Efficient integral equation formulation of diffraction at the edge of a truncated dielectric structure based on PO solutions: Application to the case of arbitrarily polarized line sources

Abstract

[1] The radiation patterns of electric and magnetic line sources placed near the truncation of a semi-infinite grounded dielectric layer structure have been investigated. Two polarizations (parallel and normal to the edge) have been considered for both sources. In order to perform the analysis a new formulation is proposed for the aperture integral equations derived from the principle of equivalence. The novelty of this formulation is that it involves only the fringe components of the magnetic current. The total magnetic current flowing on the aperture is expressed in terms of the physical optics (PO) current and the fringe current. Although the PO current is not known analytically, we can calculate the field excited by this current using the relationship between the surface magnetic PO current on the aperture and the electric polarization PO current in the grounded dielectric slab. The latter PO current is approximated analytically by the expansion wave concept. This step opens a simple and effective way to calculate the right part of the integral equations and as a consequence the radiation pattern of the line sources. For comparison reasons the problem is solved also by using the method of Physical Optics and the Uniform Theory of Diffraction.

High‐frequency scattering on a semi‐infinite dielectric slab with a rising ground: TM case

“…Eq. (1) can be reduced to a fringe aperture integral equation (FA-IE) for a fringe magnetic-current component in a similar way as in [4,5]. The magnetic current can be expressed as…”

“…In this case, electromagnetic fields in the infinite dielectric slab generated by the line source can be approximated in a closed form at some above distance from the line source by using the expansion wave concept (EWC) [6,7]. We have shown in [5] that the field excited by the magnetic PO current K PO in a free half-space can be expressed in terms of a so-called truncated electric PO current J T PO . The basic relationship is given by…”

“…These approaches allow us to calculate amplitudes of reflected surface waves and scattering patterns generated by incident surface waves or line sources. Using this solution and the postulates of the geometrical theory of diffraction, an approximate solution for the scattering of electromagnetic fields at the edge of a semi-infinite dielectric slab on a rising ground can be obtained [2,4,5]. This approximate solution has two drawbacks.…”

“…The configuration under investigation looks very similar to a semi-infinite grounded dielectric slab. In recent years, several approaches to modelling the scattering on a semi-infinite grounded dielectric slab have been proposed [1][2][3][4][5]. These approaches allow us to calculate amplitudes of reflected surface waves and scattering patterns generated by incident surface waves or line sources.…”

“…In order to avoid this extra calculation, we directly consider a semiinfinite slab on a rising ground. Our method is based on the expansion technique in [2,4,5].…”