Variational-based approach to investigate Fano resonant plasmonic metasurfaces

Considering the widespread applications of resonant phenomena in metasurfaces to bend, slow, concentrate, guide and manipulate lights, it is important to gain deep analytical insight into different types of resonances. Fano resonance and its special case electromagnetically induced transparency (EIT) which are realized in coupled resonators, have been the subject of many studies due to their high-quality factor and strong field confinement. In this paper, an efficient approach based on Floquet modal expansion is presented to accurately predict the electromagnetic response of two-dimensional/one-dimensional Fano resonant plasmonic metasurfaces. Unlike the previously reported methods, this method is valid over a wide frequency range for different types of coupled resonators and can be applied to practical structures where the array is placed on one or more dielectric layers. Given that the formulation is written in a comprehensive and flexible way, both metal-based and graphene-based plasmonic metasurfaces under normal/oblique incident waves are investigated, and it is demonstrated that this method can be posed as an accurate tool for the design of diverse practical tunable/untunable metasurfaces.