Local field and radiative relaxation rate in a dielectric medium

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.