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Physics, Optics, and Spectroscopy of Materials. Edition No. 1

  • Book

  • 544 Pages
  • September 2022
  • John Wiley and Sons Ltd
  • ID: 5837249

PHYSICS, OPTICS, AND SPECTROSCOPY OF MATERIALS

Bridges a gap that exists between optical spectroscopists and laser systems developers

Physics, Optics, and Spectroscopy of Materials provides professionals and students in materials science and engineering, optics, and spectroscopy a basic understanding and tools for stimulating current research, as well as developing and implementing new laser devices in optical spectroscopy. The author - a noted expert on that subject matter - covers a wide range of topics including: effects of light and mater interaction such as light absorption, emission and scattering by atoms and molecules; energy levels in hydrogen, hydrogen-like atoms, and many electron atoms; electronic structure of molecules, classification of vibrational and rotational motions of molecules, wave propagation and oscillations in dielectric solids, light propagation in isotropic and anisotropic solids, including frequency doubling dividing and shifting, solid materials optics, and lasers.

The book provides a basic overview of the laser and its comprising components. For example, the text describes methods for achieving fast Q-switching in laser cavities, and illustrates examples of several specific laser systems used in industry and scientific research. This important book:

  • Provides a comprehensive background in material physics, optics, and spectroscopy
  • Details examples of specific laser systems used in industry and scientific research including helium/neon laser, copper vapor laser, hydrogen-fluoride chemical laser, dye lasers, and diode lasers
  • Presents a basic overview of the laser and its comprising components
  • Elaborates on several important subjects in laser beams optics: divergence modes, lens transitions, and crossing of anisotropic crystals

Written for research scientists and students in the fields of laser science and technology and materials optical spectroscopy, Physics, Optics, and Spectroscopy of Materials covers knowledge gaps for concepts including oscillator strength, allowed and forbidden transitions between electronic and vibrational states, Raman scattering, and group-theoretical states nomenclature.

