A finite element method with polygonal elements for analyzing band gap characteristic in two-dimensional photonic crystals

Abstract

Finite element method (FEM) based on Wachspress interpolation on polygonal elements for analyzing the band gap characteristic of two-dimensional photonic crystals (2D PCs) is proposed in this. The proposed FEM has been coded into program and validated with other method such as conventional finite element method based on triangular elements and plane wave expansion method. Numerical examples on triangular lattice and square lattice photonic crystals have been carried out. The comparison of accuracy between the conventional FEM and the proposed method has been also provided in this thesis. The comparison results show that the polygonal element can yield better accuracy than the conventional FEM with the same number of unknowns in system equations.