Electromagnetic diffraction and scattering of a complex-source beam by a semi-infinite circular cone

Abstract

Abstract. A complex-source beam (CSB) is used to investigate the electromagnetic scattering and diffraction by the tip of a perfectly conducting semi-infinite circular cone. The boundary value problem is defined by assigning a complex-valued source coordinate in the spherical-multipole expansion of the field due to a Hertzian dipole in the presence of the PEC circular cone. Since the incident CSB field can be interpreted as a localized plane wave illuminating the tip, the classical exact tip scattering problem can be analysed by an eigenfunction expansion without having the convergence problems in case of a full plane wave incident field. The numerical evaluation includes corresponding near- and far-fields.

Electromagnetic complex-source beam diffraction by the tip of a circular cone

“…Moreover, as has been shown in [6], |m| is bounded by m 2 < σ τ (σ τ + 1) with τ ∈ {s, h}. Finally, the multipole amplitudes a σs,m and b σ h ,m are derived for a Hertzian dipole located at (r D , ϑ D , ϕ D ) and characterized by the "current moment" c e according to [7] a σs,m = −κ 2 0 Z 0…”

“…It allows to probe the scattering characteristics of a certain area of the cone, particularly of the tip by means of a (localized) plane-wave front. We then obtain a multipole expanion of diffracted fields, which outside of the area of the incident beam can be interpreted as the scattered field [6], [7]. Moreover, the resultant multipole expansions turn out to be strongly convergent.…”

Acoustic scattering of a complex-source beam by the edge of a plane angular sector

“…A complex-source beam (CSB) is a powerful tool to describe focused beams analytically. As shown by (Katsav et al, 2012) and (Brüns and Klinkenbusch, 2013), the Green's function of a point source at a complex-valued location can be used to approximately describe a Gaussian beam with an arbitrary beam direction. However, in contrast to a Gaussian beam, the CSB exactly satisfies the Helmholtz equation.…”

Spherical-multipole analysis of an arbitrarily directed complex-source beam diffracted by an acoustically soft or hard circular cone

“…By using a sphericalmultipole eigenfunction expansion of the cone for the total field and a free-space type multipole expansion of the scattered field, in Klinkenbusch (2007), Kijowski and Klinkenbusch (2011) solutions were derived which, however, suffered from a missing convergence of the finally obtained multipole series. Rather than using an incident full plane wave the new approach in Katsav et al (2012), Brüns and Klinkenbusch (2013) started from a complex-source beam (CSB) as the incident field. One main advantage of this method is the ability to probe just the section of interest, for instance the area near to the cone's tip.…”

“…Furthermore, the convergence problems mentioned above are avoided using a CSB. While Katsav et al (2012), Brüns and Klinkenbusch (2013) investigated the scattering and diffraction of a CSB pointed directly towards the tip of the circular cone the present contribution deals with the more general case of an arbitrarily directed CSB illuminating any desired part of the cone.…”