LASER FUNDAMENTALS
`
`SECOND EDITION
`
`WILLIAM T. SILFVAST
`
`School 01 Optic".-5 I CREOL
`Uni\vnrs‘rt} of Central Florida
`
`
`
`CAMBRIDGE
`’>;:;s’»‘ UNIVERSITY PRESS
`
`
`ASML 1006
`
`

`
`PUBLISHED BY THE FIJSSS SYNDKIATE OF THE UNIVERSITY OF Csulllklliili
`The I'll Building. 'I'1'I1fl:pi1QIIJll Strael.Cuubtidg¢. United
`
`CAMBIIIE UNIVERSITY PRESS
`11:9 Edinhurgll Building. Canialidge ca: zxu. UK
`-tows: zmusueez. Nwwrk. NY 10011-4211. usa
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`I’-im|II3bIishBdI99fi
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`First edition Dcnmbriw University Press
`5eu:ndafiIiuuDWiIIl.am'l'.5ilfiI3sl2£D4
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`l.aserI'I:nIlameIII.BIWilI‘|I.m T. Silfvast.—2ndul..
`p.
`cm.
`Includes b|‘bIiogrI.fln‘cal refinances and ‘autism
`ISBN D-S2!-B3345-0
`I. users.
`I. Title.
`
`TAl675.S52 ‘EDI
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`
`ISBN 0 52I 33345 0 hnrdhnrk
`
`EEKIIISSJSI
`
`

`
`Contents
`
`Preface to the Second Edition
`
`Preface to the First Edition
`
`Acknowlrdgrrrenrs
`
`1
`
`INTRODUCTION
`O°\"EIl\"IEW
`Introduction
`Definition Ii’ the Laser
`
`Silnplil.-ily of: Laser
`Unique Pmperiies of a Laser
`The Laser Spa-drum and Wan-lengliis
`A Brit!’ I'lislory of the Laser
`Overview 01' the Book
`
`SECTICIII 1. FUNDAMENTAL WAVE PROPERTIES OF LIGHT
`
`2 WAVE NATURE OF LIGHT —THE INTERACTION OF LIGHT
`WITH MATERINL5
`IIVERV-'l£W
`
`2.] Maxwc1I’s Fgqualiun.-5
`2.2 Maxwell’: I-‘I'a\‘e Equafions
`Maxwell's Wave Equatiorts for a Vacuum
`Solution of the General Wave Equation — Equivalence of Light and
`Electromagnetic Radialion
`Wave Velocity - Phase and Group Velocitics
`Genemlized Solution of Lhc Wave Equalion
`Traluverse Electromagnetic Waves and Polarized Light
`Flow ofEIecIromag1'|e.tic Energy
`Radiation from a Point Source (Electric Dipole Radiation)
`2.3 Interaction of Electromagnetic Radiation {Light} with Mailer
`Speed of Light in a Medium
`Maxwell's Equations in a Medium
`Appficalion of Maxwell's Equations to Dieleclric Materials-
`Lascr Gain {Media
`
`Complex Index of Refracfion — Optical Constants
`Alnsorplion and Dispersion
`
`page xix
`
`xxi
`
`xxiii
`
`UI-Ih-‘-a-|l*Jl-..Io—o-oI-n--
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`
`
`
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`-Ii-".aJ‘.allw.)--I-I*--Ila-II“-J!‘-J|O\-D‘-OI-JIQMJl-Jl-JlNJl~J!-Jl‘~JE)-—----—\O%LI|
`
`
`
`
`

`
`viii
`
`CONTENTS
`
`Estimating Particle Densitia of Materials for Use in lhe
`Dispersion Equations
`2.4 Colterence
`
`Temporal Coherence
`Spatial Coherence
`REFERENCES
`PROBLEMS
`
`Efififlflisit
`
`SECTION 2. FUNDAMENTAL QIMNTIJM PROPERTIES OF LIGHT
`3 PARTICLE NATURE OF LIGHT - DISCRETE ENERGY LEVELS
`OVERVIEW
`
`3.1 Bohr Theory of the H_\'tI.roge:n Mom
`Historical Developrnent of the Concept of Discrete Eiergy Levels
`Energy Levels oi the Hydrogen Atom
`Frequency and Wavelength of Emission Lines
`Ionization Energies and Energy levels of Ions
`Photons
`
`3.2 Quantum Theory of Atomic Energy Lewis
`Wave Nature of Particles
`
`Heisenberg Uncaettainty Principle
`Wave Theory
`Wave Functions
`Quantum Slates
`The Schrodinger Wave Equation
`Energy and ‘Wave Function for the Ground State of the
`Hydrogen Atorn
`Excited States of Hydrogen
`Allowed Quantum Numbers for Hydrogen Atom Wave Functions
`3.3 Anguhr Momentum ol Atoms
`Orbital Angular Momentum
`Spin Angular Momenmrn
`Total Angular Montenlum
`3.4 Em-rgy l..evels Associated with One-Electron Atoms
`[Tine Structure of Spectral Lines
`Pauli Exclusion Principle
`3.5 Periodic Table ofthe Elements
`
`Quantum Conditions Associated with Multiple Eiectrons Attached
`to Nuclei
`
`Shorthand Notation for Electronic Configurations of Atoms Having
`More Than One Electron
`
`3.6 Elleljgy Levels of llrlulti-Eleclmn Atoms
`Energy-Level Designation for Mulli-Electron States
`Russell—Saund¢:rs or L5 Coupling — Notation for Energy Levels
`Energy Levels Associated with Two Electrons in Unfilled Shells
`Rules for Obtaining S. L, and J for L5 Coupling
`Degeneracy and Statistical Weights
`j—j Coupling
`Isoelectronic Scaling
`
`

