| This thesis investigates the application of a recently developed numerical technique, the Flexible Local Approximation Method (FLAME) to compute the resonances of 2D photonic crystal (PC) cavities, formed by a defect in a regular array of dielectric rods. FLAME is a finite-difference-like method which is ideally suited to problems consisting of large numbers of identical structures.; The anisotropic perfectly matched layer (PML) is used as an artificial absorbing layer to truncate the computational domain. The parameters of the PML are chosen carefully to provide adequate absorption without a large computational cost.; FLAME method and PML boundaries are applied to cavities with 3x3, 5x5 and 7x7 arrays of rods. The resonant modes, field distribution, and quality factor are computed and compared with previously-published results. Good agreement is obtained. However, the matrix eigenproblem generated by FLAME is of a kind for which sparse-matrix algorithms are not available and dense-matrix software had to be used. This limitation will have to be overcome if FLAME is to be widely used for PC cavities. |
