A new approach for analysis of photonic crystal based on the spatial finite-difference and temporal differential formulation

摘要

In this paper, we present a new procedure for computing the band structure of semiconductor-based photonic crystals using the spatial finite-difference and temporal differential formulation. Unlike the conventional plane wave expansion (PWE) method where the wavelet expansion and Fourier transform are required; this new scheme only forces the finite-difference to the Maxwell's equation in the spatial domain. When applying the Bloch's boundary condition to the algorithm for solving the band-diagram, it will result in a system of first-order differential equations in a matrix format. A band mode can be obtained directly by solving the eigen-value and the eigen-vector of this matrix. Numerical examples to demonstrate the accuracy and efficiency of the proposed approach are given.