`
`COHTETS
`
`at-zrantznct-.'s
`monLEMs
`
`4 IIADIATNE TRANSITIONS AND EMISSION LINEINIDTH
`ovt-".Imr:w
`
`4.1 Decay ol‘ Excited States
`Radiative Decay of Excited States of Isolated Atoms —
`Spontaneous Emission
`Spontaneous Emission Decay Rate - Radiative Transition
`Probability
`Lifetime ofa Radiating Electron — The Electron as 3 Classical
`Radiating Harmonic Oscillator
`Nonradiative Decay ol the Excited States — Collisional Decay
`4.2 Fjni.-Eion Bmatlfililtg and Linewitllll Due to Ilalliallzive Decay
`Classical Emission l_.ine\tridtl‘i of a Radiating Electron
`Natural Emission Linewidlh as Deduoed by Quantum Meclulnics
`(Minimum Linewidth)
`4.3 Additional Emission-Broadening Processes
`Broadening Due lo Nonmdiative (ColIisiona]) Decay
`Broadening Due to Depltasing Collisions
`Amorphous Crystal Broadening
`Doppler Brodening in Gases
`Vbigt Ljneshape Profile
`Broadening in Gases Due to Isotope Shifts
`Comparison of Various Types of Emission Broadening
`-1.4 Quantum Mechanical Description of Radiating Atoms
`Electric Dipole Radiation
`Electric Dipole Matrix Element
`Electric Dipole Transition Probability
`Oscillator Strength
`Selection Rules for Electric Dipole Transitions Involving Atoms
`with a Single Electron in an Unfilled Subshell
`Selection Rules for Radiative Transitions Involving Atoms with
`More Than One EIcc1ron in an Unfilled Subshcll
`
`Parity Selection Rule
`Inefficient Radiative Transitions — Electric Quadrupole and Other
`Higher-Order Transitions
`nnrnnr-:NcEs
`raomaaus
`
`5 ENERGY LEVELS AND RADIATIVE PROPERTIES OF MOLECULES.
`LIQUIDS, AND SOLIDS
`ovanvisw
`
`5.1 Molecular Energy Levels and Spectra
`Energy Levels of Molecules
`Classification of Simple Molecules
`Rotational Energy Levels of Linear Molecules
`Rotational Energy Levels of Symrnetric-Top Molecules
`Selection Rules for Rotational Transitions
`
`86
`86
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`89
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`I05
`I06
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`I I5
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`I31
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`I35
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`

