All-dielectric metasurfaces with trapped modes: Group-theoretical description

Abstract

An all-dielectric metasurface featuring resonant conditions of the trapped mode excitation is considered. It is composed of a lattice of subwavelength particles which are made of a high-refractive-index dielectric material structured in the form of disks. Each particle within the lattice behaves as an individual dielectric resonator supporting a set of electric and magnetic modes. In order to access a trapped mode (which is the TE01δ mode of the resonator), a round eccentric penetrating hole is made in the disk. In the lattice, the disks are arranged into clusters (unit supercells) consisting of four particles. Different orientations of holes in the supercell correspond to different symmetry groups producing different electromagnetic responses of the overall metasurface when it is irradiated by the linearly polarized waves with normal incidence. We perform a systematic analysis of the electromagnetic response of the metasurface as well as conditions of the trapped mode excitation involving the group-theoretical description, the representation theory, and the microwave circuit theory. Both polarization-sensitive and polarization-insensitive arrangements of particles and conditions for dynamic ferromagnetic and antiferromagnetic orders are derived. Finally, we observe the trapped mode manifestation in the microwave experiment.