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physica status solidi (b)

Quantum‐Statistical Theory of Light Propagation in Crystals

A. S. Davydov, Alexander A. Serikov

Published Mar 1, 1973• 48 citations
Publisher

Abstract

Abstract The density matrix method is used to investigate the passage of light (the frequency of which corresponds to the exciton excitation) through an optically isotropic crystal, The investigation is made in a wave packet representation which enables one to observe the spatial motion of photons and excitons. The radiationless energy transfer from an electronic excitation to a dissipative subsystem is taken into account.

DOI
10.1002/pssb.2220560136

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Abstract The density matrix method is used to investigate the passage of light (the frequency of which corresponds to the exciton excitation) through an optically isotropic crystal, The investigation is made in a wave packet representation which enables one to observe the spatial motion of photons and excitons. The radiationless energy transfer from an electronic excitation to a dissipative subsystem is taken into account.
The dispersion of electromagnetic waves in molecular crystals has been studied using the second quantization formalism. The excitation spectrum, the Green's functions for the optical exciton and photon field, as well as the corresponding distribution functions, are calculated and discussed. The ground state energy of the crystal is derived in a closed form with the polarization of the medium taken into account explicitly. In the low-density limit the expression for the ground state energy corresponds to the summation of an infinite sequence of terms in a perturbation-theory approach.
This paper contains the second part of a theory of the coherent propagation of a light wave in semiconductors. After considering the interaction among the electrons, we discuss the matter of the interaction of a semiconductor with light and derive equations of motion for the polarization wave of the excitons which have been excited by the light. We show how our equations can be approximated by linear ones and how the exciton polarization wave can be regarded as a Bose field in the limit of low excitation. In this paper we also discuss in detail the problem of the coherent excitation of discrete exciton levels. We show that the coherently excited discrete exciton is approximately equivalent to a two-level atom which is excited by a light wave; the atom energy-level spacing is a function of the degree of excitation, and the density of equivalent "two-level atoms" is determined by features of the exciton-state wave function.
The phenomenon of self-induced transparency (SIT) in the exciton range of the spectrum consists of the propagation through the crystal of solitary wave packets of coherent excitons and photons with anomalous small losses. In the running frame of reference at the site occupied by the soliton a single aperiodic transformation of photons into excitons and a reverse motion of the energy into the field takes place. The solutions of the SIT equations have been received in the slowly-varying amplitude approximation. Taking into account the phase modulation, the authors have shown the appearance of the branch of the carrier wave frequency with anomalous dispersion not only at the given pulse width but at the given pulse amplitude. They have also found the exact solution of the above mentioned equations taking into account the effect of saturation of the dipole momentum transition from the crystal ground state to the exciton state. It leads to the increasing of the soliton time width, to the decreasing of its amplitude and worsens the SIT observation.
Abstract In consequence of the nonconservation of excitons, the excitation number operator as well as the exciton pair creation and annihilation operators are expressed as functions of time and of the corresponding stationary operators. The nonstationary pair correlation processes and the nonstationary excitation density fluctuation processes are analysed using the nonstationary operators. It is found that the nonstationary pair correlations are characterized by a specific kind of dissipation that is linearly proportional with time. In contradistinction to stationary processes, the corresponding nonstationary ones, lead to elementary excitations having a double energy: E (nonstationary) = 2E (stationary). It is shown that in contrast to exciton density fluctuations, pair correlations have a tendency of localization related to a lattice point. It is also shown that the exciton non‐statinoary pair correlations are in many respect similar to the density fluctuations that take place in the crystal due to a near slow neutron passage. Finally, a general method for the evaluation of the correlation function, applicable even in the case when the Green's function has a n‐th order pole, is developed in the Appendix.
Abstract A coherent radiation‐exciton interaction model is employed to study analytically the phenomenon of nonlinear absorption in important III—V semiconductors (viz., GaAs, GaSb, InSb, InAs), the crystals being irradiated by suitable lasers with energies (hω) nearly equal to the band gap energies (hωg). The nonoptical processesare accounted for phenomenologically by introducing a damping parameter into the equation of motion of the probability amplitude of the excited electron—hole pair state. The Wannier‐Mott type of exciton wave function is found to be responsible for the giant nonlinearity of the crystal absorption coefficient in the near resonant optical interband transition regime with h | ω ‐ ωg | of the order of the crystal exciton binding energy. The effect of renormalization of the crystal band gap in the presence of Coulomb interaction and Starkbroadening is also discussed.
An exciton-phonon mechanism for producing cavityless optical bistability is suggested. We consider the influence of the oscillating subsystem of a crystal on the absorption process of a laser wave in the region of exciton frequencies. It is shown that exciton-phonon interaction leads to nonlinear dependence of the absorption coefficient on the density of the exciton gas. The increase of absorption with increasing exciton density, however, is possible only in the frequency region on the long-wavelength tail of the exiton band. As a result, the exciton density of the crystal becomes a hysteresis function of external parameters (intensity of the incident wave, temperature, etc.). We calculate the absorption coefficient of excitons and define the frequency and temperature regions where optical bistability may exist. We analyze different relaxation mechanisms of excitons and explain the experimental results of observing optical bistability in different semiconductor crystals.