`
`CONTENTS
`
`Vibrational Energy Levels
`Selection Rule for Vibrational Transitions
`Rotational—Vibrational Transitions
`Probabilities of Rotational md Vibrational Transitions
`
`Electronic Energy Levels ofhllolecules
`Electronic Transitions and Associated Selection Ruies of
`Molecules
`Emission Liricwidth of Molecular Transitions
`
`"Hie Franclt—Condon Principle
`Excimer Energy Levels
`5.2 Liquid Energy Levels and Their Radiation Properties
`Structure of Dye Moiecules
`Energy Levels of Dye Molecules
`Excitation and Emission of Dye Molecules
`Dcuirrienlal Triplet States o:‘Dye Molecules
`5.3 Fnergy Levels in Solids - Dielectric Laser Materials
`Host Materials
`
`Laser Species — Dopant lam
`Narrow-Linewidth Laser Materials
`Broadband Tunable Laser Materials
`
`Broadening Mechanism for Solid-State Lasers
`5.4 Energy Levels in Solids - St-nliconductor Laser Materials
`Energy Bands in Crystalline Solids
`Energy Levels in Periodic Structures
`Energy Levels of Conductors. Insulators. and Semicondudors
`Excitation and Decay of Excited Energy Levels — Recombination
`Radiation
`
`Direct and Indirect Bandgap Serniconductols
`Ekxtron l)isn'ibutior1 Function and Density of States in
`Semiconductors
`lnoinsic Serniconductor Materials
`
`Extrinsic Semiconductor Materials — Doping
`p-n Junctions — Recombination Radiation Due to Electrical
`Excitation
`
`Heterojunclion Semiconductor Materials
`Quantum Wells
`Variation of Eandgap Energy and Radiation Wavelength with
`Alloy-Composition
`Recombination Radiation Transition Probability and Linewidth
`IEI-‘EIIENCFS
`FROBLI-IMS
`
`6 RADIATION AND 1'-l-IERMAI. EQUILIBRIUM — ABSORPTION AND
`STIMULATED EMISSION
`orvsiwicw
`
`6.1 Equilibrium
`Thermal Equilibrium
`Thermal Equilibrium via Conduction and Convection
`Therniid Equilibritun via Radiation
`
`143
`I43
`I44
`I48
`149
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`150
`I50
`i5!
`152
`153
`153
`155
`I56
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`l5B
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`159
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`168
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`172
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`N3
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`I79
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`I84
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`I9!
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`199
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`
`CONTENTS
`
`6.2 Radiating Bodies
`Stefan—BoltznIann Law
`Wmn‘s Law
`lrmdiance and Radiance
`
`6.3 Cavity Radiation
`Counting the Number of Cavity Modes
`Rayici_gh—Jeans Formula
`Planck's Law for Cavity Radiation
`Relationship between Cavity Radiation and Blackbody
`Radiation
`
`Wavelength Dependence of Blnckbody Emission
`6.4 Absorption and Stimulated Emission
`The Principle of Detailed Balance
`Absorption and Stimulated Emission Coefficients
`REFERENCES
`PROBLEMS
`
`SECTION 3. LASER AMPLIFERS
`
`7 CONDITIONS FOR PRODUCING A LASER — POPULATION
`INVERSIONS. GAIN. AND GAIN SATURAUON
`CW ERVIEW
`
`7.] Absorption and Cain
`Absorption and Gain on a Homogcneously Broadened Radiative
`Ttansition (Lonentzinn Frequency Distribution}
`Gain Cocfficient and Stimulated Emission Cross Soction for
`
`Homogeneous Broadening
`Absorption and Gain on an Inhomogeneously Broadened Radiative
`Transition (Doppler Broadening with a Gaussian Distribution}
`Gain Coeflicient and Stimulated Emission Cross Section for
`Doppler Broadening
`Statistical Weights and the Gain Equation
`Relationship of Gain Coefficient and Stirnulded Emission
`Cross Section to Absorption Cocfiieient and Absorption
`Cross Section
`
`7.2 Population Inversion Ifiiecessary Condition for a Laser!
`7.3 Saturation Intensity tSnl'[icienl Condition for :1 Laser)
`7.4 Development and Cnowth ol' a Laser Beam
`Growth of Beam for a Gain Medium with Homogeneous
`Broadening
`Shape or Geometry of Amplifying Medium
`Growth of Beam for Doppler Btoadening
`7.5 Exponential Growth Factor ICa.inJ
`7.6 Threshofld Reqttiretnents [or a Laser
`Laser with No Minors
`Laser with One Mirror
`laser with Two Mirrors
`REFERENCES
`Pttonu-:Ms
`
`20 I
`204
`205
`206
`20?
`208
`209
`2 I O
`
`2!!
`EM
`ZI5
`EH5
`2!?
`222i
`112i
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`230
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`Bi
`232
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`233
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`235
`238
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`233
`24]
`244
`245
`247
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`249
`253
`153
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`

`
`xii
`
`CONTENTS
`
`LASER OSCILLATION ABOVE THRESHOLD
`OVERVIEW
`8.1 Laser Gain Saturation
`
`Rate Equations of the Laser Levels That Include Stimulated
`Emission
`
`Population Densities of Upper and Lower Laser Levels with
`Beam Present
`Small-Signal Gain Coefficient
`Saturation of the Laser Gain above Threshold
`
`8.2 [mar Be-am Growth beyond the Saturation Intensity
`Change from Exponuitial Growth to l..ine:t.r Growth
`Steady-State Laser Intensity
`8.3 Optimization ol' Laser Output Power
`Optimum Output Mirror Transmission
`Optimum Laser Output Intensity
`Estimating Optimum laser Output Power
`8.4 Energy Exdnttgu between Upper Laser Level Population and
`Laser Photons
`Decay Time of a Laser Beam within an Optical Cavity
`Basic Laser Cavity Rab: Equations
`Steady-State Solutions below LaserTlm:shold
`Steady-State Operation above L-iser'I'hreshold
`8.5 Lust-r Output Fludualiolls
`Laser spiking
`Relaxation Oscillations
`
`8.6 Laser Amplifiers
`Basic Amplifier Uses
`Propagation ofa High-Power. Short-Duration Optical Pulse through
`an Amplifier
`Saturation Energy Fluence
`Amplifying Long Laser Pulses
`Amplifying Short Laser Pulses
`Comparison of Eflicient Laser Amplifiers Based upon Fundamental
`Saturation Limits
`
`Minor Array and Resonator {Regcuerath-e_l Amplifiers
`REFERENCES
`PROBLEMS
`
`REQUIREMENTS FOR OBTAINING POPULATION INVERSIONS
`OVERVIEW
`
`9.1 lnversions and Two-Level Systems
`9.2 Relative Decay Rates -— Radiative versus Collisions!
`9.3 Steady-State lmnersions in 'I'hree- and Four-I.e\'el Systems
`'I11.roe-Level Laser with the Intermediate Level as the Upper Laser
`Level
`
`Tl1roe—Lx:vel Laser with the Upper Laser Level as the Highest Level
`Four-l..e\rel Laser
`
`9.-“I Transient Population luversious
`
`255
`255
`255
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`255
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`256
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`257
`258
`253
`26 I
`26 I
`26 I
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`264
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`268
`2T0
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`273
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`279
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`285
`283
`288
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`290
`290
`290
`292
`293
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`295
`293
`30 I
`304
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`

