Analytical synthesis of high-Q bilayer all-dielectric metasurfaces with coupled resonance modes

We propose a structure of bilayer dielectric metasurfaces consisting of silicon nano-cuboids with high-quality (Q) transmittance due to the coupling effect between Fabry-Perot and Mie resonances. The synthesis of the structure is done by using a novel straightforward analytical method, to the best of our knowledge, based on finding the equivalent parameters of the dielectric metasurfaces. Considering the dielectric metasurface as an array of meta-atoms with dipole moments addresses the theoretical calculation of the equivalent parameters of the metasurface. Because the main aspect of the analytic manner is precisely finding these equivalent parameters, providing effective polarizabilites of a limited array of meta-atoms instead of polarizabilities of one meta-atom is presented. The calculated equivalent parameters are used to synthesize bilayer dielectric metasurfaces with specific distance. The design activates Fabry-Perot resonances, and coupling these modes with Mie resonances of silicon nano-cuboids causes a band-pass filtering effect with high-Q transmittance. One can tune these transmittances by changing the properties of the structures and tailor them for usage in many optical applications, such as sensing, narrow-band filters, and detectors.