An extended Huygens' principle for modelling scattering from general discontinuities within hollow waveguides

Abstract

SUMMARYThe modal "elds, generalized scattering matrix (GSM) theory and dyadic Green's functions relating to a general uniform hollow waveguide are brie#y reviewed in a mutually consistent normalization. By means of an analysis linking these three concepts, an extended version of the mathematical expression of Huygens' principle is derived, applying to scattering from an arbitrary object within a hollow waveguide. The integral-equation result expresses the total "eld in terms of the incident waveguide modal "elds, the dyadic Green's functions and the tangential electromagnetic "eld on the surface of the object. It is shown how the extended principle may be applied in turn to perfect conductor, uniform material and inhomogeneous material objects using a quasi method of moments (MM) approach, coupled in the last case with the "nite element method. The work reported, which indicates how the GSM of the object may be recovered, is entirely theoretical but displays a close similarity with established MM procedures.

Application of extended Huygens' principle to scattering discontinuities in waveguide

“…Recently a new technique was proposed [33] for the solution of waveguide scattering problems. This is a hybrid technique that includes a region discretized into finite elements and a moment method type double integration over the surface of the object.…”

“…This details all theoretical aspects of the new technique and is in part a summary and in part a discussion of the material found in [33]. The theory is general and is not limited to a specific scatterer or waveguide In chapter 5 the technique and results are evaluated and possible further extensions to this work, which may form the basis of future projects, are described.…”

“…The fields inside the empty waveguide region are written as sums of waveguide modes, both TE and TM [33]. Suppressing an e jwt phase factor, The waveguide modal functions that are considered here are T Epo modes only, a result of the simplified geometry of loads that will be introduced in chapter 3.…”

“…Stellenbosch University http://scholar.sun.ac.za is derived in [33]. It is suggested that the factor T = { 2 R' and R both on r,…”

“…The Huygens' principle [33] described in this chapter provides a solution to the problem of wasted degrees of freedom. This chapter details how the finite element discretization may be confined to the interior volume and the exterior surface of the volume.…”