A Simple Equivalent Circuit Approach for Anisotropic Frequency Selective Surfaces and Metasurfaces

TL;DR

This paper introduces a simple equivalent circuit model for anisotropic frequency selective surfaces and metasurfaces, enabling efficient analysis and design of polarization conversion devices with minimal parameters.

Contribution

The authors develop a compact circuit model using impedance matrix rotation and LC networks to represent anisotropic FSSs, simplifying analysis and design processes.

Findings

The model accurately predicts anisotropic FSS behavior at various azimuth angles.

It accounts for dielectric substrates and periodicity variations without extra computation.

Applied to design polarization converters based on anisotropic metasurfaces.

Abstract

An equivalent circuit model for Frequency Selective Surfaces (FSS) comprising anisotropic elements is presented. The periodic surface is initially simulated with an arbitrary azimuthal incidence angle and its surface impedance matrix is derived. The impedance matrix is subsequently rotated by an angle $\varphi^{rot}$ on the crystal axes $\chi_1$, $\chi_2$ thus nullifying its extra diagonal terms. The rotation angle $\varphi^{rot}$ is derived according to the spectral theorem by using the terms of the matrix initially extracted. The diagonal terms of the rotated matrix, that is, the impedances $Z_{\chi_1}$ and $Z_{\chi_2}$, are finally matched with simple LC networks. The circuit model representation of the anisotropic element can be used to analyse anisotropic FSSs rotated by a generic azimuth angle. The methodology provides a compact description of generic FSS elements with only five parameters: the lumped parameters of the LC network $L_{\chi_1}$, $C_{\chi_1}$, $L_{\chi_2}$, $C_{\chi_2}$ and the rotation angle $\varphi^{rot}$. The circuit model can take into account the presence of dielectric substrates close to the FSS or a variation of the FSS periodicity without additional computational efforts. The equivalent circuit model is finally applied to the design of two transmitting polarization converts based on anisotropic metasurfaces.