Table of Contents

Introduction XIII

1 Electromagnetic Radiation/Matter Interaction - A Classical Approach 1

1.1 Electromagnetic Radiation by Atoms and Molecules 1

1.2 Spectral Line Widths 5

1.2.1 Natural Width 5

1.2.2 Doppler Broadening 7

1.2.3 Additional Broadening Mechanisms 9

1.3 Electromagnetic Radiation Absorption by Atoms and Molecules 10

1.4 Radiation Scattering by Atoms and Molecules 14

1.5 Reminder: Multipole Moments Expansion 18

Exercises for Chapter 1 20

2 Electromagnetic Radiation/Matter Interaction - A Semi-Quantum Approach 21

2.1 A Reminder of Perturbation Theory 21

2.1.1 Static Perturbation Theory 21

2.1.2 Time-Dependent Perturbation Theory 23

2.2 A Reminder of Planck’s Black-Body Radiation 26

2.3 An Atom or Molecule in an Electromagnetic Radiation Field 28

2.4 Stimulated Emission and Einstein’s Coefficients 30

2.5 Radiation Absorption and Amplification in Matter 32

2.6 Black Body Radiation - Continuation and Completion 36

Exercises for Chapter 2 39

3 The Hydrogen Atom - Electrostatic Attraction Approximation 41

3.1 De Broglie Waves and Schrödinger’s Equation 41

3.2 Differential Operators and Physical Quantities 44

3.3 Schrödinger Equation Solution for Hydrogen and Hydrogen-Like Atoms 45

3.4 Physical Meanings of Schrödinger Equation Solutions for Hydrogen-Like Atoms 55

3.5 Spectroscopy of Hydrogen and Hydrogen-Like Atoms 60

3.6 Selection Rules 61

Exercises for Chapter 3 64

4 Hydrogen Atom - Corrections to the Electrostatic Attraction Approximation 67

4.1 Angular Momentum and the Orbital Quantum Number 67

4.2 Mechanical Relativistic Correction to the Eigenenergies of the Hydrogen Atom 71

4.3 Electron Spinning 72

4.3.1 Infinitesimal Rotations and the Angular Momentum Operator 73

4.3.2 Generalization of the Angular Momentum Concept 75

4.3.2.1 Basis Functions Properties 75

4.3.2.2 Eigenvalues of the J 2 Operator 76

4.3.2.3 Matrix Elements of Angular Momentum Operators 77

4.3.2.4 Electron Spin 77

4.4 Combining Orbital Angular Momentum and Spin 80

4.5 Gyromagnetic Ratio and Spin/Orbit Coupling 82

4.5.1 The Gyromagnetic Ratio 82

4.5.2 Spin/Orbit Interaction 83

4.5.2.1 Electric Dipole of a Moving Magnetic Dipole 83

4.5.2.2 Thomas Precession 84

4.5.2.3 Total Spin/Orbit Coupling 85

4.5.3 Summed Energy Spectrum Correction 85

4.6 Landé Factor 86

4.7 Lamb Shift 87

4.8 Selection Rules and Transition Probabilities 91

4.9 Static External Magnetic and Electric Fields: Zeeman and Stark Effects 95

4.9.1 Zeeman Splitting 95

4.9.1.1 Weak Magnetic Field 95

4.9.1.2 Strong Magnetic Field 97

4.9.2 Stark Splitting 98

4.9.2.1 Ground State; First-Order Perturbation Theory 98

4.9.2.2 Ground State; Second-Order Perturbation Theory 98

4.9.2.3 First Excited State; First-Order Perturbation Theory 101

4.10 The Fine Structure 103

4.10.1 Isotope Shifting 103

4.10.2 Nuclear Magnetic Shifting 104

4.10.3 Nuclear Quadrupole Shifting 104

4.11 Appendix: Clebsch-Gordan Coefficients for Coupling of Two Angular Momentums 104

Exercises for Chapter 4 104

5 Many-Electron Atoms 107

5.1 Preamble 107

5.2 Helium-Like Atoms 107

5.2.1 Zero-Order Approximation under the Independent Electron Model 108

5.2.2 First-Order Correction and the Effective Screening Idea 109

5.2.3 Exchange Symmetry 111

5.2.4 Helium Energy Level Scheme 114

5.3 Bosons, Fermions, and Pauli Exclusion Principle 115

5.3.1 Harmonic Oscillator 115

5.3.1.1 Hamiltonian and Creation and Destruction Operators 115

5.3.1.2 Energy Levels Scheme of the Harmonic Oscillator 117

5.3.1.3 Eigenfunctions of the Harmonic Oscillator 117

5.3.1.4 Bosons 119

5.3.2 Angular Momentum 119

5.3.2.1 Annihilation, Creation, and Occupation Operators 119

5.3.2.2 Pauli Exclusion Principle 121

5.4 Electronic Structure of Many-Electron Atoms 122

5.4.1 Slater Determinant 122

5.4.2 Electron Configuration and the Shell Structure 122

5.4.3 Electronic Configuration and Chemical Stability 124

5.4.4 Spin/Orbit Coupling and Term Determination 125

5.5 Excited-States Structure in Many-Electron Atoms 133

5.5.1 States Structure of Single Valence Atoms 133

5.5.2 States Structure of Two-Valence Atoms 135

5.5.3 Classical Approximations 138

Exercises for Chapter 5 139

6 Electron Orbits in Molecules 141

6.1 Preamble 141

