Anapole mechanism of bound states in the continuum in symmetric dielectric metasurfaces

We present a general multipole mechanism based on the lattice anapole effect leading to the excitation of high-$Q$ resonances in dielectric metasurfaces with the simplest unit cell (i.e., a unit cell with inversion symmetry containing only one nanostructure) and irradiation conditions (i.e., normal incidence). Using multipole techniques, we show analytically and numerically that these resonances are related to the conversion of bound states in the continuum (BICs) to quasi-BICs by simply changing the metasurface period. It is also shown that BICs and quasi-BICs, in turn, are realized through destructive interference (anapole effect) between multipoles of the same parity. The main advantage of such a conversion BIC to quasi-BIC compared to those proposed earlier is that it does not require distortion of symmetric properties of metasurfaces, special conditions of irradiation, or displacement of elements in composite unit cells. The results obtained give an important insight into the physics of high-$Q$ resonances in meta-optics and can simplify and expand the application of metasurfaces for tunable lasing, nonlinear generation, energy trapping manipulation, and enhanced sensing techniques.