Substrated inhomogeneous metasurfaces analysis using interaction constant method

Inhomogeneous metasurfaces as a periodic array of supercells in which each supercell consists of different types of particles are good candidates for increasing the bandwidth in many applications. However, the presence of a substrate is often apparent in many cases; therefore, analyzing substrated inhomogeneous metasurfaces is highly attractive and important. In this paper, an efficient analysis of the plane-wave scattering by inhomogeneous substrated metasurfaces is presented using interaction constant method (ICM). In our proposed method, we calculate the total effective polarizability tensors of inhomogeneous substrated metasurfaces using both the individual polarizabilities of each particle and the closed-form interaction coefficients that relate to the interactions of the particles with each other. Since the interaction constants are calculated analytically, this method is time effective for different arrangements of particles in supercells, and with different array periods. The reflectance and transmittance of different inhomogeneous metasurfaces have been obtained and compared to full-wave simulations by a commercial EM solver, here, and this has confirmed the accuracy of the numerical results of our proposed method. Moreover, in our last example, we present a wideband terahertz absorber, and analyze its structure with our method. It seems that our proposed method is a step forward in the analysis and design of inhomogeneous substrated metasurfaces, for various applications.