Diffraction by a Dielectric Wedge by Use of the Dual Integral Equations

Abstract

A physical optics approximation for the fields scattered by a dielectric wedge is obtained in analytic representations by solving the Kirchhoff integrals inside as well as outside the wedge by taking the geometric optics fields as the approximate boundary fields in the interfaces for plane wave incidence. One may add the correction surface currents along the wedge interfaces to the physical optics solutions, where the correcting currents are expanded in Neumann series, for example, and the expansion coefficients are obtained numerically by nullifying two extinction integrals in the mathematically complementary regions of the free space and the dielectric medium, respectively. The accuracy of the edge diffracted field of the physical optics solution plus the correcting fields, calculated from the correction currents obtained from the extinction integrals, may be checked by the degree of nullification of the extinction integrals.

Two cases of the calculated dynamic fields will be shown. The dynamic field distributions near the edge tip from 0.01 to 3 wavelengths shows a smooth transition from the static behavior to the dynamic far field behavior. Similar method with the multi-pole correction source at the wedge tip gives the correction to the edge diffraction by the lossy dielectric wedge which gives close results with Maliuzhinets’ impedance wedge for the high loss tangent wedge but considerable difference for the low loss tangent wedge.

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