Abstract
We study the multiple toroidal dipoles (TD) bound states in the continuum (BICs) in dielectric metasurfaces consisting of four square patches arranged in the unit cell of a square lattice. Symmetric-protected BICs occur at the Brillouin zone center, having extremely large quality factors and tiny linewidths. In particular, the BICs are identified as the electric (magnetic) TD modes characterized by the electric (magnetic) fields bent into a torus, with the magnetic (electric) fields circling around the surface. The TDs can be gathered in the unit cell to form the multiple TD modes, which are oriented normal or parallel to the metasurface. The multiple TD BIC appears at the polarization singularity in the momentum space, which carries an integer topological charge defined by the number of times the polarization vectors wind around the singularity. The multiple TD BICs can be trivial or nontrivial, depending on the sensibility of quality factors to the change of lattice period.
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