Optical Spectroscopy of Glasses

During the last fifteen years the field of the investigation of glasses has experienced a period of extremely rapid growth, both in the development of new theoretical ap­ proaches and in the application of new experimental techniques. After these years of intensive experimental and theoretical work our understanding of the structure of glasses and their intrinsic properties has greatly improved. In glasses we are con­ fronted with the full complexity of a disordered medium. The glassy state is characterised not only by the absence of any long-range order; in addition, a glass is in a non-equilibrium state and relaxation processes occur on widely different time scales even at low temperatures. Therefore it is not surprising that these complex and novel physical properties have provided a strong stimulus for work on glasses and amorphous systems. The strikingly different properties of glasses and of crystalline solids, e. g. the low­ temperature behaviour of the heat capacity and the thermal conductivity, are based on characteristic degrees of freedom described by the so-called two-level systems. The random potential of an amorphous solid can be represented by an ensemble of asymmetric double minimum potentials. This ensemble gives rise to a new class of low-lying excitations unique to glasses. These low-energy modes arise from tunneling through a potential barrier of an atom or molecule between the two minima of a double-well.

Dynamical Theory of Optical Linewidths in Glasses.- 1. Introduction.- 2. Model Hamiltonian.- 3. TLS Line-Broadening Mechanism.- 3.1. Diagonal Modulation.- 3.2. Off-Diagonal Modulation.- 4. Homogeneous Linewidth.- 4.1. Spectral Function.- 4.2. Short-Time Behavior.- 4.3. Long-Time Behavior.- 5. Microscopic Theory.- 5.1. Green’s Functions.- 5.2. Diagonal Modulation.- 5.3. Off-Diagonal Modulation.- 5.4. General Treatment.- 6. Conclusions.- Optical Spectroscopy of Ions in Inorganic Glasses.- 1. Introduction.- 2. Inorganic Glass Structure and Composition.- 2.1. Definition of the Glassy State.- 2.2. Terminology and Structure.- 2.3. Coloring and Activation of Glasses.- 2.4. Composition and Phase Separation.- 3. Optical Properties of Impurity Centers in Inorganic Glass.- 3.1. Spectra of Ions in Solids.- 3.2. Inhomogeneous Contributions in the Spectra of Solids.- 3.3. Conventional Spectroscopy of Ions in Glasses.- 4. Laser Spectroscopy of Ions in Glasses.- 4.1. Static Spectroscopic Studies and Structure.- 4.2. Radiative and Non-Radiative Transitions.- 4.3. Thermalization and Homogeneous Linewidths.- 4.4. Energy Transfer of Optical Excitation in Glasses.- 5. Concluding Remarks.- Model Calculation of Optical Dephasing in Glasses.- 1. Introduction.- 1.1. Anomalous Low-Temperature Properties of Amorphous Solids — Experiments and Interpretations.- 1.2. Optical Low-Temperature Properties of Glasses.- 1.3. Organization of the Paper.- 2. The Model and its Hamiltonian.- 2.1. Theoretical Description of the Dynamics of Glasses.- 2.2. Interaction between a Guest Molecule and the TLSs.- 2.3. The Total Model.- 3. Optical Line Shape Calculated with Mori’s Formalism.- 3.1. Correlation Functions for the Optical Line Shape.- 3.2. Calculation of Correlated Functions with Mori’s Formalism.- 4. Guest Molecule Coupled to a Single TLS.- 4.1. Dipole Moment Operator.- 4.2. Equations for Correlation Functions.- 4.3. Evaluation of the Coefficients (Debye Model).- 4.4. Solution to the Eigenvalue Problem.- 4.5. Dependence of the Eigenvalues on System Parameters.- 4.6. Analytical Approximations.- 5. Line Shape.- 6. Averaging over Two-Level Systems.- 6.1. Averaging Procedures.- 6.2. Numerical Averaging of the Linewidth.- 6.3. Analytical Approximations for the Averaged Linewidth.- 6.4. Averaging of the Line Shape.- 7. Coupling of the Impurity to Several Two-Level Systems.- 7.1. The System without Phonons: Eigenvalues and Eigenstates.- 7.2. Representation of the Dipole Moment Operator.- 7.3. Calculation of the Correlation Function Evolution Matrix.- 7.4. Approximate Calculation of the Eigenvalues.- 7.5. Line Shape Formula.- 7.6. Linewidth Calculation: Comparison with Experiment.- 7.7. Numerical Line Shapes.- 8. Concluding Remarks.- Structural Relaxation Processes in Polymers and Glasses as Studied by High Resolution Optical Spectroscopy.- 1. Introduction.- 2. The’ site-Memory’ Function.- 3. The Non-Equilibrium Nature of Glasses and its Relation to Optical Properties.- 4. Dynamic and Adiabatic Optical Relaxation Processes.- 5. Reversibility and Irreversibility.- 6. The Residual Linewidth.- 7. Spectral Diffusion and Structural Relaxation: Model Description.- 7.1. The Decay Law of Persistent Spectral Holes in Amorphous Solids.- 7.2. The Time Evolution of the Optical Width.- 8. The Logarithmic Decay Law and its Relation to Other Dispersive Time Dependencies.- 9. Experimental Investigation of Spontaneous Structural Relaxation Processes.- 9.1. The Photochemical Systems.- 9.2. Experimental Results.- 9.3. Investigation of the Microscopic Rate Parameters of the Logarithmic Law: the Deuteration Effect.- 9.4. Polarization Diffusion.- 10. Field Effects and Spectral Diffusion Phenomena.- 10.1. Electric Field Effects for Molecules with Inversion Symmetry.- 10.2. Electric Field Effects for Molecules without Inversion Symmetry.- 10.3. Hole-Burning Experiments under External Pressure.- Models for Reaction Dynamics in Glasses.- 1. Introduction.- 2. Relaxation Viewed as Chemical Reaction: the Kinetic Approach.- 3. A Parallel Relaxation Scheme: the Direct Transfer.- 3.1. Regular Lattices with Impurities.- 3.2. Restricted Geometries.- 3.3. Fractals.- 4. Parallel-Sequential Schemes: Random Walks.- 4.1. Random Walks on Regular Lattices.- 4.2. Random Walks on Fractals.- 5. Continuous-Time Random Walks (CTRW).- 6. Ultrametric Spaces (UMS).- 7. The Bimolecular Reactions A + A ? 0, A + B ? 0 (A0 = B0).- 7.1. Bimolecular Reactions on Regular Lattices and on Fractals.- 7.2. Bimolecular Reactions: CTRW and Ultrametric Spaces.- 8. Conclusions.