`
`CONTENTS
`
`9.5 Processes The! [nhibil or I)estro_v lnversions
`Radiation Trapping in Atoms and Ions
`Electron Collisional ThcrmaI.izai;ion oi" the Laser Levels in Atoms
`and Ions
`
`Comparison of Radiation Trapping and Electron Collisional Mixing
`in a Gas Laser
`
`Absorption within the Gain Medium
`REFERENCES
`PIIOILEIIIS
`
`10 LASER PUMPING REQUIREMENTS AND TECHNIQUES
`OVERVIEW
`
`IILI Excitation or Puluphg 'l1:rcsl|oId Requiremenls
`10.2 Pumping Pathways
`Excitation by Direct Pumping
`Excitation by Indirect Pumping (Pump and Transfer)
`Specific Pump-and-Transfer Processes
`10.3 Specific Excitation Parameters An-ciaied with
`Optical Pumping
`Pumping Geometries
`Pumping Rcqttirerrlenls
`A Simplified Optical Pumping Approximation
`Trallwnrse Pumping
`End Pumping
`Diode Pumping of Sa1id—StanIc Lasers
`Characterization of a Laser Gain Medium with Optical Pumping
`{Slope Eflicicncy)
`10.4 Specific Excitation Parameters Associated with
`Particle Pumping
`Electron Collisiona] Pumping
`Heavy Parlicle Pumping
`A More Accurate Description of Electron Excilzuion Rate to a
`Specific Energy Laval in a Gas Discharge
`Electrical Pumping of Sorniconductors
`REFERENCES
`PIIOEI-EMS
`
`SECTION 4. 'I.ASER RESONATORS
`11 LASER CAVITY MODES
`OVERVIEW
`1].] Inlmduclion
`
`11.2 Longitudinal Laser Cavity Modes
`Fabry—Pemt Resonalor
`Fabry—Perot Cavity Modes
`Lon-_girudinal Lnscr Cavity Modes
`Longitudinal Mode Number
`Requirements for the Development of Longitudinal
`Laser Modes
`
`307
`308
`
`31]
`
`315
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`319
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`322
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`339
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`37]
`372
`372
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`380
`380
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`382
`
`

`
`xiv
`
`CONTENTS
`
`1 L3 Transverse Laser Cavity Modes
`Fresnel—Kir'chhofi' Diffraction Integral Formula
`Development of Transverse Modes in a Cavity with Plane-Parallel
`Minors
`
`Transverse Modes Using Curved Mirrors
`Transverse Mode Spatial Distributions
`Transverse Mode Frequencies
`Gaussian-Shaped Transverse Modes within and beyond the
`Laser Cavity
`11.4 Properties of Laser Modes
`Mode Characteristics
`Effect of Modes on the Gmn Medium Profile
`REFERENCES
`PRDBLEMS
`
`12
`
`STABLE LASER RESONATORS AND GAUSSIAN BEAMS
`OVERVIEW
`12.1 Stable (‘urved Mirror Cavities
`Curved Minor Cavities
`ABCD Matrices
`
`Cavity Stability Critcria
`12.2 Properties ofczmsian Beams
`Propagation of a Gaussian Beam
`Gaussian Beam Properties of Two«Mirror Laser Cavities
`Properties of Specific Two-Minor Laser Cavities
`Mode Volume 0-Fa Hen11ite—Gaussian Mode
`
`'12.! Properties of Real Laser Beams
`12.4 Propagation 0|’ Gaussian Beams Using ABCD Matrices «-
`Complex Beam Parameter
`Complex Beam Parameter Applied to a Two-Mirror Laser Cavity
`REFERENCES
`PROBLEMS
`
`13
`
`SPECIAI. LASER CAVITIES AND CAVITY EFFECTS
`{IN ERVIEW
`13.1 Unstable Resorralurs
`
`13.2 Qfiwfiching
`General Description
`Theory
`Methods of Producing Q-Switching within a Laser Cavity
`13.3 Gain-Switching
`13.4 Mode-Loclting
`General Description
`Theory
`Techniques for Producing Mode—Lo1:king
`13.5 Pulse Shortening Techrtiques
`Self-Phase Modulation
`
`Pulse Shortening or Lengthening Using Group Velocity Dispersion
`Pulse Compression (Shortening) with Gratings or Prisms
`Ultrashort-Pulse Laser and Arrlplifer System
`
`386
`
`39]
`392
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`393
`396
`396
`397
`399
`399
`402
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`402
`402
`
`410
`4!!
`412
`4!?
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`423
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`423
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`434
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`439
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`4-50
`45 I
`45 I
`45 I
`456
`462
`463
`
`465
`467
`
`

