Physics of Solid-State Laser Materials (eBook)

Preface 6
About This Book 8
Contents 9
About the Authors 13
1 Energy Level of Free Ions 14
1.1 Energy Levels of the Single Electron in Atoms (Free Ions) 14
1.2 General Properties of Energy Level in Multi-electron of Free Ions 20
1.3 Energy Levels of Free Transition-Metal Ions 24
1.4 Energy Levels of Free Rare Earth Ions 28
1.5 Theory of Interactions in Rare Earth Ions 37
References 42
2 Group Theory and Quantum Theory 44
2.1 Mathematical Description of the Symmetry 44
2.2 Basic Conception of the Group 46
2.3 Theory of Group Representations 49
2.4 Direct Product Group and Direct Product Representation 53
2.5 Sketches of the Group in Spectroscopy 54
2.5.1 Finite Group 54
2.5.2 Permutation Group 56
2.5.3 Continuous Groups 59
2.6 Point Group and Their Representation 61
2.7 Symmetry and Quantum Theory of the Ions in Solids 65
2.8 Full Rotation Group and Angular Momentum Theory 68
2.9 Irreducible Tensor Operators and the Calculation of Matrix Elements 74
References 80
3 Rare Earth Ions in Materials 81
3.1 Crystal Field on the Active Ions 81
3.2 Energy Level Splitting of the Rare Earth Ions 84
3.3 Crystal Field Quantum Number 93
3.4 Group Chain Scheme Method in Crystal Field Analysis 102
References 113
4 Theory of Radiative Transition 114
4.1 Interactions Between Active Ions and Radiation 114
4.2 Probability of Emission and Absorption Processes 118
4.3 Selection Rules for Radiative Transition 126
4.3.1 Selection Rules for Radiative Transition of Free Ions and Atoms 126
4.3.2 Selection Rules for Radiative Transition of Ions in Materials 127
References 134
5 Spectroscopic Parameter and Their Calculation 135
5.1 Absorption Coefficient, Absorption (Emission) Cross-Section, and Oscillator Strength 135
5.2 Analysis of the Absorption Coefficients of Anisotropic Crystal 142
5.3 Judd–Ofelt Approximation and Related Parameter 146
5.4 Spectroscopic Parameter Calculation of Rare Earth Ion in Crystal 155
5.5 Hypersensitive Transitions 166
References 168
6 Phonon and Spectral Line 170
6.1 Quantization of Lattice Vibration—Phonon 170
6.2 Phonon Emission and Absorption in the Optical Transition 179
6.3 Main Mechanisms of the Thermal Spectral Line Broadening and Shifting 190
6.4 The Contribution of Single-Phonon Absorption (Emission) to the Spectral Linewidth 192
6.5 The Contribution of Phonon Raman Scattering to the Spectral Linewidth 196
6.6 Calculation of the Thermal Shifting of Spectral Lines 201
6.7 Examples for the Calculation of Thermal Spectral Line Broadening and Shifting 205
References 210
7 Energy Levels and Spectroscopic Properties of Transition Metal Ions 212
7.1 Energy Levels and Spectral Properties of 3d1 Electron System 213
7.2 Energy Levels and Spectral Properties of 3d2 Electron System 219
7.3 Energy Levels and Spectral Properties of 3d3 Electronic System 228
7.4 Relative Intensity Analysis of R Line in Ruby Polarized Absorption Spectrum 237
7.5 Estimation of Trivalent Chromium Ion Spectral Parameters in Solid-State Laser Materials 241
References 247
8 Non-radiative Transition Inside Ions 249
8.1 Introduction of Non-radiative Transition Matrix Elements 250
8.2 Promoting Mode and Accepting Mode in Non-radiative Transition Process 254
8.3 Non-radiative Transition Probability for Weak Coupling Systems 256
8.4 Parallelism Between Non-radiative Transition Probability and Radiative Transition Probability 262
8.5 Temperature Dependence of Non-radiative Transition Probability in Weak Coupling Systems 264
8.5.1 Experimental 264
8.6 Non-radiative Transition in Strong Coupling Systems 266
8.7 Nonlinear Theory of Non-radiative Transition 273
8.8 Stimulated Non-radiative Transition 276
References 282
9 Energy Transfer and Migration Between Ions 284
9.1 Theory of Resonant Energy Transfer 285
9.2 Phonon-Assisted Energy Transfer Between Ions 289
9.3 Statistical Theory of Energy Transfer Between Ions 294
9.4 Energy Migration Between Ions 297
9.5 Characteristics of Concentration Dependent Fluorescence Quenching for Self-activated Laser Crystals 310
References 313
10 Laser and Physical Properties of Materials 315
10.1 Brief Introduction of Solid-State Laser Principle 315
10.2 Quality Factor of Solid-State Laser Materials 322
10.3 Relationship Between Laser Threshold and Chemical Composition of Host Materials 324
10.4 Thermo-Mechanical and Thermo-Optical Properties of Solid-State Laser Materials 328
10.5 Laser Damage and Nonlinear Optical Properties 343
References 348
11 Nonlinear Optical Properties of Laser Crystals and Their Applications 350
11.1 Second-Order Nonlinear Optical Effect of Crystal 352
11.2 Relationship Between Fundamental and Second Harmonic Waves in SFD Laser Crystal 359
11.3 Nonlinear Optical Coupling Equation of SFD Laser 364
11.4 Self Sum-Frequency Mixing Effect in Nonlinear Laser Crystal 371
11.5 Stimulated Raman Scattering Effect of Laser Crystal 379
References 388
12 Apparent Crystal Field Model of Laser Glass and Its Application 390
12.1 Structure and Spectral Characteristics of Glasses 391
12.2 Apparent Crystal Field Hamiltonian for Rare Earth Ions in Non-crystal Host 396
12.3 Crystal Field Level Analysis for Er3+ Ions in Three Typical Glasses 404
References 417
Appendix A Character Tables for Point-Symmetry Group 419
Appendix B Correlation Table of Group–Subgroup 424
Appendix C Multiplication Tables for Some Point Groups 427
Appendix D Squared Reduced-Matrix Elements of Unit Operator for J ? J? Transition in Rare Earth Ions 429
Appendix E 3jm Factors for Some Group Chains 454
Appendix F Clebsch-Gordan Coefficients of the Cubic Point Group with Trigonal Bases 459
Appendix G Integral Numerical Value Associated with the Thermal Effect of the Spectra 462
Index 465