Analysis of metasurfaces in general-form asymmetrical rectangular lattices

Abstract

In this paper, an analytical method is expanded to analyze asymmetrical metasurfaces under normal plane-wave illuminations. In our proposed method, two key factors of the polarizabilities of individual particles, and the interaction constants between them, are employed to analyze the frequency responses of some asymmetrical metasurfaces. The associated interaction constants are extracted analytically, in the general form of an asymmetrical arrangement. Our proposed semianalytical method is validated using different asymmetrical arrays of applicable structures, including plasmonic and dielectric particles, such as a gold split ring resonator and a split Si nanocone. The reflections and transmissions of these arrays are compared to the results of numerical full-wave simulations, while the applications of our suggested method, in achieving unidirectional scattering of the split Si nanocone, are also studied. This proposed method is useful in computing the effective polarizabilities of asymmetrical arrays, as it gives a comprehensive view of the metasurface. Therefore, our proposed method is a step forward in designing and synthesizing metasurfaces.