`
`CON'I'EN'l'S
`
`13.6 Ring Last.-rs
`Monolithic Unidinactional Single-Mode Nd:YAG Ring Laser
`Two-Mirror Ring Laser
`13.7 Complex Beam Parameter Analysis Applied to Mu.II.‘i-Mirror
`Laser Cavities
`
`Three-Mirror Ring Laser Cavity
`Three- or Four-Mirror Focused Cavity
`13.8 ('a\ri=Iies for Producing Spectral fiinrrowing of
`Laser Output
`Cavity with Additional Fabry—Perot EIRIOII for Narrow-Frequency
`Sckactinn
`
`Tunable Cavity
`Broadband Tunable cw Ring lasers
`Tunable Cavity for Ultrana.rrow-Frequency Output
`Distributed Feedback (DFB] Lasers
`Distributed Bragg Reflection Lasers
`13.‘) Laser Cavities Requiring Small-Diameter Gain Regions —
`Asligmnlically Compensated Cavities
`13.10 Waveguide Cavities for Ca: I.a1'.I.-is
`IIEFEIENCFS
`Pltonu-sins
`
`SECTION 5. SPECIFIC LASER SYSTEMS
`
`‘I4 LASER SYSTEMS INVOLVING LOW-DENSITY GAIN MEDIA
`ovI;iwu:n'
`l4.l Atomic Gas Lasers
`Introduction
`Helinm—Neon laser
`General Description
`Laser Structure
`Excitation Mechanism
`
`Applications
`Argon Ion Laser
`General Description
`Laser Suuctme
`Excitation Mechanism
`
`Krypton Ion Laser
`Applications
`HeliIm~—Cadmium Laser
`
`General Description
`Laser Structure
`Excitation Mecllanism
`Appiications
`Copper Vapor Laser
`General Description
`Laser Structure
`Excitation Mechanism
`
`Applications
`
`468
`469
`4710
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`470
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`470
`473
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`4?8
`
`478
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`4'78
`480
`480
`48l
`484
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`484
`485
`436
`488
`
`49|
`-1-9|
`49]
`49!
`49?
`492
`493
`494
`
`49?
`49'?
`49?
`498
`499
`
`500
`SUI
`50]
`
`SOI
`502
`S-04
`505
`505
`505
`50'?
`50'?
`
`S09
`
`

`
`CONTENTS
`
`14.2 Molecular Gas Losers
`Introduction
`Carbon Dion'do Liner
`
`General Description
`laser Stmcture
`
`Excitation Mechanism
`
`Applications
`Nitrogen Laser
`Gerteral Description
`Laser Structure and Excitation Mechanism
`Applications
`Far-Infrared Gas Lasers
`
`General Description
`Laser Stntcture
`Excitation Mechanism
`
`Applications
`Chemical Lasers
`
`General Description
`Laser Structure
`Excitation Mechanism
`
`Applications
`14.3 X-Ray Plasma Lasers
`Inlroductiun
`
`Pumping Energy Requirements
`Excitation Mechanism
`Optical Cavities
`X-Ray Laser Transitions
`Applications
`14.4 Free-Fllectrna Lasers
`Introduction
`laser Structure
`
`Applications
`REFERENCES
`
`15
`
`LASER SYSTEMS INVOLVING I-IIGI-I-DENSITY GAIN MEDIA
`OVERVIEW
`
`15.] Organic Dye Lasers
`Introduction
`Laser Smicture
`Excitation Mechanism
`
`Applications
`15.2 Solid-State Lasers
`Introduction
`
`SIO
`5|0
`5| I
`SH
`SH
`SIS
`515
`SI6
`SI6
`5|?
`SIB
`520
`520
`520
`521
`522
`522
`522
`523
`S23
`524
`524
`524
`524
`524
`525
`52.5
`535
`525
`523
`532
`S32
`532
`535
`535
`536
`537
`537
`
`539
`539
`539
`539
`
`543
`544
`545
`545
`
`

`
`Iluloy Liner
`General Description
`Laser Slur.-rut:
`
`Aplplicaims
`Nmrlyflln YMI uni Chas Imus
`Genunl I)u:.n:ti[l'mI1
`Lunar SI-acttur
`Ezcitaion Mechanism
`Appliclions
`Nady-niuIt:\'LI-' Linen
`General Description
`Laser Sncmrc
`
`Applications
`Nmtlyflunflltrhln Vandal: ¢Nd:Y\*0.) Lasers
`Genzni Dcscripion
`Lane: Slruclurc
`"Excitation Mncluniirn
`
`Applications
`YIIerbium:\'AC Lmu-rs
`
`General Description
`Laser Siruczurc
`Excimion Muclunisrn
`
`Applications
`Altundrile [mar
`Gena-al Description
`Laser Slnrclmc
`Excitation Mnchnnism
`
`Applicwiau
`Tilnhm Sapphbe Liner
`Gcuunl Description
`Lac! Snclnrc
`Euitnion Madunism
`Appiicoiom
`(‘hnnhn LEM-' ad IJCAI-' Lasers
`
`Ge-nenl Description
`Laser Srumarc
`Excitninn Mcduniun
`
`Applicatimu
`Flier luv.-n
`Gcaenl Description
`Laser Suntan:
`
`Applications
`(‘aloe (‘enter Ian-rs
`
`Gcncml Description
`Laser SI'Il1’lll'I'.'
`
`547
`547
`
`549
`550
`550
`55 I
`553
`554
`555
`555
`S56
`556
`557
`557
`557
`557
`558
`558
`S59
`S59
`
`§.‘~“.-:‘;.‘3§§§§‘§§§§§§E§§§EE§§§EE§§§
`
`

