Contents
1 Energy Level of Free Ions 1
1.1 Energy Levels of the Single Electron in Atoms Free Ions 1
1.2 General Properties of Energy Level in Multi-electron of Free Ions 7
1.3 Energy Levels of Free Transition-Metal Ions 11
1.4 Energy Levels of Free Rare Earth Ions 15
1.5 Theory of Interactions in Rare Earth Ions 24
References 29
2 Group Theory and Quantum Theory 31
2.1 Mathematical Description of the Symmetry 31
2.2 Basic Conception of the Group 33
2.3 Theory of Group Representations 36
2.4 Direct Product Group and Direct Product Representation 40
2.5 Sketches of the Group in Spectroscopy 41
2.5.1 Finite Group 41
2.5.2 Permutation Group 43
2.5.3 Continuous Groups 46
2.6 Point Group and Their Representation 48
2.7 Symmetry and Quantum Theory of the Ions in Solids 52
2.8 Full Rotation Group and Angular Momentum Theory 55
2.9 Irreducible Tensor Operators and the Calculation of Matrix Elements 61
References 67
3 Rare Earth Ions in Materials 69
3.1 Crystal Field on the Active Ions 69
3.2 Energy Level Splitting of the Rare Earth Ions 72
3.3 Crystal Field Quantum Number 81
3.4 Group Chain Scheme Method in Crystal Field Analysis 90
References 101
4 Theory of Radiative Transition 103
4.1 Interactions Between Active Ions and Radiation 103
4.2 Probability of Emission and Absorption Processes 107
4.3 Selection Rules for Radiative Transition 115
4.3.1 Selection Rules for Radiative Transition of Free Ions and Atoms 115
4.3.2 Selection Rules for Radiative Transition of Ions in Materials 116
References 123
5 Spectroscopic Parameter and Their Calculation 125
5.1 Absorption Coefficient， Absorption Emission Cross-Section， and Oscillator Strength 125
5.2 Analysis of the Absorption Coefficients of Anisotropic Crystal 132
5.3 Judd–Ofelt Approximation and Related Parameter 136
5.4 Spectroscopic Parameter Calculation of Rare Earth Ion in Crystal 145
5.5 Hypersensitive Transitions 156
References 158
6 Phonon and Spectral Line 161
6.1 Quantization of Lattice Vibration—Phonon 161
6.2 Phonon Emission and Absorption in the Optical Transition 170
6.3 Main Mechanisms of the Thermal Spectral Line Broadening and Shifting 181
6.4 The Contribution of Single-Phonon Absorption Emission to the Spectral Linewidth 183
6.5 The Contribution of Phonon Raman Scattering to the Spectral Linewidth 187
6.6 Calculation of the Thermal Shifting of Spectral Lines 192
6.7 Examples for the Calculation of Thermal Spectral Line Broadening and Shifting 196
References 201
7 Energy Levels and Spectroscopic Properties of Transition Metal Ions 203
7.1 Energy Levels and Spectral Properties of 3d1 Electron System 204
7.2 Energy Levels and Spectral Properties of 3d2 Electron System 210
7.3 Energy Levels and Spectral Properties of 3d3 Electronic System 219
7.4 Relative Intensity Analysis of R Line in Ruby Polarized Absorption Spectrum 228
7.5 Estimation of Trivalent Chromium Ion Spectral Parameters in Solid-State Laser Materials 232
References 238
8 Non-radiative Transition Inside Ions 241
8.1 Introduction of Non-radiative Transition Matrix Elements 242
8.2 Promoting Mode and Accepting Mode in Non-radiative Transition Process 246
8.3 Non-radiative Transition Probability for Weak Coupling Systems 248
8.4 Parallelism Between Non-radiative Transition Probability and Radiative Transition Probability 254
8.5 Temperature Dependence of Non-radiative Transition Probability in Weak Coupling Systems 256
8.5.1 Experimental 256
8.6 Non-radiative Transition in Strong Coupling Systems 258
8.7 Nonlinear Theory of Non-radiative Transition 265
8.8 Stimulated Non-radiative Transition 268
References 274
9 Energy Transfer and Migration Between Ions 277
9.1 Theory of Resonant Energy Transfer 278
9.2 Phonon-Assisted Energy Transfer Between Ions 282
9.3 Statistical Theory of Energy Transfer Between Ions 287
9.4 Energy Migration Between Ions 290
9.5 Characteristics of Concentration Dependent Fluorescence Quenching for Self-activated Laser Crystals 303
References 306
10 Laser and Physical Properties of Materials 309
10.1 Brief Introduction of Solid-State Laser Principle 309
10.2 Quality Factor of Solid-State Laser Materials 316
10.3 Relationship Between Laser Threshold and Chemical Composition of Host Materials 318
10.4 Thermo-Mechanical and Thermo-Optical Properties
of Solid-State Laser Materials 322
10.5 Laser Damage and Nonlinear Optical Properties 337
References 342
11 Nonlinear Optical Properties of Laser Crystals and Their Applications 345
11.1 Second-Order Nonlinear Optical Effect of Crystal 347
11.2 Relationship Between Fundamental and Second Harmonic Waves in SFD Laser Crystal 354
11.3 Nonlinear Optical Coupling Equation of SFD Laser 359
11.4 Self Sum-Frequency Mixing Effect in Nonlinear Laser Crystal 366
11.5 Stimula
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