Toroidal dipole bound states in the continuum

Toroidal multipole moments are usually underestimated as they are quite weak in most cases of light-matter interaction. Herein, we reveal a strong link between the toroidal dipole resonance and the bound state in the continuum in the context of all-dielectric metasurfaces. We introduce the concept of toroidal dipole bound states in the continuum, in which two eigenmodes of the silicon metasurface exhibit an intrinsic toroidal dipolar character and have an infinite lifetime. They can be classified as transverse (trivial) and longitudinal (nontrivial) toroidal dipole modes, which correspond to symmetry unprotected and protected bound states in the continuum, respectively. We demonstrate that such toroidal bound states in the continuum supported by the symmetry metasurface can be turned into ultrahigh-$Q$ resonances with a dominant toroidal dipole excitation, which validates their physical origin associated with the ultrahigh-$Q$ toroidal dipole leaky resonances. A full multipole decomposition with dispersive, lossy, and substrate effects further validates that the proposed concept is general and can also be generalized to other structures.