`
`xvui
`
`CONTENTS
`
`Excitation Mechanism
`
`Applications
`15.} Semiconductor Diode Lasers
`Introduction
`
`Four Basic Types of Laser Materials
`Laser Structure
`
`Frequency Control of laser Output
`Quantum Cascade Lasers
`p-Doped Germanium Lasers
`Excitation Mechanism
`Applications
`REFERENCES
`
`SECTION 6. FREQUENCY MULTIPLICATION OF LASER BEAIIS
`16 FREQUENCY MULTIPIJCATION OF LASERS AND OTHER
`NONLINEAR OPTICAL EFFECTS
`OVERVIEW
`
`l6.l Ware Propagation in an Anisotropic Crystal
`16.2 Polarizatinn Response of Materials lo Light
`l6.J Second-Order Nonlinear Oplicai Processes
`Second Harmonic Generation
`
`Sum and Diffenznce Frequency Generation
`Optical Parametric Oscillation
`I6.-I Third-Order Nonlinear Optical Proct-sses
`Third Harmonic Generation
`
`Intensity-Dependent Refractive Index — Self—Focusing
`I65 Nonlinear Optical Materials
`ltS.6 Phase Matching
`Description of Phase Matching
`Achieving Phase Matching
`Types of Phase Matching
`16.7 Saturnble Absorption
`16.8 Two-Photon Absorption
`16.9 Stimulated Raman Scattering
`16.10 Harmmlic Generation in Case-.5
`IIEFEIIENCIQS
`
`Appwidix
`index
`
`574
`576
`576
`576
`579
`58 I
`59]
`592
`594
`594
`596
`597
`
`62 I
`625
`
`

`
`1 I
`
`ntroduction
`
`OVERVIEW A laser is a device that amplifies light
`and produces a highly directional. high-intensity
`beamlhatrnostoftenhas a very pure frequency or
`watnelength. It comes in sizes ranging from approx-
`imately one tenth the diameter of a human hair to
`the sire of a very large building. in powers ranging
`from 10"’ to I03” W. and in wavelengths ranging
`from the microwave to thesoft-X-ray spectral regions
`with corresponding frrxfuencies front 10'‘ lo 10" Hz.
`Lasers have pulse energies as high as I0‘ J and pulse
`durations as short asfi x 10"" s. They can easily
`
`drill holes in the most durable of materials and can
`
`weld detachedretinas within Ihehumusteye. They are
`a lrey component of some of our most modern com-
`munication systems and are the "phomgraplt needle"
`ofourcompact disc players- They perform heat treat»
`ment ofltiglr-strength materials, such is the pistons of
`our automobile engines. and provide a special surgi-
`cal knife for many types of medical procedures. They
`act as target designator: for military weapons and pro-
`vide for the rapid chock-out we have come to expect
`at the supermarket. What rt remarkable range of char-
`acterislics for a device that is in only its fifth decade
`of existence!
`
`INTRODUCTION
`
`There is nothing magical about a laser. It can be thought of as just another type
`uf light source. It cur tafltly luau unllly tutiqut: lnuptslliuts lllul Itraku it il. spt.1t.:ir.tl light
`source. butthese properties can be understood without knowledge of sophisticated
`mathcmalsical techniques or complex idem. It is the objective of this text to explain
`the operation of the laser in a simple. logical approach that builds from one con-
`cept to the next as the chapters evolve. The concepts, as they are developed. will
`be applied to all classes of laser materials. so that the reader will develop a sense
`of the broad field of lasers while still acquiring the capability to study. design, or
`simply understand a specific type of laser system in detail.
`
`DEFINWION OF THE LASER
`
`The word laser is an acronym for Light Amplification by Stimulated Emission of
`Radiation. The laser makes use of processes that increase or amplify light signals
`after those signals have been generated by other means. These processes include
`(I) stimulated emission. a natural effect that was deduced by considerations re-
`latirrg to tlterrnodynarnzc equilibrium, and (2) optical feedback {present in most
`
`

`
`INTRODUCTION
`
`Optical resonator or cavity
`
`Atnpliyfng medium
`
`
`
`Eyre 1-1 Simplified
`sdtetnatit: onypacat laser
`
`Fully roflectlng
`rninur
`
`Partially transat-tttng
`rnirror
`
`lasers} that is usually provided by mirrors. Thus, in its simplest form, a lasercon-
`sists of a gain or amplifying medium (where stimulated etnission occurs). and a
`set of minors to feed the light back into the amplifier for continued growth of the
`developing beam. as % in Figure I-I.
`
`SIMPLICITY OF A LASER
`
`The simplicity ofa Iasercart be understood by considering the light from acandle.
`Normally, a burning candle radiates light in all directions. and therefore illumi-
`nates various objects equally if they are equidistant from the candle. A laser takes
`light that would nomtally he emitted in all directiotts. such as from E candle, and
`concentrates that light into a single direction. Thus, if the light radiating in all di-
`rections from a candle were concentrated into at single beam of the diameter of the
`pupil of your eye (approximately 3 mm). and if you were standing a distance of
`i ni from the candle. then the light intensity would be l.Ill0_.{ID times as bright as
`the light that you normally see radiating frmn the candle! That is essentially the
`underlying concept of the operation of a laser. However. a candle is not the kind of
`medium that produces arnplification, and thus there are no candle lasers. It takes
`relatively special conditions within the laser medium for amplification to occur,
`hut it is that capability of tdting light that would normally radiate from a source in
`all directions — and concentrating that light into a beam traveiing in a singie direc-
`tion -— llltfl is iuvolved in malcing a laser. These special conditions. and the media
`within which they are produced. will be desctibed in some detail in this book.
`
`UNIQUE PROPERTIES OF A LASER
`
`The beam of light generated by a typical laser can have many properties that are
`unique. When comparing laser properties to those of other light sources, it can
`be readily recognized that the values of various panttneters for laser light either
`greatly exceed or are much more restrictive than the values for many common
`light sources. We never use lasers for street illumination. or For illumination within
`our houses. We don't use them for searchlights or flashlights or as headlights in
`
`

