Fast Numerical Computation of Green's Functions for Unbounded Planar Stratified Media With a Finite-Difference Technique and Gaussian Spectral Rules

A computational methodology for the calculation of Green's functions for unbounded planar stratified media is proposed in this paper. Unlike several techniques that are based on analytical calculations in the spectral domain, this one is based on a previously proposed finite-difference discretization of the corresponding one-dimensional differential equation and the resulting spectral matrix problem. A smart approximation of the radiation boundary condition, based on the mathematical methodology of Gaussian spectral rules and the associated construction of an optimal nonuniform grid in the unbounded space, succeeds in maintaining the tridiagonal nature of the matrix spectral problem, providing a highly efficient means of computing the desired multilayer Green's function.