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1 Spontaneous and Stimulated Transitions1

1.1 Introduction1

1.2 Why'Quantum'Electronics?1

1.3 Amplification at Optical Frequencies3

1.3.1 Spontaneous Emission4

1.3.2 Stimulated Emission6

1.4 The Relation Between Energy Density and Intensity7

1.4.1 Stimulated Absorption10

1.5 Intensity of a Beam of Electromagnetic Radiation in Terms of Photon Flux11

1.6 Black-Body Radiation11

1.7 Relation Between the Einstein A and B Coefficients16

1.8 The Effect of Level Degeneracy18

1.9 Ratio of Spontaneous and Stimulated Transitions19

1.10 Problems20

2 Optical Frequency Amplifiers22

2.1 Introduction22

2.2 Homogeneous Line Broadening22

2.2.1 Natural Broadening22

2.3 Inhomogeneous Broadening26

2.3.1 Doppler Broadening27

2.4 Optical Frequency Amplification with a Homogeneously Broadened Transition30

2.4.1 The Stimulated Emission Rate in a Homogeneously Broadened System33

2.5 Optical Frequency Amplification with Inhomogeneous Broadening Included34

2.6 Optical Frequency Oscillation-Saturation35

2.6.1 Homogeneous Systems35

2.6.2 Inhomogeneous Systems38

2.7 Power Output from a Laser Amplitier44

2.8 The Electron Oscillator Model of a Radiative Transition45

2.9 What Are the Physical Significances of x'and x"?49

2.10 The Classical Oscillator Explanation for Stimulated Emission52

2.11 Problems54

References55

3 Introduction to Two Practical Laser Systems57

3.1 Introduction57

3.1.1 The Ruby Laser57

3.2 The Helium-Neon Laser63

References67

4 Passive Optical Resonators68

4.1 Introduction68

4.2 Preliminary Consideration of Optical Resonators68

4.3 Calculation of the Energy Stored in an Optical Resonator70

4.4 Quality Factor of a Resonator in Terms of the Transmission of its End Reflectors72

4.5 Fabry-Perot Etalons and Interferometers73

4.6 Internal Field Strength79

4.7 Fabry-perot Interferometers as Optical Spectrum Analyzers81

4.7.1 Example84

4.8 Problems86

References87

5 Optical Resonators Containing Amplifying Media88

5.1 Introduction88

5.2 Fabry-Perot Resonator Containing an Amplifying Medium88

5.2.1 Threshold Population Inversion-Numerical Example91

5.3 The Oscillation Frequency92

5.4 Multimode Laser Oscillation93

5.5 Mode-Beating99

5.6 The Power Output of a Laser101

5.7 Optimum Coupling105

5.8 Problems106

References107

6 LaserRadiation108

6.1 Introduction108

6.2 Diffraction108

6.3 Two Parallel Narrow Slits110

6.4 Single Slit110

6.5 Two-Dimensional Apertures111

6.5.1 Circular Aperture111

6.6 LaserModes113

6.7 Beam Divergence117

6.8 Linewidth of Laser Radiation118

6.9 Coherence Properties119

6.10 Interference121

6.11 Problems124

References124

7 Control of Laser Oscillators126

7.1 Introduction126

7.2 Multimode Operation126

7.3 Single Longitudinal Mode Operation127

7 4 Mode-Locking131

7.5 Methods of Mode-Locking134

7.5.1 Active Mode-Locking134

7.6 Pulse Compression138

References139

8 Optically Pumped Solid-Stare Lasers141

8.1 Introduction141

8.2 Optical Pumping in Three-and Four-Level Lasers141

8.2.1 Effective Lifetime of the Levels Involved141

8.2.2 Threshold Inversion in Three-and Four-Level Lasers142

8.2.3 Quantum Efficiency143

8.2.4 Pumping Power143

8.2.5 Threshold Lamp Power144

8.3 PuIsed Versus CW Operation144

8.3.1 Threshold for Pulsed Operation of a Ruby Laser145

8.3.2 Threshold for CW Operation of a Ruby Laser145

8.4 Threshold Population Inversion and Stimulated Emission Cross-Section146

8.5 Paramagnetic Ion Solid-State Lasers147

8.6 The Nd:YAG Laser147

8 6.1 Efiective Spontaneous Emission Coefficient152

8.6.2 Example-Threshold Pump Energy of a Pulsed Nd:YAG Laser153

8.7 CW Operation of the Nd:YAG Laser154

8.8 TheNd3+ Glass Laser154

8.9 Geometrical Arrangements for Optical Pumping159

8.9.1 Axisymmetric Optical Pumping of a Cylindrical Rod159

8.10 High Power Pulsed Solid-State Lasers166

8.11 Diode-Pumped Solid-State Lasers167

8.12 Relaxation Oscillations(Spiking)168

8.13 Rate Equations for Relaxation Oscillation170

