Numerical studies of mixed compact stencils for two-dimensional Helmholtz equation with circular interfaces

摘要

We present method of connected local fields to solve Helmholtz equation for high index-contrast dielectric structures with circular interfaces. Numerical examples of computing two-dimensional Green's functions for silica rods in free space are discussed. Our method is based on the piece-wise linear approximation of the dielectric curved interface combined with a wide-angle transparent boundary condition that also uses compact stencils. We report here that compared with exact Green's functions our numerical errors are well under one percent for both TE and TM polarization at a low sampling density of ten points per wavelength.