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

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.