On the theory of vibronic superradiance

The Dicke superradiance on vibronic transitions of impurity crystals is considered. It is shown that parameters of the superradiance (duration and intensity of the superradiance pulse and delay times) on each vibronic transition depend on the strength of coupling of electronic states with the intramolecular impurity vibration (responsible for the vibronic structure of the optical spectrum in the form of vibrational replicas of the pure electronic line) and on the crystal temperature through the Debye-Waller factor of the lattice vibrations. Theoretical estimates of the ratios of the time delays, as well as of the superradiance pulse intensities for different vibronic transitions well agree with the results of experimental observations of two-color superradiance in the polar dielectric KCl:O ₂ ^? . In addition, the theory describes qualitatively correctly the critical temperature dependence of the superradiance effect.     

Quantum theory of impurity migration in crystals

A quantum theory of impurity migration in crystals is proposed. The impurity state is taken in the form of a wave packet constructed out of its Bloch states in the host lattice. Its time evolution is studied including its interaction with the host lattice phonons. A correspondence is established between the classical diffusion equation and the time evolution of the probability density arising out of the impurity wave packet. The diffusion coefficient D_T and trapping rate γ_T are related to the imaginary part of the energy shift of the impurity caused by its interaction with phonons. The detailed calculations are carried out using second order perturbation theory for the energy shift. The Debye model for the host lattice and effective mass approximation for the impurity band are used. At low temperature D_T is found to be proportional to_T3/2, and at high temperature the Arrhenius formula of Vineyard is obtained. The estimated migration energy for μ⁺ migration in bcc metals agrees reasonably with the experimental values.     

Intensity and bandwidth of multiphonon vibronic transitions of rare-earth ions in crystals

The theory of multiphonon vibronic coupling to electronic transitions is applied in analysing fluorescence spectra of Eu²⁺ in BaFCI, which consist of the 4f⁷(⁶P_7/2,) → 4f⁷(⁸S_7/2) and 4f⁶5d → 4f⁷ transitions, and the 4f⁷-4f⁶5d excitation spectrum of Ce³⁺ in YPO⁴. The 4f electrons are weakly coupled to lattice vibration modes so that only weak one- and two-phonon sidebands are observable in the 4f-4f optical transitions, whereas the electron-phonon coupling is significantly stronger for a 5d electron. Accordingly, intensive multiphonon vibronic transitions overwhelmingly dominate the 4f⁶5d → 4f⁷ spectrum. It is shown that the extended Judd-Ofelt theory for weak vibronic coupling in the framework of the M-process is equivalent to the Huang-Rhys theory for the δ-process. In the analysis of experimental data, contributions from local ligand modes and lattice acoustic modes are separated, and the coupling strength is evaluated, in terms of the Huang-Rhys parameter S, for the 4f-4f and 5d-4f vibronic transitions.     

Structural form of vibronic intensities in vibronic induced transitions

A general method for calculating the overall shape of the spectrum of vibronic induced transitions in transition-metal ion systems is developed. The vibronic structure is expressed in terms of a weighted sum of medium induced lorentzian lines located at the frequencies of the fundamental odd vibrations of the complex. Each of these lines is followed by a series of vibronic lines assigned to the combination frequencies with one or more even vibrations. The relative intensities of these combination lines are determined by the values of an intramolecular distribution which includes both the effects of geometry and frequency changes of the modes involved in the transition. Values of the linear and the quadratic parameter for the molecule can be estimated from a fit to the experimental spectra.     

On the vibronic theory of resonance Raman scattering

Resonance Raman excitation profiles of totally symmetric vibrational modes are investigated using a model that analytically includes the complete subspace of Franck-Condon active vibrations associated with each intermediate electronic state. This model is used to fit data obtained in resonance with the Soret band of cytochrome c. The excitation profiles are asymmetric and peak distinctively to the blue of the Soret absorption maximum. Large damping factors and/or inhomogeneous site distributions by themselves cannot account for the observed data. The theoretical results imply that the excited state lifetime associated with the Soret band of ferrocytochrome c has a lower limit on the order of 50 fs and that, compared to the ferrous form, the ferric cytochrome has a larger x-y splitting and a shorter lifetime.In constrast to the large multidimensional heme system, we also present the results of a simple model calculation applicable to smaller molecules. A two dimensional subspace is explored, where Raman Franck-Condon (RFC) and Franck-Condon (FC) factors are calculated for different potential energy surface parameters. Under certain conditions the RFC based scattering profiles of one vibration are strongly coupled to the FC based behaviour of the other vibration. Rather complex profiles are then predicted even for the simple two- dimensional case.     

Theory of optical spectra of impurity centres in crystals: general consideration of quadratic vibronic coupling

A method is proposed for the calculation of the spectra of the multiphonon transitions caused by the quadratic vibronic coupling with a phonon continuum. In the method, the time evolution of the final state is described by the path integrals. By applying the Stratonovich-Hubbard identity, the quadratic coupling is presented as the fluctuating linear coupling; the latter is calculated by the Lax method. As a result, the problem is reduced to the calculation of the determinants of matrices, the elements of which are given by the pair correlation functions of the contributing configurational coordinates. The method has been verified for the case of two mixed modes. Numerical calculations have also been made for a modified Debye model.     

