).
`
`391.0.-rer Forms l-Vorld. January: 22 [I996].
`I. Lcisers rind Mrs.-mi‘: {Boca Raton,
`3"Marvin J. Weber. ed. Hrrnrilirlrxk of Laser .S'.~:‘t'em'e mm‘ Tz'clirmiog_\', Vol.
`FL: CRC Press. Inc, 1982); and more recently, Marvin J. Weber. ed, Hrindborik of Lt:'s't?l' Sc‘:'em‘e rnml Tet'.-‘mu.-‘ng_\'.
`Snppleitreirt I. Lasers (Boca Raton. FL: CRC Press, Inc.. 1991 }.
`
`“Waller Koeclmer. Snfir! Stare Laser Engnieen'.vig, 4th ed. (Berlin: Springer-Verlag.
`
`I996").
`
`

`
`Sec. 11.3
`
`Laser Materials
`
`349
`
`
`
`Figure 11.2
`ruhy.
`
`The energy band diagram for
`
`information can be obtained from the wide variety of review papers on alexandI‘ite33 and
`Ti:sapphire.5“'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 Wfcm-K at 300K). Ruby is
`nonhygroscopic, refractory, and is generally considered the most durable of the common laser
`crystals (with the possible exception of Ti:sapphire). 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 C15” to obtain ruby. The Cr” substitutes for the Al” in the
`crystal. Typical dopings are 0.05 weight percent of C1303. 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 ‘*Fg bands. The ground state is the 4A; band. The two pump bands form
`manifolds centered around the blue (400 nm) and green (555 nm)- The pump bands are
`
`32F. J. Duarte ed, Tn.-mbr"e Lasers Handbook {San Diego: Academic Press I995).
`
`“J. C. Walling. D. F. Heller. H. Sarnelson, D. J. Hatter. J. A. Pete. anti R. C. Morris. IEEE J’. qfQ:trm.'mn
`Electron. QE—21:l568 ([985).
`
`“A. Sanchez, A. J. Strauss, R. L. Aggarwal, and R. E. Fahey, !EEEJ'. DfQm'i‘!1fttmEll€C‘N‘0l'l'. 24:995 (1988).
`35R. Aggarwal. A. Sanchez, M. Stuppi. R. Fahey, A. Strauss. W. Rapoporl. and C. Khattak. IEEE J. of
`Qmmmm Electron. 24: 1003 (1988).
`
`"‘Major crystal suppliers are Union Carbide (ruby, alexnndrite and Tizsapphlre) and Litton Airtron
`Iialexandritej.
`‘
`
`“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 Sectinn 8.3 for a discussion of llttiaxial and biaxial crystals.
`
`
`
`

`
`350
`
`Transition-Metal Solid-Slate Lasers
`
`Chap. 11
`
`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 25 states. The upper 313 state is tenned the 274' state and the
`lower is termed the E state. The 23 and -1? 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 2X state to the ‘A2 (termed the R2 transition at 692.9 nm) and from the E
`state to the 4/313 (termed the R1 transition at 694.3 nm), laser action first occurs on the R1
`transition. Once laser action has begun, the rapid relaxation time from the 2:47 to the F
`transition prohibits laser action starting on the R2 line. The only way to start laser action
`on the R2 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 76?
`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 reflecting 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
`
`0.2
`
`7
`E
`3
`0.1
`as
`E
`-E 0.07
`
`3 0.05
`1: 0.04
`.9
`‘e 0.03
`0
`3 0.02
`
`O =
`
`O 01
`
`0.007
`
`B350
`
`E" 3
`
`IIiIIIlII|illllliL_L...1.
`6880
`6900
`6920
`6940
`6960
`
`6980
`
`7000
`
`7020
`
`Wavelength Jr [A]
`
`0.0?’
`0.05
`
`0-04
`
`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 (1966). Reprinted with the permission of the Optical Society of America.)
`
`2 1
`
`1.0
`
`.5 _
`NE
`D0
`‘T’
`0.7 O
`7%
`,5
`is
`:0
`3
`2
`3
`0-2
`0.15 -.2
`g
`,:
`
`0.5
`°"‘
`[}_3
`
`0.1
`
`R
`
`
`
`Pink ruby
`laser rod
`
`

`
`Sec. 11.3
`
`Laser Materials
`
`351
`
`
`
`Yellow
`
`Laser
`
`V‘
`'
`lbmmc
`
`Figure 11.4
`alexandrite.
`
`.
`The energy band diagram for
`
`11.3.2 A|exandrite—-Tunable from 700 nm to 818 nm
`
`Alexandrite (BeAl2O4: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 cut as a cabochon,
`it is called
`
`cat’s-eye or tige1"s—eye.')
`Alexandrite is biaxial,-‘B hard, of good optical quality, and quite thermally conductive
`(0.23 W/cm-K as compared with 0.14 WicIn~K for ‘(AG and 0.42 W/cm-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 mby 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 a1'e
`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 ale-xandrite is given in Figure ll.4. Alexanclrite 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 4 T1(higher) and the 4T3 (lower) bands.
`The ground state is the ‘A; band. The two pump hands form manifolds centered around
`
`331-\ biaxial crystal is one where all three of the Cartesian directions have dilTerent indices of refraction. See
`Section 3.3 for a discussion of uniaxiul and biaxial crystals.
`“See Section 8.3 for more discussion on the indicatrix.
`
`
`
`

`
`352
`
`Transition-Metal Solid-State Lasers
`
`Chap. 11
`
`the blue (=l|0 nm) and yellow (590 nm). The pump bands are each quite wide. with widths
`approximately I000 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
`ruby is that alexandrite possesses a higher threshold and lower efficiency. Thus, alexandrite
`is not used as a ruby replacement.
`
`The major value of alexandrite i