A finite-difference eigenvalue algorithm for calculating the band structure of a photonic crystal

A new method based on a finite difference of the governing differential equation for the eigenvalue problem is introduced to calculate the band structure of a two-dimensional photonic crystal. The effective medium technique is also used in the method. The problem is reduced to a standard matrix eigenvalue problem. Compared to the conventional plane wave expansion method, the present method improves the convergence of the solution and thus is a fast and accurate algorithm for calculating the band structure of a photonic crystal.