Toroidic and antitoroidic orders in hexagonal arrays of dielectric trimers: Magnetic group approach

Herein, we investigate the symmetry-protected toroidal dipole resonances and conditions of their excitation in a new type electromagnetic metamaterials. These metamaterials are all-dielectric planar periodic arrays dielectric disks disposed on substrate. The elementary building blocks array trimers which distributed hexagonal unit supercells. highest geometrical symmetry supercell is C6v. analysis fulfilled by using representation theory groups with application magnetic group theory, approach solving such problems. We have shown that to get access supermodes array, must be broken twice: firstly, C3v trimer, secondly, C6v needs reduced. Selection rules for symmetric antisymmetric orders moments defined. In particular, reduction C2v group, exhibits resonance an antitoroidic order. lower Cs can provide both toroidic orders. It also these always polarization sensitive. Full-wave simulations experiments confirm theoretical predictions. suggested enhanced light-matter interaction due spatially temporally confined light resonant systems very high quality factors.