Laser Physics

Preface xiii

1 Introduction to Laser Operation 1

1.1 Introduction 1

1.2 Lasers and Laser Light 3

1.3 Light in Cavities 8

1.4 Light Emission and Absorption in Quantum Theory 10

1.5 Einstein Theory of Light–Matter Interactions 11

1.6 Summary 14

2 Atoms, Molecules, and Solids 17

2.1 Introduction 17

2.2 Electron Energy Levels in Atoms 17

2.3 Molecular Vibrations 26

2.4 Molecular Rotations 31

2.5 Example: Carbon Dioxide 33

2.6 Conductors and Insulators 35

2.7 Semiconductors 39

2.8 Semiconductor Junctions 45

2.9 Light-Emitting Diodes 49

2.10 Summary 55

Appendix: Energy Bands in Solids 56

Problems 64

3 Absorption, Emission, and Dispersion of Light 67

3.1 Introduction 67

3.2 Electron Oscillator Model 69

3.3 Spontaneous Emission 74

3.4 Absorption 78

3.5 Absorption of Broadband Light 84

3.6 Thermal Radiation 85

3.7 Emission and Absorption of Narrowband Light 93

3.8 Collision Broadening 99

3.9 Doppler Broadening 105

3.10 The Voigt Profile 108

3.11 Radiative Broadening 112

3.12 Absorption and Gain Coefficients 114

3.13 Example: Sodium Vapor 118

3.14 Refractive Index 123

3.15 Anomalous Dispersion 129

3.16 Summary 132

Appendix: The Oscillator Model and Quantum Theory 132

Problems 137

4 Laser Oscillation: Gain and Threshold 141

4.1 Introduction 141

4.2 Gain and Feedback 141

4.3 Threshold 143

4.4 Photon Rate Equations 148

4.5 Population Rate Equations 150

4.6 Comparison with Chapter 1 152

4.7 Three-Level Laser Scheme 153

4.8 Four-Level Laser Scheme 156

4.9 Pumping Three- and Four-Level Lasers 157

4.10 Examples of Three- and Four-Level Lasers 159

4.11 Saturation 161

4.12 Small-Signal Gain and Saturation 164

4.13 Spatial Hole Burning 167

4.14 Spectral Hole Burning 169

4.15 Summary 172

Problems 173

5 Laser Oscillation: Power and Frequency 175

5.1 Introduction 175

5.2 Uniform-Field Approximation 175

5.3 Optimal Output Coupling 178

5.4 Effect of Spatial Hole Burning 180

5.5 Large Output Coupling 183

5.6 Measuring Gain and Optimal Output Coupling 187

5.7 Inhomogeneously Broadened Media 191

5.8 Spectral Hole Burning and the Lamb Dip 192

5.9 Frequency Pulling 194

5.10 Obtaining Single-Mode Oscillation 198

5.11 The Laser Linewidth 203

5.12 Polarization and Modulation 207

5.13 Frequency Stabilization 215

5.14 Laser at Threshold 220

Appendix: The Fabry-Pérot Etalon 223

Problems 226

6 Multimode and Pulsed Lasing 229

6.1 Introduction 229

6.2 Rate Equations for Intensities and Populations 229

6.3 Relaxation Oscillations 230

6.4 Q Switching 233

6.5 Methods of Q Switching 236

6.6 Multimode Laser Oscillation 237

6.7 Phase-Locked Oscillators 239

6.8 Mode Locking 242

6.9 Amplitude-Modulated Mode Locking 246

6.10 Frequency-Modulated Mode Locking 248

6.11 Methods of Mode Locking 251

6.12 Amplification of Short Pulses 255

6.13 Amplified Spontaneous Emission 258

6.14 Ultrashort Light Pulses 264

Appendix: Diffraction of Light by Sound 265

Problems 266

7 Laser Resonators and Gaussian Beams 269

7.1 Introduction 269

7.2 The Ray Matrix 270

7.3 Resonator Stability 274

7.4 The Paraxial Wave Equation 279

7.5 Gaussian Beams 282

7.6 The ABCD Law for Gaussian Beams 288

7.7 Gaussian Beam Modes 292

7.8 Hermite–Gaussian and Laguerre–Gaussian Beams 298

7.9 Resonators for He–Ne Lasers 306

7.10 Diffraction 309

7.11 Diffraction by an Aperture 312

7.12 Diffraction Theory of Resonators 317

7.13 Beam Quality 320

7.14 Unstable Resonators for High-Power Lasers 321

7.15 Bessel Beams 322

Problems 327

8 Propagation of Laser Radiation 331

8.1 Introduction 331

8.2 The Wave Equation for the Electric Field 332

8.3 Group Velocity 336

