Band structure calculation of one-dimensional photonic crystal by finite element method

Abstract

Finite element method (FEM) for band structure calculation in dielectric one-dimensional photonic crystal is presented. Photonic crystals are materials with periodically modulated dielectric constants which certain frequencies of EM radiation that cannot propagate. Using the adaptation of Maxwell's equations in discrete mesh, the FEM divides the problem domain into piecewise polynomial functions resulting in sparse matrices. The computation reduces to a generalized eigenvalue problem with tridiagonal matrices which are easily evaluated using standard eigenvalue solvers.