Useful Solutions for the Plane Wave Diffraction by a Configuration of Dielectric and Metallic Acute-Angled Wedges
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The plane wave diffraction by a two-dimensional composite wedge is considered and solutions in the high-frequency framework as well as in the time domain are proposed by using a well-assessed theoretical approach. The considered structure is surrounded by the free space and composed of two acute-angled infinite wedges: a lossless dielectric wedge surmounts a metallic wedge. Accordingly, the observation domain consists of the free space and the dielectric region. For each observation sub-domain, the high-frequency diffracted field is evaluated by implementing an analytical procedure that is based on the physical optics approximation of the involved surface currents, i.e., the electric and magnetic equivalent current densities over the free space / dielectric boundary and the electric surface current over the metallic faces. Such current densities are the sources of the scattered electric field in the considered sub-domain. Useful approximations and integral evaluations permit to apply an asymptotic technique to the corresponding radiation integral in order to extract the diffraction contribution. The expressions of the associated diffraction coefficients can be used in the context of the uniform geometrical theory of diffraction and are easy to compute. Then the time domain counterparts are determined by applying the inverse Laplace transform and their expressions are in simple closed form, too. At the best of the authors’ knowledge, other time domain solutions are unavailable in literature and this makes the results of this work even more interesting. The validation by means of an appreciated full-wave numerical technique enhances the importance of the proposal.
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