A Review of New Canonical Scattering Problems Solved Using a Spectral Approach Integrating the Wiener–Hopf Method with Fredholm Factorization and Network Formalism

The Wiener-Hopf technique is a fundamental analytical and semi-analytical method in applied mathematics and mathematical physics for solving PDE and integralequation boundary-value problems. Using spectral domain, it enables rigorous solutions and with the Fredholm factorization very accurate approximate solutions in computational physics and in particular in electromagnetics allowing efficient analysis of propagation, diffraction, guided-wave discontinuities, antenna radiation, and modern applications. Recent advances, as the introduction of the novel direct Fredholm factorization for arbitrary generalized Wiener Hopf equations, extend the method to more complex geometries and arbitrary media beyond rectangular, isotropic media, while preserving strong physical insight through spectral-domain interpretation. Wiener-Hopf formulations can be interpreted through equivalent networks to avoid redundancy for a practical and systematic application of the methodology.