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
