Modified spontaneous emission in cylindrical microcavities: waveguiding and distributed Bragg reflecting structures

Abstract

Abstract We study the density of modes, and associated spontaneous emission properties, of cylindrical cavities exhibiting waveguiding. A model of a microstructure composed of a metallized cylinder with multiple internal dielectric layers (distributed Bragg reflectors) has been used to describe the Helmholtz modes and their quantization. A two-level excited atom is placed within the structure and interacts in the dipole approximation with the quantized vacuum modes. To describe this we have derived expressions for the density of modes which an interacting atom sees, and which determine the subsequent time evolution of the excited-state probability of the atom. This simple model allows the investigation of the two major influences on the density of modes, the waveguiding nature of a cylinder and the frequency selectivity of the distributed Bragg reflecting mirrors and shows that the interplay between these two factors can have significant design consequences for the smallest of practical structures. We determine the so-called “β factors” characterizing the coupling efficiency and threshold properties of the structure and show that values close to unity are expected. We also show that reversible spontaneous emission, or vacuum Rabi splitting, is expected, for some practically realizable structures.