Flat metasurfaces with square supercells of 2x2 dielectric disk quadrumers: tailoring the fine structure of toroidal mode local field

We suggest and investigate a new all-dielectric flat metasurface based on high-index dielectric disks. The unit cell of the metasurface is a quadrumer of the disks providing excitation of quasi-dark toroidal dipole resonances. Four quadrumers are grouped in a supercell with the highest possible geometrical symmetry C-4v . Using representation theory of groups and the symmetry adapted linear combination method, we show that in order to access the toroidal supermodes in the metasurface, one has firstly to break the symmetry of the quadrumer and then the symmetry of the unit supercell. We discuss also in detail different mechanisms of symmetry reduction. By reducing the unit supercell geometrical symmetry to the C-s group, the metasurface can provide resonances with both toroidal and antitoroidal order. Full-wave and eigenfrequency simulations confirm the theoretical predictions. Finally, we discuss possible applications of the analyzed structures.