Complex Analysis of the Induced Currents on a Perfectly Conducting Plane Under Complex Beam Incidence

Abstract

Abstract-This paper is concerned with the analysis of the currents induced on a 2D infinite perfectly conducting plane illuminated by a complex beam obtained from the analytical continuation of the real location of a unit impulse source into a complex one. The main goal considering this well-known problem is to understand the meaning of the analytical continuation and the physical information underlying the complex quantities arising from it, and to investigate the capabilities of operating in complex spaces instead of the original real ones through a simple example. Several complex quantities directly related to this problem are analysed and translated into the real domain, leading to a clear and general description of all the possible behaviours of the currents. These results will provide some new insight to extend the complex analysis methodology to more complicated scattering problems. As expected, complex analysis appears to be a full-meaning tool to obtain parameterizations of EM problems, leading to more general solutions and their physical descriptions. 300González-Morales, Gago-Ribas, and Dehesa-Martínez

Complex Polar Coordinates in Electromagnetics

“…In last years, some work has been concentrated on the understanding of particular aspects of the complex extension procedure, specially those concerning its physical meaning, the fundamental basis of the procedure and the generalization of the methodology, [9,10]. This research has given rise to the concept of complex angle that is useful, for example, when dealing with angular plane wave spectrum characterization of Helmholtz equation solutions, [11].…”

3d Complex Beams in the Spatial and the Spectral Domains

“…A complex angle can also be defined accordingly. Solutions to radiation and scattering problems [5][6][7][8] may be constructed within the framework of the complex beams [4,9], and complex distances and angles are very natural variables in the analysis of such problems [10,11].…”