Band calculations using broadband Green’s functions and the KKR method with applications to magneto-optics and photonic crystals

Abstract

In this paper, we develop a method of simulations of using the broadband Green’s function (BBGF) in the Korringa Kohn Rostoker (KKR) method. The merit of the method is broadband such that once the initial setup is completed, the calculation at every frequency is calculated rapidly. The broadband Green’s function consists of a frequency-independent spatial summation and a spectral summation that has most of the factors frequency independent. Both summations have fast convergence. Analytical expressions of broadband coefficients of cylindrical waves are derived from the BBGF. The broadband cylindrical waves coefficients are then combined with the KKR method to calculate the determinant equation for a wide range of frequencies. Numerical results of the band diagrams and band surface currents are illustrated for magneto-optics and photonic crystals. The CPU time requirements, including setup, using MATLAB on a standard laptop, for computing the determinant at 1000 frequencies at a Bloch vector are 0.411 s and 1.206 s, respectively, for the cases of topological crystal of small scatterer relative to cell size and the photonic crystal of large scatterer comparable to cell size.