The Wiener-Hopf formulation of the dielectric wedge problem.Part I

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 generalizedWiener-Hopf equa- tions. 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 paper