Reduction of the staircasing error in the single-domain pseudospectral frequency-domain method for analysis of photonic crystals

Abstract

An improved Fourier pseudospectral frequency-domain (PSFD) method is proposed for the analysis of two-dimensional photonic crystals. Similar to the conventional Fourier PSFD, this method also uses trigonometric basis functions to expand various components of the pseudoperiodic electromagnetic field. However, to avoid the staircasing error for curved boundaries, a convolution technique is introduced in the spectral domain. This results in a matrix representation of the Helmholtz eigenvalue problem. The latter can be solved readily for the photonic band diagram of a photonic crystal. This method shows not only excellent accuracy but also fast convergence in analyzing different types of symmetrical and nonsymmetrical photonic crystals.