8.14 Undamped Relaxation Oscillations174

8.15 Giant Pulse(Q-Switched)Lasers175

8.16 Theoretical Description of the Q-Switching Process179

8.16.1 Example Calculation of Q-Switched Pulse Characteristics182

8.17 Problems183

References183

9 Gas Lasers185

9.1 Introduction185

9.2 Optical Pumping185

9.3 Electron lmpact Excitation187

9.4 The Argon Ion Laser188

9.5 Pumping Saturation in Gas Laser Systems190

9.6 Pulsed Ion Lasers191

9.7 CW Ion Lasers192

9.8 'Metal'Vapor Ion Lasers196

9.9 Gas Discharges for Exciting Gas Lasers199

9.10 Rate Equations for Gas Discharge Lasers201

9.11 Problems204

References205

10 Molecular Gas Lasers Ⅰ207

10.1 Introduction207

10.2 The Energy Levels of Molecules207

10.3 Vibrations of a Polyatomic Molecule212

10.4 Rotational Energy States214

10.5 Rotational Populations214

10.6 The Overall Energy State of a Molecule216

10.7 The Carbon Dioxide Laser217

10.8 The Carbon Monoxide Laser222

10.9 Other Gas Discharge Molecular Lasers224

References224

11 Molecular Gas Lasers Ⅱ225

11.1 Introduction225

11.2 Gas Transport Lasers225

11.3 Gas Dynamic Lasers228

11.4 High Pressure Pulsed Gas Lasers232

11.5 Ultraviolet Molecular Gas Lasers238

11.6 Photodissociation Lasers241

11.7 Chemieal Lasers241

11.8 Far-Infrared Lasers244

11.9 Problems244

References246

12 Tunable Lasers248

12.1 Introduction248

12.2 Organic Dye Lasers248

12.2.1 Energy Level Structure248

12.2.2 Pulsed Laser Excitation251

12.2.3 CW Dye Laser Operation252

12.3 Calculation of Threshold Pump Power in Dye Lasers253

12.3.1 Pulsed Operation256

12.3.2 CW Operation259

12.4 Inorganic Liquid Lasers260

12.5 Free Electron Lasers260

12.6 Problems266

References266

13 Semiconductor Lasers267

13.1 Introduction267

13.2 Semiconductor Physics Background267

13.3 Carrier Concentrations271

13.4 Intrinsic and Extrinsic Semiconductors274

13.5 The p-n Junction275

13.6 Recombination and Luminescence280

13.6.1 The Spectrum of Recombination Radiation281

13.6.2 External Quantum Efficiency283

13.7 Heterojunctions285

13.7.1 Ternary and Quaternary Lattice-Matched Materials285

13.7 2 Energy Barriers and Rectification286

13.7.3 The Double Heterostructure286

13.8 Semiconductor Lasers290

13.9 The Gain Coefficient of a Semiconductor Laser292

13.9.1 Estimation of Semiconductor Laser Gain293

13.10 Threshold Current and Powet-Voltage Characteristics295

13.11 Longitudinal and Transverse Modes296

13.12 Semiconductor Laser Structures297

13.12.1 Distributed Feedback(DFB)and Distributed Bragg Reflection(DBR) Lasers299

13.13 Surface Emitting Lasers304

13.14 Laser Diode Arrays and Broad Area Lasers306

13.15 Quantum Well Lasers307

13.16 Problems310

References311

14 Analysis of Optical Systems Ⅰ312

14.1 Introduction312

14.2 The Propagation of Rays and Waves through Isotropic Media312

14.3 Simple Reflection and Refraction Analysis313

14.4 Paraxial Ray Analysis316

14.4.1 Matrix Formulation316

14.4.2 Ray Tracing324

14.4.3 Imaging and Magnification325

14.5 The Use of Impedances in Optics327

14.5.1 Reflectance for Waves Incident on an Interface at Oblique Angles331

14.5.2 Brewster's Angle332

14.5.3 Transformation of Impedance through Multilayer Optical Systems332

14.5.4 Polarization Changes334

14.6 Problems335

References336

15 Analysis of Optical Systems Ⅱ337

15.1 Introduction337

15.2 Periodic Optical Systems337

15.3 The Identical Thin Lens Waveguide339

15.4 The Propagation of Rays in Mirror Resonators340

15.5 The Propagation of Rays in Isotropic Media342

15.6 The Propagation of Spherical Waves346

15.7 Problems347

References347

16 Optics ofGaussian Beams348

16.1 Introduction348

16.2 Beam-Like Solutions of the Wave Equation348

16.3 Higher Order Modes354

16.3.1 Beam Modes with Cartesian Symmetry354

16.3.2 Cylindrically Symmetric Higher Order Beams355

16.4 The Transformation of a Gaussian Beam by a Lens357

16.5 Transformation of Gaussian Beams bv General Optical Systems371

16.6 Gaussian Beams in Lens Waveguides371

