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

The work investigates a new kind of all-dielectric planar electromagnetic metamaterial made from periodic hexagonal arrays of dielectric disk trimers on a substrate. The authors focus on toroidal dipole resonances that are protected by symmetry. Using magnetic group theory and representation theory, the study derives conditions for when toroidal “supermodes” can be excited. It shows that the unit supercell symmetry must be reduced in two steps: first the trimer’s C3v symmetry, and then the unit supercell’s C6v symmetry. With the unit supercell reduced to C2v, the array supports a toroidal dipole resonance with an antitoroidic order; lower-symmetry cases can provide both toroidal and antitoroidal orders. The arrays are also reported to be polarization sensitive. The abstract states that full-wave simulations and experiments confirm the theoretical predictions, and that the resonant systems can enhance light-matter interaction with very high quality factors.