A Pseudospectral Time-Domain Algorithm for Calculating the BandStructure of a Two-Dimensional Photonic Crystal

A pseudospectral time-domain (PSTD) method is developed for
calculating the band structure of a two-dimensional photonic crystal. Maxwell's equations are rewritten in terms of period fields by using the Bloch theorem. Instead of spatial finite differences, the fast Fourier transform is used to calculate the spatial derivatives. To reach a similar accuracy, fewer sample points are required in the present PSTD method as compared to the conventional finite-difference-time-domain methods. Our numerical simulation shows that the present PSTD method is an efficient and accurate method for calculating the band structure of a photonic crystal.