# All-dielectric metasurfaces with trapped modes: group-theoretical description

## TL;DR

This paper presents a group-theoretical analysis of all-dielectric metasurfaces with trapped modes, demonstrating how particle arrangement and symmetry influence electromagnetic responses and trapped mode excitation, validated by microwave experiments.

## Contribution

It introduces a systematic group-theoretical framework to analyze and design dielectric metasurfaces supporting trapped modes with controllable responses.

## Key findings

- Trapped modes can be excited using specific symmetry configurations.
- The electromagnetic response depends on particle orientation and symmetry group.
- Experimental validation confirms theoretical predictions.

## 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 (Mie-type) modes. In order to access a trapped mode (which is the TE01 mode of the resonator), a round eccentric penetrating hole is made in the disk. In the lattice, the disks are arranged into clusters (unit super-cells) consisting of four particles. Different orientations of holes in the super-cell correspond to different symmetry groups producing different electromagnetic response 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, representation theory and microwave circuit theory. Both polarization-sensitive and polarization-insensitive arrangements of particles and conditions for dynamic ferromagnetic and antiferromagnetic order are derived. Finally, we observe the trapped mode manifestation in the microwave experiment.