Toward Modeling of Complimentary Metamaterial Elements using Higher-order Moments for Metasurface Antenna Design

Abstract

We study the model of a complementary metamaterial element embedded in a waveguide wall as a collection of dipole and quadrupole moments. The metamaterial element is a resonant, electrically-small aperture designed to leak energy from the guided mode into free space and is an essential building block—as a radiator—for waveguide-fed metasurface antennas. In the analytic model of a metasurface, the elements are often characterized as electric and magnetic point dipoles, with their higher-order moments ignored. However, the dipolar approximation is often not sufficient to accurately predict the field scattered by the element—especially the field in close proximity to the element—and thus results in errors when the analytic description of the element is applied. In this study, we present the retrieval of the quadrupole moments of a metamaterial element etched into the top wall of a parallel-plate waveguide. We also demonstrate that considering the quadrupole moments of the element, in addition to its dipole moments, can improve the accuracy of the analytic model of a metamaterial element. The proposed method can be used to improve the accuracy of the analytic model of metasurface antennas for various applications.