  We consider light scattering by dielectric gratings supporting optical bound
states in the continuum. Due to the presence of instantaneous Kerr nonlinearity
the 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 into the form of a singly
field-driven nonlinear oscillator. The theoretical results are verified in
comparison against full-wave numerical simulations.