6.2 The Hydrogen Molecule Ion 142

6.2.1 The Hamiltonian of the Hydrogen Molecule Ion 142

6.2.2 A Qualitative Approach to Solution Using a Linear Combination of Atomic Orbitals 143

6.2.3 Energy States Calculation by LCAO Method 145

6.2.4 Improvements in the LCAO Method 149

6.2.5 Optical Transition Probabilities 149

6.3 Molecular Electronic Angular Momentum 150

6.3.1 Eigenfunctions of L 2 and L 2 Z in a Lone Atom 150

6.3.2 Orbital Angular Momentum of an Independent Electron in a Molecule 152

6.3.3 Electronic Spin in a Diatomic Molecule 153

6.4 Many-Electron Homonuclear Diatomic Molecules 153

6.5 Many-Electron Heteronuclear Diatomic Molecules 158

6.6 Multiatomic Molecules 160

6.6.1 Nonconjugated Molecules 161

6.6.2 Conjugated Molecules 166

6.7 Appendix: Calculation of an Infinitesimal Volume Element in Elliptic Coordinates 170

Exercises for Chapter 6 172

7 Molecular (Especially Diatomic) Internal Oscillations 173

7.1 Preamble 173

7.2 The Born-Oppenheimer Approximation 173

7.3 Vibrational and Rotational Modes of Diatomic Molecules 176

7.3.1 Empiric Analytic Potential 176

7.3.2 Molecular Vibrational Modes 177

7.3.3 Molecular Rotational Modes 178

7.3.4 Molecular Vibrational/Rotational Modes 180

7.3.5 Transition Probabilities and Selection Rules 182

7.4 Vibrational/Rotational Absorption Spectra 185

7.4.1 Pure Rotational Transitions 185

7.4.2 Temperature Dependence of Pure Rotational Transitions 185

7.4.3 Mixed Vibration/Rotation Transitions 188

7.5 Electronic Transitions and the Franck-Condon Principle 189

7.5.1 General Considerations 189

7.5.2 Selection Rules for Electronic Transitions 190

7.5.3 Temperature Dependence of the Electronic Transitions Spectrum 192

7.5.4 The Franck-Condon Principle 193

7.5.5 Fluorescence and Stokes-Shift 195

7.5.6 Selection Rules for Electronic Transitions Including Vibrations and Rotations 197

Exercises for Chapter 7 199

8 Internal Oscillations of Polyatomic Molecules 201

8.1 Preamble 201

8.2 Zero-Order Mechanical Energy Approximation of a Polyatomic Molecule 201

8.3 Molecular Vibrational Modes 204

8.4 Vibrational Energy Scheme 207

8.5 Rayleigh and Raman Scattering 207

8.5.1 General Rayleigh Scattering by Molecules 207

8.5.2 Raman Scattering 212

8.6 Point Symmetry 215

8.7 Group Representations, Characters, and Reduction Equation 220

8.8 Similarity Classes, Irreducible Representations, and Character Tables 221

8.9 Selection Rules for Electric Dipole Absorption and Raman Scattering 223

8.10 Method for Calculation and Description of Molecular Vibrational Species 225

8.11 Examples of Molecular Vibrational Symmetry Species 227

8.11.1 The Ammonia NH 3 Molecule 227

8.11.2 The Ethylene C 2 H 4 Molecule 228

8.11.3 The Carbon Tetrachloride CCl 4 Molecule 230

8.12 Point Groups, Character Tables, and Selection Rules 232

8.12.1 The C p group 232

Exercises for Chapter 8 241

9 Crystalline Solids 245

9.1 Preamble 245

9.2 Periodic Crystals 245

9.3 Lattice-Vector and Lattice-Plane Orientations 251

9.4 The Reciprocal Lattice 251

9.5 Internal Crystalline Oscillations 252

9.5.1 Introduction 252

9.5.2 Hamiltonian and Dynamic Equations 253

9.5.3 Allowed Wave-Number States and Their Density 255

9.5.4 Dispersion Curves 257

9.5.4.1 Acoustic Modes 259

9.5.4.2 Optical Oscillation Modes 264

9.5.5 Theoretical Dispersion Curve Calculations - A Basic Approach 272

9.5.6 Dispersion Curves and Specific Heats 273

9.6 Appendix: Intermediate Calculation for Justifying Eq. (9.11) 274

Exercises for Chapter 9 275

10 Dielectric Crystalline Solids 277

10.1 Light Propagation in a Dielectric Medium 277

10.2 Light Transition from Vacuum into a Dielectric Medium 283

10.3 Kramers-Kronig Relations 286

10.4 A Microscopic Model of the Dielectric Function 289

10.5 A Reminder: Gradient, Divergence, Rotor, and the Cauchy Equation 297

10.5.1 Gradient, Divergence, and Rotor 297

10.5.2 Cauchy’s Equation 298

Exercises for Chapter 10 299

11 Crystalline Oscillation Species 301

11.1 Introduction 301

11.2 Crystalline Sites 301

11.3 Tabulation Method 302

11.4 Calculation of Crystalline Oscillation Species - An Example 305

11.5 Tabulation of Crystalline Space Group Properties 310

Exercises for Chapter 11 346

12 Atoms and Ions in Crystalline Sites 347

