The Wiener–Hopf Fredholm factorization technique to solve scattering problems in coupled planar and angular regions

The Wiener–Hopf (WH) technique is a very powerful tool in the spectral domain to solve field problems in the presence of discontinuities. This chapter introduces a generalization of this technique that allows to study geometries where coupled planar and angular region are present. Since exact solutions with closed form factorizations are available only in few cases, most of the problems require an alternative approximate technique as the Fredholm factorization. The Fredholm factorization reduces the solution of WH equations to a system of Fredholm integral equations (FIE) of second kind amenable of very efficient numerical solution. The deduction of the FIE is presented in this chapter for a relatively simple novel problem. The numerical solution of FIEs provides an analytical element of the spectra, which in general is not sufficient to evaluate the different components of the diffracted field. To obtain the whole spectrum of the unknowns, analytical continuations and recursive equations deduced by the WH equations are presented. The work ends with a short description of the numerical simulations for the novel scattering problem