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Diffraction of a skewly incident plane wave by an anisotropic impedance wedge – a class of exactly solvable cases. (English) Zbl 1067.78501

Summary: The Sommerfeld-Malyuzhinets’ technique and the special function \(\chi_\Phi\), which is originally introduced in the study of wave diffraction by a wedge located in a gyroelectric medium, have been used to find the exact solution for diffraction of a skewly incident and arbitrarily polarized plane wave by wedges with an arbitrary opening angle and with a class of specific, but in general non-axial anisotropic face impedances. Just for these impedance faces suitable linear combinations of the field components parallel to the edge of the wedge are no longer completely related to each other on the wedge surfaces; an application of the Sommerfeld-Malyuzhinets’ technique to these boundary conditions then leads to inhomogeneous difference equations for the spectral functions; in terms of the \(\chi_\Phi\) function these functional equations are transformed to such simple forms that their closed-form exact solutions are given immediately. The uniform asymptotic expansion is then obtained via the method of saddle point. This solution coincides with exact solutions for tensor impedance wedges illuminated by a normally incident plane wave and agrees very well with both analytical perturbation solution as well as numerical results of the method of parabolic equation for a skewly incident plane wave. Typical diffraction behavior dependent on the skewness of the incident wave is also shown.

MSC:

78A45 Diffraction, scattering
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