Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics

This paper presents a detailed analysis, based on the first-principles finite-difference time-domain method, of the resonant frequency, quality factor $\mathrm{}\left(Q\right),$ mode volume $\mathrm{}\left(V\right),$ and radiation pattern of the fundamental ${(HE}_{11})$ mode in a three-dimensional distributed-Bragg-reflector (DBR) micropost microcavity. By treating this structure as a one-dimensional cylindrical photonic crystal containing a single defect, we are able to push the limits of $Q/V$ beyond those achievable by standard micropost designs, based on the simple rules established for planar DBR microcavities. We show that some of the rules that work well for designing large-diameter microposts (e.g., high-refractive-index contrast) fail to provide high-quality cavities with small diameters. By tuning the thicknesses of mirror layers and the spacer, the number of mirror pairs, the refractive indices of high- and low-refractive index regions, and the cavity diameter, we are able to achieve Q as high as ${10}^4,$ together with a mode volume of $1.6$ cubic wavelengths of light in the high-refractive-index material. The combination of high Q and small V makes these structures promising candidates for the observation of such cavity-quantum-electrodynamics phenomena as strong coupling between a quantum dot and the cavity field, and single-quantum-dot lasing.