Efficient method for analyzing leaky cavities in two-dimensional photonic crystals

An efficient numerical method is developed for analyzing leaky cavities in two-dimensional photonic crystals, assuming that the cavities are located in the vicinity of a photonic crystal waveguide or close to a homogeneous medium. A leaky cavity mode is characterized by its complex eigenfrequency and by the outgoing wave behavior of the field in the nearby waveguide or homogeneous medium. In our method, the eigenfrequency of a leaky cavity mode is determined from a condition formulated on one single edge of a defect unit cell. Such a condition is obtained by using rigorous boundary conditions to terminate photonic crystal waveguides and homogeneous media, Dirichlet-to-Neumann maps of the unit cells to reduce the problem to the cell edges, and standard Gaussian elimination to further reduce the problem to one single edge. The reduction process can be performed efficiently. Accurate solutions can be obtained when a small number of discrete points are used on each edge of the unit cells. © 2009 Optical Society of America.