International Symposium on Antennas and Propagation


Session Number:3B10



On Approximation for Spectral Expression of Scattered Field from A Thick Half-Plate

Mayumi NAKAGAWA,  Hironori FUJII,  Kazunori UCHIDA,  


Publication Date:2008/10/27

Online ISSN:2188-5079


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The two-dimensional (2D) plane-wave scattering by a thick conducting half-plane is one of the fundamental electromagnetic field problems. It includes reflection at the faces of the half-plate as well as multiple diffractions at the two wedges. Although this problem can be solved rigorously in spectral domain by applying Wiener-Hopf (WH) technique to the 2D wave equation [1]- [4], its Fourier inverse transformation cannot be performed analytically because the rigorous WH solutions in the spectral domain include coefficients to be solved by infinite simultaneous equations and factorization of kernel functions [5] [6]. From these reasons, the rigorous WH solutions are too complicated for us to apply them to practical electromagnetic field problem. When we analyze the complicated problems such as propagation in urban area, the analytical scattered fields should be expressed in a compact form and the results should exhibit versatility, high accuracy and stability. In this context, we attempt to introduce an approximate spectral expression based on the WH solutions for the present problem. In this paper, we deal with the case of E-wave incidence focusing on the far fields. Before we introduce the approximate spectral expressions, we first rewrite the WH solutions in spectral domain so as to calculate analytically its Fourier inverse transformation, that is, the spectral expression by the two half-planes is expressed by using the Fresnel integral and the spectral expression by the thickness of the half-plate is expressed by using the saddle point method [7]. Then, we investigate the behavior of the WH solutions numerically in spectral domain focusing on the effect of the incident angle and the thickness of the half plane. As the numerical results, we introduce the approximation for the spectral expression of the scattered field by the thickness of the half-plate and it is expressed in some compact forms by using the principal values at the pole and sampling function. In order to check the accuracy of this approximation, we compare the approximated solutions at the grazing incident angle with the WH ones in spectral domain. It is demonstrated that both solutions are in good agreement.