Analytical Equivalent Circuits for Three-dimensional Metamaterials and Metagratings

TL;DR

This paper introduces an analytical framework using Floquet-Bloch modal expansions and integral equations for efficiently analyzing 3D metamaterials and metagratings, enabling physical insight and polarization control.

Contribution

It presents a novel fully-analytical method for 3D metamaterials analysis, including an equivalent circuit for better physical understanding, tested against full-wave simulations.

Findings

Analytical framework is computationally efficient compared to full-wave methods.

The method accurately predicts electromagnetic behavior of 3D structures.

Structures demonstrate independent polarization control.

Abstract

In recent times, three-dimensional (3D) metamaterials have undergone a revolution driven mainly by the popularization of 3D-printing techniques, which has enabled the implementation of modern microwave and photonic devices with advanced functionalities. However, the analysis of 3D metamaterials is complex and computationally costly in comparison to their 1D and 2D counterparts due to the intricate geometries involved. In this paper, we present a fully-analytical framework based on Floquet-Bloch modal expansions of the electromagnetic fields and integral-equation methods for the analysis of 3D metamaterials and metagratings. Concretely, we focus on 3D configurations formed by periodic arrangements of rectangular waveguides with longitudinal slot insertions. The analytical framework is computationally efficient compared to full-wave solutions and also works under oblique incidence conditions. Furthermore, it comes associated with an equivalent circuit that allows to gain physical insight into the scattering and diffraction phenomena. The analytical equivalent circuit is tested against full-wave simulations in commercial software CST. Simulation results show that the proposed 3D structures provide independent polarization control of the two orthogonal polarizations states. This key property is of potential interest for the production of full-metal polarizers, such as the one illustrated.