8.4 Group Velocity Dispersion 340

8.5 Chirping 351

8.6 Propagation Modes in Fibers 355

8.7 Single-Mode Fibers 361

8.8 Birefringence 365

8.9 Rayleigh Scattering 372

8.10 Atmospheric Turbulence 377

8.11 The Coherence Diameter 379

8.12 Beam Wander and Spread 388

8.13 Intensity Scintillations 392

8.14 Remarks 395

Problems 397

9 Coherence in Atom-Field Interactions 401

9.1 Introduction 401

9.2 Time-Dependent Schrödinger Equation 402

9.3 Two-State Atoms in Sinusoidal Fields 403

9.4 Density Matrix and Collisional Relaxation 408

9.5 Optical Bloch Equations 414

9.6 Maxwell–Bloch Equations 420

9.7 Semiclassical Laser Theory 428

9.8 Resonant Pulse Propagation 432

9.9 Self-Induced Transparency 438

9.10 Electromagnetically Induced Transparency 441

9.11 Transit-Time Broadening and the Ramsey Effect 446

9.12 Summary 451

Problems 452

10 Introduction to Nonlinear Optics 457

10.1 Model for Nonlinear Polarization 457

10.2 Nonlinear Susceptibilities 459

10.3 Self-Focusing 464

10.4 Self-Phase Modulation 469

10.5 Second-Harmonic Generation 471

10.6 Phase Matching 475

10.7 Three-Wave Mixing 480

10.8 Parametric Amplification and Oscillation 482

10.9 Two-Photon Downconversion 486

10.10 Discussion 492

Problems 494

11 Some Specific Lasers and Amplifiers 497

11.1 Introduction 497

11.2 Electron-Impact Excitation 498

11.3 Excitation Transfer 499

11.4 He–Ne Lasers 502

11.5 Rate Equation Model of Population Inversion in He–Ne Lasers 505

11.6 Radial Gain Variation in He–Ne Laser Tubes 509

11.7 CO₂ Electric-Discharge Lasers 513

11.8 Gas-Dynamic Lasers 515

11.9 Chemical Lasers 516

11.10 Excimer Lasers 518

11.11 Dye Lasers 521

11.12 Optically Pumped Solid-State Lasers 525

11.13 Ultrashort, Superintense Pulses 532

11.14 Fiber Amplifiers and Lasers 537

11.15 Remarks 553

Appendix: Gain or Absorption Coefficient for Vibrational-Rotational Transitions 554

Problems 558

12 Photons 561

12.1 What is a Photon 561

12.2 Photon Polarization: All or Nothing 562

12.3 Failures of Classical Theory 563

12.4 Wave Interference and Photons 567

12.5 Photon Counting 569

12.6 The Poisson Distribution 573

12.7 Photon Detectors 575

12.8 Remarks 585

Problems 586

13 Coherence 589

13.1 Introduction 589

13.2 Brightness 589

13.3 The Coherence of Light 592

13.4 The Mutual Coherence Function 595

13.5 Complex Degree Of Coherence 598

13.6 Quasi-Monochromatic Fields and Visibility 601

13.7 Spatial Coherence of Light From Ordinary Sources 603

13.8 Spatial Coherence of Laser Radiation 608

13.9 Diffraction of Laser Radiation 610

13.10 Coherence and the Michelson Interferometer 611

13.11 Temporal Coherence 613

13.12 The Photon Degeneracy Factor 616

13.13 Orders of Coherence 619

13.14 Photon Statistics of Lasers and Thermal Sources 620

13.15 Brown–Twiss Correlations 627

Problems 634

14 Some Applications of Lasers 637

14.1 Lidar 637

14.2 Adaptive Optics for Astronomy 648

14.3 Optical Pumping and Spin-Polarized Atoms 658

14.4 Laser Cooling 671

14.5 Trapping Atoms with Lasers and Magnetic Fields 685

14.6 Bose–Einstein Condensation 690

14.7 Applications of Ultrashort Pulses 697

14.8 Lasers in Medicine 718

14.9 Remarks 728

Problems 729

15 Diode Lasers and Optical Communications 735

15.1 Introduction 735

15.2 Diode Lasers 736

15.3 Modulation of Diode Lasers 754

15.4 Noise Characteristics of Diode Lasers 760

15.5 Information and Noise 774

15.6 Optical Communications 782

Problems 790

16 Numerical Methods for Differential Equations 793

16.A Fortran Program for Ordinary Differential Equations 793

16.B Fortran Program for Plane-Wave Propagation 796

16.C Fortran Program for Paraxial Propagation 799

Index 809