Theory and application of the recursive Green's function method for analysis of electromagnetic waves in inhomogeneous media
A Recursive Green's Function Method (RGFM) that computes the full-wave solution of the scalar Helmholtz equation is presented. RGFM is a numerical method that recursively constructs the Green's function for inhomogeneous domains. This Green's function is subsequently used in the boundary integral technique to calculate the field in and around inhomogenous objects. For one-dimensional problems, RGFM is demonstrated by finding important device characteristics for DFB lasers, including resonant wavelength, threshold gain and spatial hole burning factors. The method is shown to have computational and storage complexities of O(N log2 N) and O(N), respectively, when calculating internal field values and O(N) and O(4) for calculation of external field values. For two-dimensional problems, RGFM is used to analyze scattering by several canonical cylindrical obstacles for both TE and TM waves. Results from bistatic scattering and absorption by these canonical obstacles are presented. The method is shown to have computational and storage complexities of O(N2 ) and O(N1.5), respectively, when calculating internal field values and O(N 1.5) and O(N) when calculating external field values. Application of the two-dimensional RGFM algorithm to slab waveguide analysis is given. A technique combining this analysis with one-dimensional RGFM to analyze the effects of coupling discontinuities in DFB lasers is also presented.