The calculation of the atomic spontaneous emission rate between two dielectric slabs

Abstract

In this paper, the spontaneous emission rate of an excited atom between the two dispersive and dissipative dielectric slabs is determined. It is assumed that the atom has a definite transition electric dipole moment, and the dielectric function of the slabs is an arbitrarily complex function of frequency satisfying Kramers–Kronig relations. In this research, by noting to the connection between the spontaneous emission rate and the imaginary part of the vector potential Green function, only by evaluating the vector potential Green function tensor of the system of the two slabs, an expression for the spontaneous emission rate is introduced. In this formalism, it is needless to derive the vacuum electric field operator. The emission rate is obtained in terms of the dielectric function, the thickness and the distance between the slabs. By considering a Lorentz model for the dielectric function of the slabs, the typical spatial variations of the spontaneous emission rate between the two slabs are demonstrated.