Optical bistability with bound states in the continuum in dielectric gratings

We consider light scattering by dielectric gratings supporting optical bound states in the continuum. Due to the presence of instantaneous Kerr nonlinearity critical field enhancement in the spectral vicinity of the bound state triggers the effect of optical bistability. The onset of bistability is explained theoretically in the framework of the temporal coupled-mode theory. As the central result we cast the problem in the form of a single field-driven nonlinear oscillator. The theoretical results are verified in comparison with numerical simulations.