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Journal of Experimental and Theoretical Physics

Local field and radiative relaxation rate in a dielectric medium

Денис Кузнецов, V. Roerich, M. G. Gladush

Published Oct 1, 2011• 52 citations
Publisher

Abstract

The effect of macroscopic parameters of a substance on the optical characteristics of impurity particles is investigated. A generalized control equation is derived for two-level emitters forming an ensemble of optical centers in a transparent dielectric medium. In this equation, the effective values of the acting pump field and the radiative relaxation rate of an optical center are taken into account. The formalism developed here is a completely microscopic approach based on the chain of the Bogoliubov-Born-Green-Kirkwood-Yvon equations for reduced density matrices and correlation operators for material particles and modes of a quantized radiation field. The method used here makes it possible to take into account the effects of individual and collective behavior of emitters, which are associated with the presence of an intermediate medium, consistently without using phenomenological procedures. It is shown that the resultant analytic expression for the effective lifetime of the excited state of an optical center conforms with experimental data.

DOI
10.1134/s1063776111100050

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The effect of macroscopic parameters of a substance on the optical characteristics of impurity particles is investigated. A generalized control equation is derived for two-level emitters forming an ensemble of optical centers in a transparent dielectric medium. In this equation, the effective values of the acting pump field and the radiative relaxation rate of an optical center are taken into account. The formalism developed here is a completely microscopic approach based on the chain of the Bogoliubov-Born-Green-Kirkwood-Yvon equations for reduced density matrices and correlation operators for material particles and modes of a quantized radiation field. The method used here makes it possible to take into account the effects of individual and collective behavior of emitters, which are associated with the presence of an intermediate medium, consistently without using phenomenological procedures. It is shown that the resultant analytic expression for the effective lifetime of the excited state of an optical center conforms with experimental data.
We obtained the system of Maxwell-Bloch equations (MB) that describe the interaction of cw laser with optically active impurity centers (particles) embedded in a dielectric material. The dielectric material is considered as a continuous medium with sufficient laser detuning from its absorption lines. The model takes into account the effects associated with both the real and the imaginary part of the dielectric constant of the material. MB equations were derived within a many-particle quantum-kinetic formalism, which is based on Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for reduced density matrices and correlation operators of material particles and the quantized radiation field modes. It is shown that this method is beneficial to describe the effects of individual and collective behavior of the light emitters and requires no phenomenological procedures. It automatically takes into account the characteristics associated with the presence of non-resonant and resonant particles filling the space between the optical centers.
We develop a consistent quantum theory of the collective effects that take place when electromagnetic radiation interacts with a dense ensemble of impurity centers embedded in a transparent dielectric and placed in a Fabry–Perot cavity. We have calculated the spontaneous decay dynamics of an excited impurity atom as a specific example of applying the developed general theory. We analyze the dependence of the decay rate on the density of impurity centers and the sample sizes as well as on the characteristic level shifts of impurity atoms caused by the internal fields of the dielectric. We show that a cavity can affect significantly the pattern of collective processes, in particular, the lifetimes of collective states.
The current paper demonstrates theoretical analysis of two types of spectral curves for several configurations of system of two-level light emitters, considering the influence of local field and close environment inside a transparent medium. Probe field absorption spectra and resonant fluorescence spectra are calculated under excitation of a strong monochromatic cw laser. The sensitivity of absorption and emission optical spectroscopy method is compared for revealing the effects of the medium on individual emitters and their ensembles. Spectral curves were calculated for model emitters considering local field influence of a transparent dielectric medium and local electron-phonon interactions, which determined the response of the emitters to an external laser field and effective relaxation mechanisms. The calculation formalism is based on a semiclassical approach, while the relaxation processes associated with the phonon contribution are introduced phenomenologically with references to other studies.
Abstract The current paper demonstrates theoretical analysis of two types of spectral curves for several configurations of system of two-level light emitters, considering the influence of local field and close environment inside a transparent medium. Probe field absorption spectra and resonant fluorescence spectra are calculated under excitation of a strong monochromatic cw laser. The sensitivity of absorption and emission optical spectroscopy method is compared for revealing the effects of the medium on individual emitters and their ensembles. Spectral curves were calculated for model emitters considering local field influence of a transparent dielectric medium and local electron-phonon interactions, which determined the response of the emitters to an external laser field and effective relaxation mechanisms. The calculation formalism is based on a semiclassical approach, while the relaxation processes associated with the phonon contribution are introduced phenomenologically with references to other studies.
The current paper demonstrates theoretical analysis of two types of spectral curves for several configurations of system of two-level light emitters, considering the influence of local field and close environment inside a transparent medium. Probe field absorption spectra and resonant fluorescence spectra are calculated under excitation of a strong monochromatic cw laser. The sensitivity of absorption and emission optical spectroscopy method is compared for revealing the effects of the medium on individual emitters and their ensembles. Spectral curves were calculated for model emitters considering local field influence of a transparent dielectric medium and local electron-phonon interactions, which determined the response of the emitters to an external laser field and effective relaxation mechanisms. The calculation formalism is based on a semiclassical approach, while the relaxation processes associated with the phonon contribution are introduced phenomenologically with references to other studies.
Scattering of resonance radiation in a dense two-level medium is considered with allowance for the local field effects. The system is studied in the framework of the mean-field approximation for a modified hierarchy of the Bogoliubov-Born-Green-Kirkwood-Yvon equations for reduced density matrices of an ensemble of atoms and modes of a quantized electromagnetic field. The local field correction is consistently derived from the initial Hamiltonian of the system. The problem of scattering of a short rectangular pulse from a quasi-point sample is considered numerically and theoretically. The possibility of a multimode spectrum of scattered radiation with frequencies multiple of the Rabi frequency and with other intermediate frequencies is demonstrated. The relative intensities of spectral lines are determined.