High-Q resonant modes in a finite array of dielectric particles

We trace the $Q$ factor of the resonant modes which are limited to bound states in the continuum (BICs) for $N=\infty$ in the finite array of $N$ dielectric spheres and disks. For the symmetry-protected BICs we observe the quadratic dependence of the $Q$ factor on $N$ for high-refractive-index particles, while for low-refractive-index particles there is an interplay between the quadratic and cubic dependencies. The $Q$ factor of accidental BICs grows cubically with $N$. We show that a plane wave can excite these quasi-BICs for tuning of the angle of incidence.