Uniformly accurate layered medium green’s function approximation via scattered field formulation of the spectral differential equation method

Abstract

Evaluation of the multilayer medium Green’s function is essential in many practical applications of electromagnetic analysis including the design of microwave circuits and microstrip antennas, modeling of high-speed interconnects, remote sensing, geoscience, and others. Expansion of the layered medium dyadic Green’s function’s components over cylindrical waves obtained through the finite-difference solution to 1D differential equation governing their spectra is an effective method to approximate the fields in the intermediate and far zones of the point source (Okhmatovski et al., IEEE TAP 2002). In the near vicinity of the point source, however, such approximation becomes inaccurate. This is due to spherical waves dominating the solution near the source and counted number of cylindrical waves becoming inadequate to their accurate description. To develop uniformly accurate approximation, we decompose the spectrum of the total potential into the incident and scattered potential contributions. The 1D differential equation governing the spectrum of the layered medium Green’s function is formulated with respect to the scattered potential rather than the total potential as it was done previously (Okhmatovski et al., IEEE TAP 2002). The boundary conditions at dielectric layer interfaces, based on the continuity of the Green’s function and the normal component of electric flux density are enforced. As a result, the pole-residual approximation of the scattered potential spectrum is obtained which leads to accurate cylindrical wave approximation in the spatial domain in both the intermediate and far zones since singularity of Green’s function resides in the incident potential. The incident field is subsequently added in the analytic form and, hence, accurately describes the field near the source.