Nonlinear bound states in the continuum of a one-dimensional photonic crystal slab

Optical bound state in the continuum (BIC) is characterized by infinitely high quality factor resulting in drastic enhancement of light-matter interaction phenomena. We study the optical response of a one-dimensional photonic crystal slab with Kerr focusing nonlinearity in the vicinity of BIC analytically and numerically. We predict a strong nonlinear response including multistable behaviour, self-tuning of BIC to the frequency of incident wave, and breaking of symmetry protected BIC. We show that all of these phenomena can be observed in silicon photonic structure at the pump power of several $\mu$W/cm$^2$. We also analyze the modulation instability of the obtained solutions and the effect of the finite size of the structure on the stability. Our findings have strong implications for nonlinear photonics and integrated optical circuits.