Band characterization of topological photonic crystals using the broadband Green's function technique

A novel method is developed in this paper to characterize the band diagram and band modal fields of gyromagnetic photonic crystals that support topological one-way edge states. The proposed method is based on an integral equation formulation that utilizes the broadband Green's function (BBGF). The BBGF is a hybrid representation of the periodic lattice Green's function with imaginary extractions that has accelerated convergence and is suitable for broadband evaluations. The effects of the tensor permeability of the gyromagnetic scatterers are incorporated in a new formulation of surface integral equations (SIEs) with BBGF as the kernel that can be solved by the method of moments. The results are compared against Comsol simulations for various cases to demonstrate the accuracy and efficiency of the proposed method. Simulations results are illustrated and discussed for the modes of topological photonic crystals in relation to the physics of degeneracy, applied magnetic fields, and bandgaps.