Research Article

Riemann–Hilbert technique scattering analysis of metamaterial-based asymmetric 2D open resonators

¹ Department of Electrical Engineering Technical, University of Denmark, Kgs. Lyngby 2800, Denmark
² Department of Electrical and Computer Engineering, University of Arizona, Tucson, 85721-0104, USA
³ Global Big Data Technologies Centre, University of Technology Sydney, Ultimo, NSW 2007, Australia

^* e-mail: pmarka@elektro.dtu.dk

Received: 16 March 2017
Received in final form: 8 September 2017
Accepted: 19 September 2017
Published online: 1 December 2017

Abstract

The scattering properties of metamaterial-based asymmetric two-dimensional open resonators excited by an electric line source are investigated analytically. The resonators are, in general, composed of two infinite and concentric cylindrical layers covered with an infinitely thin, perfect conducting shell that has an infinite axial aperture. The line source is oriented parallel to the cylinder axis. An exact analytical solution of this problem is derived. It is based on the dual-series approach and its transformation to the equivalent Riemann–Hilbert problem. Asymmetric metamaterial-based configurations are found to lead simultaneously to large enhancements of the radiated power and to highly steerable Huygens-like directivity patterns; properties not attainable with the corresponding structurally symmetric resonators. The presented open resonator designs are thus interesting candidates for many scientific and engineering applications where enhanced directional near- and far-field responses, tailored with beam shaping and steering capabilities, are highly desired.