Calculation of a nonlinear eigenvalue problem based on the MMP method for analyzing photonic crystals

Abstract

The multiple multipoles (MMP) method is used to solve a nonlinear eigenvalue problem for analysis of a 2D metallic and dielectric photonic crystal. Simulation space is implemented in the first Brillouin zone, in order to obtain band structure and modal fields and in the supercell to calculate waveguide modes. The Bloch theorem is used to implement fictitious periodic boundary conditions for the first Brillouin zone and supercell. This method successfully computes the transmission and reflection coefficients of photonic crystal waveguide without significant error for termination of the computational space. To validate our code, the band structure of a cubic lattice is simulated and results are compared with results of the plane wave expansion method. The proposed method is shown to be applicable to photonic crystals of irregular shape and frequency dependent (independent) materials, such as dielectric or dispersive material, and experimental data for different lattice structures. Numerical calculations show that the MMP method is stable, accurate and fast and can be used on personal computers.