  This article presents a detailed analysis, based on the first-principles
finite-difference time-domain method, of the resonant frequency, quality factor
(Q), mode volume (V), and radiation pattern of the fundamental (HE11) 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.