On the theory of the central peak at structural phase transitions

A universal mechanism is proposed, which explains the appearance of the central peak by means of a transition from ergodic to nonergodic dynamical behaviour of the system at some temperatureT _g above the phase transition. A detailed investigation of the scalar lattice ⁴-model with defects is given. The relation between the nonergodic state and the appearance of precursor clusters and Raman scattering experiments is discussed.     

Some expected anomalies in the impurity vibronic spectra of ferroelectrics

The influence of the soft phonon branch on some characteristics of the impurity vibronic absorption spectra in ferroelectrics is qualitatively analyzed and illustrated using simple models. The following quantities are discussed: the intensity, the temperature shift and the half width of the no-phonon line, the one-phonon wing, the integral intensity of a parity forbidden band. It is shown that near the phase transition point (T > T_c) all these characteristics must show anomalous dependencies on temperature, if compare with usual matrix crystals. The observation of “plateaus” may be expected in these dependencies. Various aspects of obtaining information from measured impurity vibronic spectra of ferroelectrics are discussed.     

On the theory of germ formation at phase transitions in elastic-plastic bodies

Abstract

Non-uniform fluctuations of the order parameter (OP) in solids give rise to elastic shift deformations which considerably affect the OP fluctuation energy and the phase transition character itself. However, in the vicinity of the second order phase transition line and also near the stability boundaries at the first order transition the OP fluctuations become abnormally big. So it becomes necessary to account not only elastic but plastic deformations as well. These aspects are considered in the present paper.     

Crystal field at the impurity center sites in ionic crystals

Perturbation theory is developed for second-quantized operators in a basis of partly nonorthogonal orbitals. This method may be helpful in carrying out ab initio calculations of the parameters of the crystal field at the impurity center sites. As an illustration, when estimating the crystal field parameters for Yb³⁺: KZnF₃, some fitting parameters are calculated using this method. The results agree well with experimental data, which indicates that this theory shows considerable promise.     

Advances in vanadate laser crystals at a lasing wavelength of 1 micrometer

Sapphire, garnet and vanadate crystals are the most prominent optical materials, and vanadates play important roles in optics, especially in lasers and nonlinear optics. Neodymium‐doped yttrium vanadate (Nd:YVO₄) is representative and available commercially. Based on Nd:YVO₄, several vanadate crystals are being developed with the goal of fulfilling the need for differential applications and improvement of certain operational aspects, such as with pulsed lasers or high‐power continuous‐wave lasers. In recent years, some important effects, including energy enhancement, bistability of output performance, self‐Raman frequency shifting, etc., and some novel applications, such as quantum optics, pulsed lasers modulated by the two‐dimensional crystals, etc., have been discovered with vanadates as gain materials. In this paper, the preparation, characterization and laser applications of vanadate laser crystals at the lasing wavelength of 1 micrometer, including YVO₄, GdVO₄, LuVO₄, Gd_xY_1–xVO₄ and Lu_xGd_1–xVO₄ (0 < x < 1) doped with Nd³⁺ and ytterbium (Yb³⁺) are systematically reviewed by highlighting the most recent research progress. Their specific properties are presented, generation mechanisms of novel physical effects are discussed, new applications are given and possible future applications proposed by focusing on some potential strengths.     

On the theory of transient nucleation at the intermediate stage of phase transitions

The evolution of a system of growing aggregates in a macroscopically homogeneous medium with account of both the reduction in metastability and the continuing initiation of new nuclei is studied. The corresponding integro-differential model describing the intermediate stage of phase transitions is solved analytically for arbitrary nucleation kinetics and growth rates of nuclei. An exact solution of the Fokker–Planck equation is found with allowance for the diffusivity along the axis of nucleus radii. In limiting cases of purely kinetic and mixed kinetic-diffusion rates of crystal growth for a special form of diffusivity, the obtained solutions transform to earlier known expressions.     

Ultraviolet lasing in cholesteric liquid crystals

We report the observation of stimulated emission and mirrorless lasing in pure cholesteric liquid crystals. The lasing action is attributed to the combination of the fluorescence and the distributed feedback that are due to the inherent periodic structure of the liquid crystal. If the reflection band matches the intrinsic emission of the cholesteric liquid crystal, the crystal becomes a natural laser material, which will self-lase, without any optical elements or the addition of dyes, under picosecond excitation at 355 nm. Samples have been made to lase at different wavelengths in the near UV by shifting of the edge of the reflection band in the range of 385-405 nm. Typical linewidths observed are of the order of 0.5 nm.     

Low-threshold lasing at the edge of a photonic stop band in cholesteric liquid crystals

Low-threshold lasing is observed at the edge of the stop band of a one-dimensional structure-a dye-doped cholesteric liquid-crystal film. The mode closest to the edge has the lowest lasing threshold. The rates of spontaneous and stimulated emission are suppressed within the stop band and enhanced at the band edge. The ratio of right to left circularly polarized spontaneous emission is in good agreement with calculated density of photon states.     

On the theory of the isothermal Hall effect in impurity semiconductors

The theory of the isothermal Hall effect in impurity semiconductors is ameliorated by regarding edge effects of the Hall specimen explicitly and allowing for arbitrary bulk and surface recombination.