Chapter
1.5.4 Nonlinear frequency conversion
1.6 Motivation, scope and organization of the book
2 Symmetry considerations
2.2 Principles of group theory
2.2.3 Matrix representations
2.2.4 Symmetry and quantum mechanics
2.3.2 Crystallographic point groups
2.4.4 Application to coupled systems
2.4.5 Wigner-Eckart theorem
2.5 Some additional applications of group theory
2.5.1 Evaluation of matrix elements
2.5.2 Projection operators
2.5.3 Subduced representations
2.5.4 Time-reversal invariance
2.5.5 Crystal-field levels
2.5.7 Selected tables for symmetry groups
3 Optical crystals: their structures, colours and growth
3.1 Natural minerals and gemstones
3.2 Synthetic and imitation gemstones
3.3 Laser and other optical materials
3.3.1 Octahedral and distorted octahedral structures
3.3.2 Tetrahedral structures
3.3.3 The garnet structure
3.3.4 Apatites and related crystals
3.3.5 Nonlinear optical crystals
3.4 Growth of optical crystals
3.4.1 Growth by directional solidification
3.4.2 Crystal pulling techniques
3.4.3 Other melt growth techniques
3.4.4 Hydrothermal growth
3.4.5 Growth from high temperature solutions (HTSG)
3.5 General materials considerations
4 Energy levels of ions in crystals
4.1.1 Assumptions of crystal-field theory
4.1.2 Hierarchy of perturbations
4.2 Free-ion electronic structure
4.2.1 Central-field approximation
4.2.2 Electrostatic interaction
4.2.3 Spin-orbit interaction
4.3.1 Point-ion crystal-potential expansion
4.3.2 Operator equivalents
4.3.3 Explicit formulas for crystal-potential matrix elements
4.4.1 Free-ion energy levels
4.4.2 One-electron configuration
4.4.3 Intermediate-field approximation
4.4.4 Strong-field approximation
4.4.5 Tanabe-Sugano theory
4.4.6 Spin-orbit interaction
4.4.7 Lower symmetry fields
4.4.8 Empirical parameters
4.5.1 Free-ion energy levels
4.5.2 Crystal-field splitting of fine-structure levels
4.6.2 Laser-active colour centres
4.6.3 Perturbed F centres
5 Spectra of ions in crystals
5.1 Theory of optical transitions
5.1.1 Free-ion transition probabilities
5.1.2 Free-ion selection rules
5.1.3 Crystal-field selection rules
5.1.4 Electric-dipole transitions
5.1.5 Spontaneous emission
5.2 Electron-lattice coupling
5.2.1 Born-Oppenheimer approximation
5.2.2 Harmonic approximation
5.2.3 Electric-dipole transitions between Born-Oppenheimer states
5.2.4 Configuration-coordinate diagram
5.2.5 Linear coupling to many modes
5.2.6 Static Jahn-Teller effect
5.2.7 Dynamic Jahn-Teller effect
5.3.1 Electric-dipole-allowed transitions
5.3.2 Crystal-field spectra
5.3.3 Odd modes of vibration
5.4 Examples of crystal-field spectra
5.4.1 Octahedrally-coordinated Cr3+
5.4.2 Tetrahedrally-coordinated Cr4+
5.4.3 Octahedrally-coordinated Ti3+
5.5 Approximate line-shape functions
5.5.1 Alternative energy units
5.5.2 Typical Huang-Rhys factors
5.5.3 Strong-coupling limit
5.5.4 Approximations for linear coupling to many modes
5.5.5 Lattice Green's function method for linear coupling to many modes
5.5.6 Approximations for quadratic and an harmonic coupling
5.6 Nonlinear susceptibilities
6 Radiationless transitions
6.1.2 Radiationless transition rate
6.2.2 Adiabatic-coupling scheme
6.2.3 Static-coupling scheme
6.2.5 Quadratic and an harmonic coupling
6.3.1 Landau-Zener theory
6.3.3 Dexter-Klick-Russell criterion
6.4 Manifestations of radiationless transitions
6.4.2 Transition-metal and rare-earth impurities
6.4.4 Recombination-enhanced defect reactions
7 Energy transfer and excited state absorption
7.1 Microscopic theory of donor-acceptor energy transfer
7.2 Macroscopic theory of donor-acceptor energy transfer
7.2.1 No donor-donor transfer
7.2.2 Influence of donor-donor energy transfer
7.3 Excited state absorption
7.4 Experimental studies of excited state processes
7.4.1 Quenching of luminescence and laser efficiency
7.4.2 High dopant concentrations
7.4.3 Energy transfer and sensitization
7.4.4 Upconversion processes
8.1.1 Limitations of crystal-field theory
8.1.3 Variational principle
8.1.5 Charge transfer model
8.2.2 Hartree-Fock approximation
8.3.2 Configuration interaction
8.3.3 Perturbation theory
8.4 Additional approximations
8.4.1 Effective core potentials
8.4.2 Local exchange approximation
8.4.3 Approximate SCF semi-empirical methods
8.4.4 Extreme semi-empirical methods
8.5.1 Embedding potentials
8.6.1 Cr3+in halide elpasolites
8.6.2 The 77°(1) centre and its analogues
8.6.3 Ti3+ in distorted octahedral coordination
8.6.4 Odd-parity distortions of (CrF6)3"
9 Engineering the crystal field
9.1 Principles and objectives
9.1.1 Manipulating the unit cell
9.1.2 Composition of the unit cell
9.2 The positions and shapes of optical transitions
9.2.1 F-type centres in the alkali halides
9.2.2 77°(1)- centre in the alkali halides
9.2.3 Transition-metal ions
9.2.5 Optical line shape and laser tuning
9.3 Other aspects of transition-metal ion spectroscopy
9.3.1 Mixed vibronic states and avoided level crossings
9.3.2 Dominant symmetry and low symmetry distortions
9.4 Laser efficiency and threshold
9.4.1 Strength of optical transitions
9.4.2 Quenching of luminescence and laser efficiency
9.4.3 Excited state absorption
9.5 Energy transfer processes
9.6 Empirical rules for transition-metal and rare-earth ions
9.6.1 Unit cell dimensions
9.6.2 Spectrochemical series
9.6.3 Nephelauxetic effect
9.6.4 Crystal-field stabilization energies
9.6.5 The crerR product rule
9.7 All-solid-state lasers
9.8 Optical nonlinearities
10 The crystal field engineered
10.1 Tunable solid state lasers
10.2 Colour centre lasers
10.3 Transition-metal ion lasers
10.3.2 Cr3+: colquiriite lasers
10.3.3 Other Cr3+-activated lasers
10.3.4 Ti3+-activated lasers
10.3.5 Lasers based on Co2+ ions
10.3.6 Lasers based on (3d)2 and (3d) 8 configuration ions
10.3.7 Mid-infrared laser transitions of Cr2+-doped chalcogenides
10.4 Tunable rare-earth ion lasers
10.5 Fixed-wavelength rare-earth ion lasers
10.5.1 Spectroscopy and laser transitions of Pr3+ and Tm3+
10.5.2 Nd3+ and Er3+-activated lasers
10.5.3 Other rare-earth ions
10.6 Energy transfer and upconversion lasers
10.8 All-solid-state lasers (ASSLs)
10.8.1 Fixed wavelength LD-pumped solid state lasers
10.8.2 Tunable solid state lasers pumped by laser diodes
10.8.3 Opical nonlinearities and diode-pumped lasers
Crystal-Field Engineering of Solid-State Laser Materials
( Cambridge Studies in Modern Optics )
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