Abstract

It is well known that atomic spontaneous emission is modified when the atom is placed in an optical cavity,^1-2 The electric dipole interaction between the atom and the field depends on the scalar products of the atomic dipole operator and the vector mode functions for the field at the position of the atom,^2-4 and the latter are changed by the presence of the cavity. The spontaneous emission rate, which thus depends on the atomic position and the orientation of the atomic dipole matrix element, can be written as the sum of contributions from all the field modes. A planar Fabry-Perot structure, in which an optical cavity is situated between a perfect mirror and a thin dielectric layer acting as a low-transmission (high-reflection) mirror to the external region,⁵ is a simple model used to study the modification of spontaneous emission rates, and has been used for this purpose by Dutra and Knight⁶ for the case of a microcavity. In the case of such Fabry-Perot structures, there are two types of modes: traveling modes whose mode functions are combinations of plane waves in both the cavity and external regions, and trapped modes, which have mode functions that decrease exponentially in these regions. Since the trapped modes can be significantly non-zero at atomic positions within the microcavity, the question arises whether the trapped modes contribution to the spontaneous emission rate is negligible. In the case of Fabry-Perot multilayer dielectric microcavities, Rigneault and Monneret⁷ found that the contribution from guided modes is important. In this paper we present the results of a fully quantum treatment of the contribution of trapped modes to the total spontaneous emission rate. For the case of a high Q Fabry- Perot microcavity of the simple type treated by Dutra and Knight,⁶ we find that for both normal and parallel orientations of the atomic dipole matrix element, the trapped mode contribution is negligible for all atomic positions in the microcavity, so that almost all the energy radiated goes into the traveling modes.

© 1998 Optical Society of America