Modified Bresler-Marcuvitz Transverse Equation Theory for Wedge Shaped Regions to derive Generalized Wiener-Hopf Equations

In this work, we present a novel and general mathematical technique to get Generalized Wiener-Hopf Equations (GWHEs) in angular regions filled by an arbitrary linear medium and with arbitrary boundary conditions [1]–[2]. We first extend the transverse equation theory developed in [3] by Bresler and Marcuvitz for stratified media. We develop the theory for angular regions in electromagnetics using oblique Cartesian coordinates, starting from Maxwell’s equations. It yields a matrix differential problem of first order (1) whose unknowns are the field component ψt tangent to the faces of the angular regions (i.e. the field components continuous on the boundaries).\begin{equation*} - \frac{\partial }{{\partial y}}{\psi _t} = \mathcal{M}\left( {\frac{\partial }{{\partial z}},\frac{\partial }{{\partial x}}} \right)\cdot{\psi _t}\tag{1}\end{equation*}