Spontaneous emission from radiating atoms in cylindrically and spherically symmetric periodic structures

Abstract

Recently there has been considerable interest in the concept of a manufactured structure exhibiting a "photonic band gap"—an energy band in the electromagnetic spectrum for which wave propagation is isotropically forbidden. Conventional treatments have employed a Bloch-wave approach to explore the spectral and directional nature of wave propagation in multi-dimensional, translationally invariant, Cartesian periodic structures. Utilizing a classical model, we directly treat the interaction of a radiating dipole with the fields supported by cylindrical and spherical Bragg structures. These novel structures, which are not translationally invariant, are capable of effectively confining light emitted from a central, but finite-sized, region. The size of this region depends on both source and structure characteristics, including the modulation and radial extent of the Bragg structure. We examine the radiative lifetime variations and resonance frequency shifts associated with particular idealizations of the structure and source. The results presented are of fundamental and practical interest owing to the unique geometry of the considered Bragg structures, which have recently been realized as semiconductor laser resonators in the form of cylindrical waveguide diffraction gratings.