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.

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“…Zhang et al proposed a new type of two-dimensional lattice photonic crystal with different windmill shape defects, and studied the influence of the translation and rotation of the defect structure of different windmill models on the transverse magnetic field band gap, further reducing the defect symmetry of the photonic crystal [3]. Based on the traditional plane wave expansion method, Gharaati Abdolrasoul et al proposed a general method for calculating the Faraday rotation and transmission spectra of two-dimensional magneto-optical photonic crystals based on the plane wave expansion method [4]. Dena M. El-Amassi et al assumed that one of the layers constituting the ternary photonic crystal is a left-handed material with both negative permittivity and permeability.…”