16.7 The Propagation of a Gaussian Beam in a Medium with a Quadratic Refractive Index Profile372

16.8 The Propagation of Gaussian Beams in Media with Spatial Gain or Absorption Variations372

16.9 Propagation in a Medium with a Parabolic Gain Profile373

16.10 Gaussian Beams in Plane and Spherical Mirror Resonators375

16.11 Symmetrical Resonators377

16.12 An Example of Resonator Design379

16.13 Difiraction Losses381

16.14 Unstable Resonators382

16.15 Problems384

References386

17 Optical Fibers and Waveguides387

17.1 Introduction387

17.2 Ray Theory of Cylindrical Optical Fibers387

17.2.1 Meridional Rays in a Step-Index Fiber387

17.2.2 Step-lndex Fibers390

17.2.3 Graded-Index Fibers392

17.2.4 Bound,Refracting,and Tunnelling Rays393

17.3 Ray Theory of a Dielectric Slab Guide395

17.4 The Goos-H？inchen Shift397

17.5 Wave Theory of the Dielectric Slab Guide399

17.6 P-Waves in the Slab Guide400

17.7 Dispersion Curves and Field Distributions in a Slab Waveguide404

17.8 S-Waves in the Slab Guide406

17.9 Practical Slab Guide Geometries407

17.10 Cylindrical Dielectric Waveguides408

17.10.1 Fields in the Core413

17.10.2 Fields in the Cladding414

17.10.3 Boundary Conditions414

17.11 Modes and Field Patterns415

17.12 The Weakly-Guiding Approximation416

17.13 Mode Patterns417

17.14 Cutoff Frequencies419

17.14.1 Example421

17.15 Multimode Fibers423

17.16 Fabrication ofOptical Fibers423

17.17 Dispersion in Optical Fibers425

17.17.1 Material Dispersion427

17.17.2 Waveguide Dispersion428

17.18 Solitons430

17.19 Erbium-Doped Fiber Amplifiers430

17.20 Coupling Optical Sources and Detectors to Fibers433

17.20.1 Fiber Connectors434

17.21 Problems435

References437

18 Optics of Anisotropic Media438

18.1 Introduction438

18.2 The Dielectric Teusor438

18.3 Stored Electromagnetic Energy in Anisotropic Media440

18.4 Propagation of Monochromatic Plane Waves in Anisotropic Media441

18.5 The Two Possible Directions of D for a Given Wave Vector are Orthogonal443

18.6 Angular Relationships between D,E,H,k,and the Poynting Vector S444

18.7 The Indicatrix446

18.8 Uniaxial Crystals448

18.9 Index Surfaces450

18.10 Other Surfaces Related to the Uniaxial Indicatrix452

18.11 Huygenian Constructions453

18.12 Retardation457

18.13 Biaxial Crystals461

18.14 Intensity Transmission Through Polarizer/Waveplate/Polarizer Combin-ations464

18.14.1 Examples465

18.15 The Jones Calculus465

18.15.1 The Jones Vector466

18.15.2 The Jones Matrix467

18.16 Problems470

References471

19 The Electro-Optic and Acousto-Optic Effects and Modulation of Light Beams472

19.1 Introduction to the Electro-Optic Effect472

19.2 The Linear Electro-Optic Effect472

19.3 The Quadratic Electro-Optic Effect479

19.4 Longitudinal Electro-Optic Modulation480

19.5 Transverse Electro-optic Modulation482

19.6 Electro-Optic Amplitude Modulation486

19.7 Electro-Optic Phase Modulation488

19.8 High Frequency Waveguide Electro-Optic Modulators489

19.8.1 Straight Electrode Modulator490

19.9 Other High Frequency Electro-Optic Devices493

19.10 Electro-Optic Beam Deflectors495

19.11 Acousto-Optic Modulators495

19.12 Applications of Acousto-Optic Modulators502

19.12.1 Diffraction Efficiency of TeO2502

19.12.2 Acousto-Optic Modulators502

19.12.3 Acousto-Optic Beam Deflectors and Scanners503

19.12.4 RF Spectrum Analysis504

19.13 Construction and Materials for Acousto-Optic Modulators504

19.14 Problems507

References507

20 Introduction to Nonlinear Processes508

20.1 Introduction508

20.2 Anharmonic Potentials and Nonlinear Polarization508

20.3 Nonlinear Susceplibilities and Mixing Coefficients512

20.4 Second Harmonic Generation514

20.4.1 Symmetries and Kleinman's Conjecture516

20.5 The Linear Electro-Optic Effect516

20.6 Parametric and Other Nonlinear Processes517

20 7 Macroscopic and Microscopic Susceptibilities518

20.8 Problems522

References522

21 Wave Propagation in Nonlinear Media524

21.1 Introduction524

