Spontaneous emission rate of an electric dipole in a general microcavity

Abstract

A simple method to obtain the spontaneous emission rate of a dipole placed in a general microcavity is proposed and demonstrated. In our approach, Maxwell’s equations are solved directly in real space instead of k space by the finite-difference time-domain method with a free-space boundary condition. It is advantageous that allowed eigenmodes need not be calculated and the total radiation rates to all the allowed modes are obtained from the beginning. All the localized modes, guided modes, and extended modes are inherently included in this formulation. The validity of the method is tested for a dipole placed in an ideal planar microcavity and the calculated results agree well with the closed-form analytic solutions. The enhancement and the inhibition of the spontaneous emission rate in several photonic band-gap structures are studied. Point dipole analyses show three-dimensional effects in two-dimensional in-plane photonic band gaps and the effects of localized, guided and extended modes on radiation rates.