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The Wiener-Hopf Formulation of the Penetrable Wedge Problem: Part I

Abstract The diffraction by a dielectric wedge of an arbitrary aperture angle is studied by means of the generalized Wiener-Hopf technique. Generalized Wiener-Hopf equations are deduced that apparently cannot be solved in closed form. The factorization of the kernels can be reduced to Fredholm equations of the second kind by using a standard procedure (Fredholm factorization). The solutions of the Fredholm equations are obtained through a simple quadrature technique that very quickly yields a numerically stable evaluation of the unknowns of the generalized Wiener-Hopf equations. The generalized Wiener-Hopf technique provides a representation of the fields only in certain regions of the spectral domain. To obtain valid solutions everywhere, a process of analytical continuation is required. This latter task is accomplished in the companion article.