2D TM scattering problem for finite dielectric objects in a dielectric stratified medium employing Gabor frames in a domain integral equation

Abstract

We present a method to simulate two-dimensional scattering by dielectric objects embedded in a dielectric layered medium with transverse magnetic polarization through a domain integral equation formulation. A mixed spatial-spectral discretization is employed with both a spatial and a spectral representation along the direction of the layer interfaces. In the spectral domain, a discretization on a path through the complex plane is used on which the Green function is well behaved. To calculate the field-material interaction in the spatial domain, an auxiliary field is employed similar to the Li factorization rules. Numerical results show that this auxiliary-field formulation significantly improves accuracy, compared to a formulation that directly employs the electric field.

A 3D spatial spectral integral equation method for electromagnetic scattering from finite objects in a layered medium

“…Analoguous to Dilz and Beurden (2016, 2017), Dilz et al. (2017), we represent the Green function, the contrast current density , and scattered field in the spectral domain in the transverse xy -plane. We denote coordinates in the transverse plane as , and in the spectral domain as .…”

“…Consequently, we havewith the three-dimensional effective reflection coefficient that contains both h and e polarization, which can be calculated from the effective reflection coefficients for h polarization (Dilz and Beurden 2017), and for e polarization (Dilz et al. 2017) asThis matrix projects the e and h polarized parts of the electric field to effective transmission coefficients and , respectively. The definition of these effective reflection coefficients is given in Dilz and Beurden (2017), Dilz et al.…”

“…This effect was also observed for a Gabor-frame based solver for TM-polarized scattering (Dilz et al. 2017). For periodic scattering problems with a discrete spectral expansion a reformulation of the field-material interactions corrects this poor rate of convergence (Granet and Guizal 1996; Lalanne and Morris 1996), which is explained in more detail in Li (1996) introducing the so-called Li-rules.…”

“…In Dilz et al. (2017) it is shown that the same mechanism can also be used for a continuous spectral expansion and the algorithm of Dilz and Beurden (2017) is extended to efficiently deal with the discontinuous field-material interaction in a way that does abide these Li-rules. Here, we propose a generalization of this method to three dimensions.…”

Computational aspects of a spatial-spectral domain integral equation for scattering by objects of large longitudinal extent

“…Gabor frames are used as a discretization for the contrast current density on the regions k α < −A and k α > A. For the two-dimensional algorithms in [2,4,5], where the y direction is absent, a Taylorseries approximation with N a +1 terms is employed on the connecting part −A < k x < A. A function f (k x ) is approximated on the spectral path of Eq.…”