The behavior of electromagnetic fields at edges

Abstract

The research reported in this document has been made possible through support and sponsorship extended by the Air Force Cambridge Research Center, under Contract No. AF-19(122)- 42.It is published for technical information only and does not necessarily represent recommendations or conclusions of the sponsoring agency.

Scattering of an arbitrary plane wave by a dielectric wedge: Integral equations and fields near the edge

“…Clearly, t = 0 is always a solution of equation (13), and the next larger solution satisfies 0 < t 1 [Meixner, 1972]. [8] We have to match the fields along the sides of the wedge for all r, thus the fields have to depend on r by means of the same solution, R(r), of equation (6).…”

“…In Sommerfeld's approach the form of the analytic solution differs depending on whether the wedge angle is a rational multiple of p or not. Meixner [1972] extended his approach from perfectly conducting wedges to dielectric ones, although it was shown [Bach Andersen and Solodukhov, 1978] that some of the coefficients in the power series expansion Meixner derived become infinite for wedge angles that are rational multiples of p. In that case, powers of log r, where r is the radial distance from the edge, have to be included in the series [Makarov and Osipov, 1986;Marx, 1990b]. Still, the consensus is that the behavior of the fields near the edge of the wedge is that of static fields, which was later proved for oblique incidence by Bergljung and Berntsen [2001].…”

Fast Converging Cfie-Mom Analysis of Electromagnetic Scattering From Pec Polygonal Cross-Section Closed Cylinders

“…This approach has been successfully used for studying propagation, radiation and scattering problems involving PEC and dielectric objects in homogeneous and layered media . In these works, the selection of expansion bases reconstructing the physical behaviour of the unknowns at edges [55] has demonstrated to guarantee fast convergence.…”

Gaussian Beam Electromagnetic Scattering From Pec Polygonal Cross-Section Cylinders

“…This suggests to formulate the problem in the spectral domain so that the convolution integrals can be interpreted as the Fourier transforms in the complex plane of the expansion functions. Moreover, the choice of expansion bases reconstructing the behaviour of the fields on the wedges [19] leads to a fast convergence, i.e., small size of resulting coefficient matrix to achieve highly accurate results. The proposed method is efficient even in terms of computation time since the elements of the coefficient matrix, which are improper integrals of oscillating functions with a slow asymptotic decay in the worst case, are efficiently evaluated by means of an analytical asymptotic acceleration technique.…”