`
`INTRODUCTION
`
`our ('35. Lasers generaly have a narrower Frequency distribution, or much higher
`intensity, or a much greater degree of collimation. or much shorter pulse duration.
`than that available from more common types of light sources. Therefore. we do use
`them in oompact disc players. in supennarlnet check-out scanners, in surveying in-
`slrurnents. and in medical applications as a surgical knife or for welding detached
`retinas. We also use l.l1.en1 in communications systems and -in radar and military
`targeting applications, as well as many other areas. .4 laser is a specialized light
`source that slumld be mad only when its unique properties are required.
`
`THE LASER SPECTRUM AND WAVE.ENGTHS
`
`A portion of the electromagnetic radiation spectnrm is shown in Figure 1-2 for the
`region covered by currently existing lasers. Such lasers span the wavelength range
`from the fa: infrared part of the spectrum (1 : L000 um) tothe soft—X-ray region
`(A. = 3 nm), thereby covering a range of wavelengths of almost six orders of mag-
`nitude. There are several types of units that are used to define laser wavelengths.
`These range from micrometers or microns (pm) in the infrared to nanometers (run)
`and angstroms (A) in the visible. ultraviolet (UV ). \'acutI.1J1 ultraviolet (VUV ). ex-
`treme ultraviolet {EUVa1' XUV). and soft—X-my (SXR) spectral regions.
`
`WAVEIENGTH UNITS
`
`lpm = 104' m;
`IA=1o'"’m;
`I nm 2 10''“ I11.
`
`Consequently. I micronurmj = |0,000 angstroms (A) : LIIJU nanometers {am}.
`For example. green ligh: has a wavelength ol'5 x 10‘? m = 0.5 pm = 5.0003 =
`SW nm.
`
`I
`
`'
`"F
`
`CD
`
`I
`£j‘1L__"* 9
`it
`-I
`
`9
`
`-
`
`'
`
`-_
`
`Figu-I1-2 Wavdangth
`range ofvaious lasers
`
`FIR user:
`..___ .__.._..
`
`N2
`“"5!
`KTF
`I-Iwte
`Nd'YM3
`t-le-Cu
`
`Serra:-flay
`I--Han
`.__..._......;
`
`5°:
`
`"° "°
`
`Far hharad
`
`hlrarecl
`
`ESE??? D1‘;
`1.-~20;
`W51
`
`AIF
`Lfltrawalet
`
`Sufi I-Ray:
`
`soprii
`
`{ohm
`
`1pri1
`3|.irn
`
`
`'aEm'nm1ou..m 3-Onrn
`gm
`
`tllitm
`
`-— ENERGY ('§)—.
`
`

`
`INTRODUCTION
`
`WAVELENGTH REGIONS
`
`Far irrfrared: 10 to IADOD urn;
`middleinfrared: I to It] um;
`rwarinfrured: 0.? to 1 run;
`visible: 0.4 to 0.7 urn. or 400 to 700 nm;
`ultraviolet: 0.2 to 0.4 um, 0r200 to 400 run;
`vacuum ultraviolet: 0.} to 0.1 prm. or I00 to 200 nm;
`extrerne ultraviolet; 10 to 100 mu;
`soft X-rays: l nm to approximately 20-30 run (some overlap with EUVL
`
`A BRSEF HISTORY OF THE LASER
`
`Charles Townes took advaruage of the stimulated emission process to construct a
`microwave amplifier, referred to as a mnxer. This device produced a coherent beam
`ol microwaves to be used for communications. The first rnaser was produced in
`ammonia vapor with the inversion between two energy levels that produced gain at
`a wavelength of 1.25 cm. The wavelengths produced in the rnaser were compara-
`ble to the clilnellsiuns of tl1e device, so extmpolation to the optical regime — where
`wavelengths were five orders of magrrimde smaller — was not an obvious extension
`of that work.
`
`In I958, Townes and Sciiawluw published a paper concerning their ideas about
`extending the rnaser concept to optical frequencies. They developed the concept
`of an optical amplifier surrounded by an optical mirror Itcsonant cavity to allow for
`growth of the beam. Townes anr:' Schawlow each received a Nobel Prize for his
`work in this field.
`
`In 1960. Theodore -Maiman of Hughes Research Laboratories produced the
`first laser using a ruby crystal as the amplifier and a flashlarnp as the energy source.
`The helical flashlamp surrounded a rod—shaped ruby crystal. and the optical cavity
`was formed by coating the flattened ends of the ruby rod with a highly reflectirtg
`material. Arr intense red beam vras observed to emerge from the end of the rod
`when the fiashlamp was fired!
`The first gas laser was developed in I96! by A. Javan, W. Bennett, and D. Har-
`riott of "Bell Laboratories, using a mixture of helium and neon gases. Al the same
`laboratories. L. F. Johnson and K.Na.ssau demonstrated the first neodymium laser,
`which has since be-corrre oneofthe most reliable lasers available. This was followed
`
`in 1962 by the first serrriconduc-tor laser, dernorrslrated by R. Hall at the General
`Electric Research Laboratories. In 1963. C. K. N. Patel of Bell laboratories dis-
`covered the irrfraretl ca.rborr dioxide laser. which is one of the most ellicierrt and
`powerful lasers available today. Later that same year. E. Bell of Spectra Physics
`discovered the first ion laser. in rrercury vapor. In 1964 W. Bridges of Hughes Re-
`search Laboratories discovered the argon ion laser, and in 1966 W. Silfvast, G. R.
`Fowles, and B. D. Hopkins produced the first blue helium—cadrnirrm metal vapor
`
`

