Ring of bound states in the continuum in the reciprocal space of a monolayer of high-contrast dielectric spheres

We consider light scattering by two-dimensional arrays of high-index dielectric spheres arranged into a triangular and square lattices. We demonstrate the appearance of the double degenerate accidental super-BIC modes with extremely suppressed radiative losses in the vicinity of the $\mathrm{\ensuremath{\Gamma}}$ point of the leaky band of the triangular lattice. Two rings of BICs (circular lines of BICs in reciprocal space) with different polarization appear at the point of the super-BIC destruction. The radius of the ring BIC (RBIC) changes as a function of the sphere's radius. We propose a generic analytical expression to describe the behavior of the guided mode decay rate as a function of the sphere radii and the wave vector in the vicinity of the RBIC. The results are explained using a multipolar approach.