Analysis of 2d Photonic Crystal Cavities Using a Multi-scattering Approach Based on Weighted Bessel Functions

A semi-analytic method, based on scattering approach is applied to analyze the finite size photonic crystal cavities surrounded by cylindrical dielectric rods. The resonant frequency and the quality factor (Q) are determined by this method. Also, with a source at the center of the cavity, field and energy distribution can be obtained at different frequencies. The algorithm is simple to simulate on PCs. There is no need for absorbing boundary conditions which are required in most numerical methods. Using the symmetry of the structure the computational cost is reduced to 1/8 and 1/12 those of the square and hexagonal lattices respectively. Since the computational time is very low (in the order of one minute) the variation in size and dielectric constant of the rods can be examined easily. It is shown as an example that by varying the radius of the rods according to their distance from the center of the cavity, the Q factor is increased considerably in comparison with that of uniform structures.