E-Polarized Diffraction by Dielectric Wedge

Geometrical optics (GO), the most widely used tool in analysis of high frequency electromagnetic problems, provides the first term of an asymptotic series solution to the Maxwell's equations [1]. It is implemented completely by employing the ordinary ray-tracing technique. To include the second asymptotic term systematically, Keller [2] suggested a generalization of the Fermat's principle on diffracted rays. It is called the geometrical theory of diffraction (GTD), where the initial value of diffracted rays should be determined from the exact diffraction coefficients of canonical structures, e.g., perfectly conducting half-plane, wedge, and cone. In spite of some improved GTD versions, those applications to penetrable objects have been hindered by the lack of rigorous diffraction coefficients of such canonical structures as penetrable wedges and cones. Until now, there is no rigorous solution to the diffraction by a dielectric wedge [3]. Some heuristic modification of the exact diffraction coefficients of perfectly conducting wedge have been performed to account finite dielectric constant or conductivity. But their diffraction coefficients could not satisfy the edge condition at wedge tip [4]. Numerical calculations of diffraction coefficients of dielectric wedges have also been performed using the method of moment and the FDTD method. But numerical techniques could not provide comparable achievements in the physical understanding of edge diffraction. In recent, an approximate but accurate analytical solution to the diffraction coefficients of composite wedge was constructed by employing the method of hidden rays [5]. The hidden rays obey the usual principle of geometrical optics (GO) but do not exist in the physical region. These rays can be traced only in the complementary region, in which original media of background and scatterer are exchanged each other. While the physical optics (PO) approximation of ordinary rays provides not only GO term but also diffracted field in physical region, the PO approximation of hidden rays contributes only to diffracted field in physical region. Hence the method is called the hidden rays of diffraction (HRD). In this paper, the HRD method is applied to E-polarized diffraction by a dielectric wedge.