Bound states in the continuum and Fano resonances in the Dirac cone spectrum

We consider light scattering by two-dimensional arrays of high-index dielectric spheres arranged into a triangular lattice. It is demonstrated that in the case of a triple degeneracy of resonant leaky modes in the gamma point, the scattering spectra exhibit a complicated picture of Fano resonances with extremely narrow linewidth. The Fano features are explained through coupled-mode theory for a Dirac cone spectrum as a signature of optical bound states in the continuum (BIC). It is found that the standing wave in-gamma BIC induces a ring of off-gamma BICs due to different scaling laws for real and imaginary parts of the resonant eigenfrequencies in the Dirac cone spectrum. A quantitative theory of the spectra is proposed