21.2 Electromagnetic Wayes and Nonlinear Polarization524

21.3 Second Harmonic Generation528

21.4 The Effective Nonlinear Coefficient deff530

21.5 Phase Matching532

21.5.1 Second Harmonic Generation533

21.5.2 Example533

21.5.3 Phase Matching in Sum-Frequency Generation535

21.6 Beam Walk-Off and 90°Phase Matching535

21.7 Second Harmonic Generation with Gaussian Beams536

21.7.1 Intracavity SHG537

21.7.2 External SHG538

21.7.3 The Effects of Depletion on Second Harmonic Generation538

21.8 Up-Conversion and Difference-Frequency Generation541

21.9 Optical Parametric Amplification542

21.9.1 Example544

21.10 Parametric Oscillators545

21.10.1 Example547

21.11 Parametric Oscillator Tuning548

21.12 Phase Conjugation550

21.12.1 Phase Conjugation in CS2553

21.13 Optical Bistability554

21.14 Practical Details of the Use of Crystals for Nonlinear Applications557

21.15 Problems558

References559

22 Detection of Optical Radiation561

22.1 Introduction561

22.2 Noise561

22.2.1 Shot Noise561

22.2.2 Johnson Noise564

22 2.3 Generation-Recombination Noise and l/fNoise567

22.3 Detector Performance Parameters568

22.3.1 Noise Equivalent Power568

22.3.2 Detectivity569

22 3.3 Frequency Response and Time Constant569

22.4 Practical Characteristics of Optical Derectors570

22.4 1 Photoemissive Detectors570

22.4.2 Photoconductive Detectors576

22.4.3 Photovoltaic Detectors（Photodiodes）582

22.4.4 p-i-n Photodiodes586

22.4.5 Avalanche Photodiodes587

22.5 Thermal Delectors589

22.6 Detection Limits for Optical Detector Systems591

22.6.1 Noise in Photomultipliers592

22.6.2 Photon Counting593

22.6.3 Signal-to-Noise Ratio in Direct Detection594

22.6.4 Direct Detection with p-i-n Photodiodes595

22.6.5 Direct Detection with APDs597

22.7 Coherent Detection598

22.8 Bit-Error Rate603

References605

23 Coherence Theory607

23.1 Introduction607

23.2 Square-Law Detectors607

23.3 The Analytic Signal608

23.3.1 Hilbert Transforms610

23.4 Correlation Functions611

23.5 Temporal and Spatial Coherence614

23.6 Spatial Coherence618

23.7 Spatial Coherence with an Extended Source620

23.8 Propagation Laws of Partial Coherence622

23.9 Propagation from a Finite Plane Surface625

23.10 van Cittert-Zernike Theorem630

23.11 Spatial Coherence of a Quasi-MonochromaticfUniform,Spatially Incoherent Circular Source632

23.12 Intensity Correlation Interferometry634

23.13 Intensity Fluctuations635

23.14 Photon Statistics638

23.14.1 Constant Intensity Source639

23.14.2 Random Intensities640

23.15 The Hanbury-Brown-Twiss Interferometer643

23.16 Hanbury-Brown-Twiss Experiment with Photon Count Correlations645

References646

24 Laser Applications647

24.1 Optical Communication Systems647

24.1.1 Introduction647

24.1.2 Absorption in Optical Fibers649

24.1.3 Optical Conmmunication Networks650

24.1.4 Optical Fiber Network Architectures651

24.1.5 Coding Schemes in Optical Networks653

24.1.6 Line-of-Sight Optical Links654

24.2 Holography656

24 2.1 Wavefront Reconstruction656

24.2.2 The Hologram as a Diffraction Grating660

24.2.3 Volume Holograms661

24.3 Laser Isotope Separation664

24.4 Laser Plasma Generation and Fusion669

24.5 Medical Applications of Lasers671

24.5.1 Laser Angioplasty673

References673

Appendix 1 Optical Terminology676

Appendix 2 Theδ-Function679

Appendix 3 Black-Body Radiation Formulas681

Appendix 4 RLC Cireuit683

A4.1 Analysis of a Driven RLC Circuit683

Appendix 5 Storage and Transport of Energy by Electromagnetic Fields686

Appendix 6 The Reflection and Refraction of a Plane Electromagnetic Wave at the Boundary Between Two Isotropic Media of Different Refractive Index689

Appendix 7 The Vector Differential Equation for Light Rays692

Appendix 8 Symmetry Properties of Crystals and the 32 Crystal Classes695

A8.1 Class 6mm696

A8.2 Class 42m696

A8.3 Class 222697

Appendix 9 Tensors698

Appendix 10 Bessel Function Relations701

Appendix 11 Green's Functions702

Appendix 12 Recommended Values of Some Physical Constants705

Index706