Tailoring Accidental Double Bound States in the Continuum in All-Dielectric Metasurfaces

Bound states in the continuum (BICs) have been thoroughly investigated due to their formally divergent Q-factor, especially those emerging in all-dielectric, nanostructured metasurfaces from symmetry protection at the Gamma point (in-plane wavevector k(||) = 0). Less attention has been paid to accidental BICs that may appear at any other k||not equal 0${k_{||}} \ne 0$ in the band structure of supported modes, being in turn difficult to predict. Here, a coupled electric/magnetic dipole model is used to determine analytical conditions for the emergence of accidental BICs, valid for any planar array of meta-atoms that can be described by dipolar resonances, which is the case of many nanostructures in the optical domain. This is explored for all-dielectric nanospheres through explicit analytical conditions that allow in turn to predict accidental BIC positions in the parameter space (omega, k(||)). Finally, such conditions are exploited to determine not only single, but also double (for both linear polarizations) accidental BICs occurring at the same position in the dispersion relation omega - k(||) for realistic semiconductor nanodisk meta-atoms. This might pave the way to a variety of BIC-enhanced light-matter interaction phenomena at the nanoscale such as lasing or nonlinear conversion, that benefit from emerging at wavevectors away from the Gamma point (off-normal incidence) overlapping for both linear polarizations.