A general method for calculation of Faraday rotation and transmittance in two-dimensional magneto-optic photonic crystals by solving vector-Helmholtz equation in anisotropic media

Abstract

We propose a general method based on the plane wave expansion method for the calculation of the Faraday rotation and transmittance spectrum of the two-dimensional magneto-optic photonic crystal. The method is an extension of the conventional plane wave expansion method by and taking into account all the three components of the electromagnetic fields and considering the permittivity tensor with off-diagonal imaginary components representing the Faraday effect and then solving the vector Helmholtz equation. The formulation is explained in detail from the implementation points of view and the computation cost of the method. In the end, numerical results are presented to verify the accuracy and convergence of the method.