Symmetry analysis of trimer-based all-dielectric metasurfaces with toroidal dipole modes

Herein, we discuss the conditions for excitation of symmetry-protected toroidal dipole modes in all-dielectric metasurfaces composed of trimer or twin-trimer clusters of dielectric disks. Such metasurfaces permit enhanced light-matter interaction due to spatially confined light in resonant systems with a high-quality factor. To describe characteristics of toroidal modes existing in the clusters, we use the magnetic dipole moments approximation, group-theoretical methods, group representation theory, symmetry-adapted linear combination method, and circuit theory. To validate the obtained theoretical results, we fulfill both full-wave numerical simulations and microwave experiments. In particular, we have shown that the toroidal dipole mode appears as a quasi-dark state of the trimer. It can be excited in the metasurface by the field of a linearly polarized wave, providing the symmetry of the trimer is properly reduced. In the metasurface, the properties of the toroidal dipole mode are determined primarily by the parameters of a single trimer and are not a consequence of the periodicity of the array. The coupling of the toroidal dipole modes in the twin-trimers can appear in both bonding and anti-bonding fashion resulting in different orders of the net toroidal dipole moment. Due to the unique field configuration of these modes, the proposed metasurfaces can be considered as a platform for efficient light-matter interaction for enhanced absorption, nonlinear switching, and sensing.