Surface integral equation method for analyzing electromagnetic scattering in layered medium

Abstract

Surface integral equation (SIE) method with the kernel of layered medium Green's

function (LMGF) is investigated in details from several fundamental aspects. A

novel implementation of discrete complex image method (DCIM) is developed to

accelerate the evaluation of Sommerfeld integrals and especially improve the far

field accuracy of the conventional one. To achieve a broadband simulation of thin

layered structure such as microstrip antennas, the mixed-form thin-stratified

medium fast-multipole algorithm (MF-TSM-FMA) is developed by applying

contour deformation and combining the multipole expansion and plane wave

expansion into a single multilevel tree. The low frequency breakdown of the

integral operator is further studied and remedied by using the loop-tree

decomposition and the augmented electric field integral equation (A-EFIE), both

in the context of layered medium integration kernel. All these methods are based

on the EFIE for the perfect electric conductor (PEC) and hence can be applied in

antenna and circuit applications. To model general dielectric or magnetic objects,

the layered medium Green's function based on pilot vector potential approach is

generalized for both electric and magnetic current sources. The matrix

representation is further derived and the corresponding general SIE is setup.

Finally, this SIE is accelerated with the DCIM and applied in quantum optics,

such as the calculation of spontaneous emission enhancement of a quantum

emitter embedded in a layered structure and in the presence of nano scatterers.