Spontaneous-Emission Rate in Microcavities: Application to Two-Dimensional Photonic Crystals

We present a simple, efficient procedure to compute the spontaneous-emission rate from short-time finite-difference time-domain (FDTD) data of the electromagnetic field energy in microcavities of arbitrary geometry. As an illustration, we apply this procedure to two-dimensional photonic crystals. For comparison, we calculate the local radiative density of states employing an unconditionally stable FDTD method, that is without solving the eigenvalue problem and integrating over the (first) Brillouin zone. We demonstrate that both methods yield the same predictions about the enhancement or suppression of the spontaneous-emission rate by photonic crystals.