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

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.