Modeling of 2D photonic bandgap structures using a triangular mesh finite difference method

A numerical model is presented for computing the out-of-plane losses of a general class of row-defect waveguides formed by the superposition of a two-dimensional photonic crystal onto a slab confinement structure. The usefulness of this model is demonstrated here by calculating the propagation loss of a single-row-defect waveguide composed of hexagonal air holes etched into two different slab structures. The results are interpreted in terms of a simple coupled-mode-theory picture in which loss is due to coupling by the waveguide corrugation between the fundamental and certain radiative slab modes. These calculations show that low-loss photonic crystal waveguides should be possible by carefully engineering the radiation modes of the slab waveguide.