Quality factors in single defect photonic crystal lasers with asymmetric cladding layers

We present calculations that allow the design of two-dimensional photonic crystal resonant cavities in dielectric slabs bonded to a sapphire substrate. Finite-difference time-domain (FDTD) calculations of quality factors in two-dimensional photonic crystal membranes on a sapphire substrate were performed. We considered a triangular lattice with a single missing hole, and it is the Q of the doubly-degenerate resonant mode associated with this missing hole that we were concerned with. The Q of the cavity was obtained by multiplying the resonant frequency, which was obtained from a Fourier transform of the field, by the energy stored in the cavity and then dividing by the power lost out of the cavity