`
`INTIIODUCTION
`
`laser. During that same year. P. P. Soroltin and J. R. Lankard of the IBM Research
`Laboratories developed the first liquid laser using an organic dye dissolved in a sol-
`vent, thereby leading to the category of broadly tunable lasers. Also at that time,
`W. Walter and co-workers at TRG reported the Iirst copper vapor laser.
`The first vacuum ultraviolet lamr was reported to occur in molecular hydro-
`gen by R. Hodgson of IBM and independently by R. Waynmt et al. of the Naval
`Research laboratories in 1970. The lirst of the well—lmowtI l‘aDe-gas——l‘talidc ex-
`cimer lasers was observed in xenon fluoride by J. J. Ewing and C. Brau of the
`Avco—Ev-erett Research Laboratory in I975. In that same year, the lirst quantum-
`well liner was made in a gallium arsenlde semiconductor by J. van der Zlel and
`co-workers at Bell Laboratories. In 1976, J. M. .l. Madey and co-workers at Stan-
`ford University demonstrated the Iirst free-electron laser amplifier operating in the
`infrared at the C0; laser wavelength. In 1979, Walling and co-workers at Allied
`Chemical Corporation obtained broadly tunable laser output horn a solid-state laser
`material called aiexandrite. and in 1985 the first soft—X-ray laser was successfully
`demonstrated in a highly ionized selenium plasma by D. Matthews and a large num-
`ber of co—workcrs at the Lawrence Liverrnore Laboratories. In 1986, P. Motrlton
`discovered die titanium sapphire laser. In I991, M. l-lasse and co-workers devel-
`oped the first blne~green diode laser in 2':rSc. In l994, F. Capasso and co-workers
`developed the quantum cascade laser. In I96. 5. Nalrarnura developed the first
`blue diode laser in Gabi-based materials.
`In I961, Fox and Li described the existence of resonant transverse modes in
`
`a laser cavit)‘- That same year. Boyd and Gordon obtained solutions of the wave
`equation for confocal resonator modes. Unstable resonators were demonstrated
`in 1969 by Krupke and Sony and were described theoretically by Siegman. Q-
`switching was first obtained by McClt.II1g and Hellwarth in I962 and described
`later by Wagner a.nd Lengyel. The first mode-locking was cbtained by Hargrove,
`Fork. and Pollack in I964. Since then. many special cavity arxangernents. feedback
`schemes, and otherdevices have been developed to improve the control. operation,
`and reliability oflascrs.
`
`OVERVIEW OF THE BOOK
`
`Isaac Newton demribed Light as small bodies emitted from shining substances.
`This view was no doubt influenced by the fact that light appears to propagate in a
`straight line. Christian Huygens. on the other hand. described light as a wave mo-
`tion in which a small source spreads out in all directions: rnost observed eflects —
`including diffraction, reflection. and refraction - can be atlrillmod to the expansion
`of primary waves and of secondary wavelets. The dual nature of light is still ausc-
`ful concept. whereby the choice of particle or wave ex planarion depends upon the
`cl’fect to be considered.
`
`Section One of this book deals with the fundamental wave properties of light,
`including Maxwell's equations. the interaction of electromagnetic radiation with
`
`

`
`I
`
`matter. absorption and dispersion, and coherence. Section Two deals with the fun-
`damental quantum properties of light. Chapter 3 describes theconeept of discrete
`energy levels in atomic laser species and also how the periodic table of the ele-
`ments evolved- Chapter 4 deals with radiative transitions and emission linewidths
`and the probability of making transitions between energy levels. Chapter 5 con-
`siders energy levels of lasers in -molecules, liquids. and solids — both dielectric
`solids and semiconductors. Chapter 6 then considers radiation in equilibriu