12.1 Introduction 347

12.2 Energy States of Alkali and Alkali-Like Atoms 347

12.3 Energy States of Many-Electron Atoms and Ions 349

12.4 Dopant Atoms or Ions in Crystalline Sites 362

12.4.1 The Full Rotation Group and its Representations 363

12.4.2 A Hydrogen-Like Atom in a Crystalline Perturbation Field 366

12.4.3 Example: States Splitting in a Cubic Perturbation Field 368

12.4.4 Tanabe-Sugano Diagrams 373

12.5 Transition Probabilities and Selection Rules 374

12.6 Spectroscopic Examples 375

12.7 Appendix: An Integral Over Three Multiplied Spherical Harmonics 378

Exercises for Chapter 12 379

13 Non-Radiative and Mixed Decay Transitions 381

13.1 Non-Radiative Transitions Between Close Electronic States 381

13.1.1 Debye Approximation of Phonon Dispersion Curves 381

13.1.2 Non-Radiative Transitions Between Very Close Electronic States 382

13.1.3 Non-Radiative Transitions Between Close Electronic States 386

13.2 Radiative Transition Lifetime and Optical Absorption and Emission Spectra 389

13.3 Multi-Phonon Non-Radiative Transitions 395

13.3.1 Principles and Methods in Experimental Measurement of Non-Radiative Lifetimes 395

13.3.2 Theoretical Calculation of the Non-Radiative Lifetime 396

Exercises for Chapter 13 406

14 Basic Acquaintance with the Laser and Its Components 407

14.1 General Description 407

14.2 The Optical Cavity 408

14.3 The Prism 409

14.3.1 A Prism Minimum Deviation Arrangement 410

14.3.2 Light Dispersion in a Prism 412

14.3.3 Prism Wavelength Resolution 412

14.4 Reflection Grating 414

14.4.1 Light Diffraction Off a Reflection Grating 414

14.4.2 Wavelength Resolution of a Reflection Grating 416

14.5 Fabry-Pérot Etalon 417

14.5.1 General Description and Fundamental Terms 417

14.5.2 The Etalon as an Optical Filter 419

14.5.3 The Etalon as a Spectrometer 421

14.5.3.1 A Solid Etalon 421

14.5.3.2 A Scanning Etalon 422

14.5.4 Etalon Transmission of Incoherent Light 423

14.6 Brewster Window and a Brewster Plate 423

14.6.1 Snell’s Law and Fresnel Equations 423

14.6.2 Achieving Polarized Laser Emission 428

14.7 Loss Presentation in a Laser Cavity 429

Exercises for Chapter 14 430

15 Transverse Optical Modes and Crystal Optics 431

15.1 Preamble 431

15.2 Transverse Single-Mode Gaussian Beam 432

15.3 Transverse Multi-Mode Beams 435

15.4 Selecting a Transverse Mode for a Laser Output 437

15.5 Lens Crossing of a Single-Mode Transverse Gaussian Beam 437

15.6 Multi-Mode Transverse Gaussian Beams 439

15.7 Crystal Optics 440

15.7.1 General Description 440

15.7.2 Uniaxial Crystals 441

15.7.3 Walk-Off 442

15.8 Retardation Plates 443

Exercises for Chapter 15 445

16 Pulsed High Power Lasers 447

16.1 Introduction 447

16.2 Passive Q-Switching Using a Saturable Light Absorber 447

16.2.1 Saturable Absorbers 447

16.2.1.1 Slow Saturable Absorber 449

16.2.1.2 Fast Saturable Absorber 450

16.2.1.3 Examples 451

16.2.2 Q-Switching Using a Saturable Absorber 455

16.3 Active Q-Switching Using Electrooptic Crystals 456

16.3.1 The Electrooptic Effect 456

16.3.2 Q-Switching Using an Electrooptic Crystal 461

16.4 Mode-Locking 462

Exercises for Chapter 16 466

17 Frequency Conversions of Laser Beams 469

17.1 Non-Linear Crystals 469

17.2 Electromagnetic Wave Propagation in a Non-Linear Crystal 475

17.2.1 Maxwell’s Equations 475

17.2.2 Overlapping Beams of Different Frequencies Propagating in the Same Direction 476

17.2.3 Frequency Doubling 477

17.3 Optical Parametric Oscillations 483

17.3.1 Forced Parametric Oscillations 483

17.3.2 Optical Parametric Amplification 485

17.3.3 Optical Parametric Oscillations Based Laser 488

17.4 A Reminder: Hyperbolic “Trigonometric” Functions 490

Exercises for Chapter 7 490

18 Examples of Various Laser Systems 493

18.1 Introduction 493

18.2 Helium-Neon Laser 493

18.3 Copper Vapor Laser 496

18.4 Hydrogen Fluoride Chemical Laser 499

18.5 Neodymium-YAG Laser 503

18.6 Dye Lasers 506

18.7 Diode Lasers 510

Exercises for Chapter 18 515

Appendix A Greek alphabet and phonetic names 517

Appendix B Table of physical constants 519

Appendix C Dirac δ function 521

Appendix D Literature references for further reading 523

Index 525

Authors

Zeev Burshtein Ben-Gurion University, Be'er Sheva, Israel.