Abstract
Network modeling in electromagnetics is an effective technique in treating scattering problems by canonical and complex structures. Geometries constituted of angular regions (wedges) together with planar layers can now be approached with the Generalized Wiener-Hopf Technique supported by network representation in spectral domain. Even if the network representations in spectral planes are of great importance by themselves, the aim of this paper is to present a theoretical base and a general procedure for the formulation of complex scattering problems using network representation for the Generalized Wiener Hopf Technique starting basically from the wave equation. In particular while the spectral network representations are relatively well known for planar layers, the network modelling for an angular region requires a new theory that will be developed in this paper. With this theory we complete the formulation of a network methodology whose effectiveness is demonstrated by the application to a complex scattering problem with practical solutions given in terms of GTD/UTD diffraction coefficients and total far fields for engineering applications. The methodology can be applied to other physics fields.
Highlights
The results show the capability of network modelling to deal with complex problems and show the convergence, the efficiency and the efficacy of the proposed method estimating the electromagnetic far field in terms of Geometrical Optics (GO) components and Uniform Theory of Diffraction (UTD) components
In this paper we focus the attention on the second method for two reasons.The first is that we want to illustrate a general procedure to study complex problems constituted by different geometries and media by obtaining simple network representations and the presence of different media does not allow to define an unique w plane because of its dependence, by definition, on the propagation constant k.The second is that the possible presence of finite layers introduce the need to handle modal representation of the field that in w plane exhibits infinite replica of the relevant structural poles
In order to demonstrate the efficacy and the novelty of the proposed methodology we present an original test case.The procedure starts from the GWHE formulation of the problem whose solution is obtained via Fredholm integral equations (FIEs) that are derived through the help of network modelling.The results show the capability of network modelling to deals with complex problems and show the convergence, the efficiency and the efficacy of the proposed method estimating the electromagnetic far field in terms of Geometrical Optics (GO) components and uniform diffracted components (UTD)
Summary
Network modeling has been widely used in electromagnetics since early developments of microwaves [1] and it is constitutive of the general theory of radiation and scattering as proposed by Marcuvitz and Felsen [2].For what concerns the scattering by stratified planar media in presence of planar discontinuities a complete reference based on network formulations is [3].Recently, geometries constituted of coupled angular and planar regions [4,5,6,7,8,9,10] have been studied through the Generalized Wiener Hopf technique introducing Laplace transform (LT) in radial direction, extending the class of solvable problems through the Wiener-Hopf (WH) technique, see [11] and references therein. Network modeling has been widely used in electromagnetics since early developments of microwaves [1] and it is constitutive of the general theory of radiation and scattering as proposed by Marcuvitz and Felsen [2]. For what concerns the scattering by stratified planar media in presence of planar discontinuities a complete reference based on network formulations is [3]. Geometries constituted of coupled angular and planar regions [4,5,6,7,8,9,10] have been studied through the Generalized Wiener Hopf technique introducing Laplace transform (LT) in radial direction, extending the class of solvable problems through the Wiener-Hopf (WH) technique, see [11] and references therein. The Wiener-Hopf technique is effectively applied to study problems with abrupt discontinuities in different physics [11] as acoustics, elasticity, fracture mechanics. . .
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