Fast band diagram simulation of 2D periodic scatterers using surface integral equations with broadband Green's function

Abstract

A novel approach of broadband Green's function with low wavenumber extraction (BBGFL)has recently been developed to calculate the band diagrams of two dimensional (2D) periodic structures using surface integral equations [1–3]. The surface integral equation takes the periodic Green's function as the propagator, provides the exact multiple scattering solution to the problem. A low wavenumber component is extracted from the periodic Green's function, leaving the remaining part fast convergent with respect to the number of Bloch waves needed in spectral domain. The periodic Green's function is only evaluated once at the selected low wavenumber. The choice of the low wavenumber is shown to be robust. The remainder, designated as the broadband periodic Green's function, has very simple and separable wavenumber dependence, can be readily evaluated over a broad band of wavenumbers. The surface integral equation is then discretized using the method of moments (MoM) and subsequently converted into a linear eigenvalue problem. The eigenvalues of the linear system correspond to multiple bands of the periodic structure and are solved all at once. The application of MoM makes the approach applicable to any shape of the geometry, any dielectric contrast, and any scatterer filling ratio. The boundary representation of the scatterer significantly reduces the number of unknowns comparing to volumetric discretization as in the finite element method (FEM) and is free of staircase representation errors as encountered in the plane wave expansion method [4] and the finite difference method in time domain (FDTD). The plane wave method is also reported to converge slowly with high permittivity contrast and filling ratio [5].