Robust bound state in the continuum in a nonlinear microcavity embedded in a photonic crystal waveguide.

We present a two-dimensional photonic crystal design of four defect dielectric rods, which form a microcavity with eigenfrequencies residing in the propagating band of a directional waveguide. In this system, a nonrobust bound state in the continuum (BSC) occurs as a result of full destructive interference of the monopole and quadrupole modes, with the same parity at certain values of the material parameters of the defect rods. Due to the Kerr effect, a robust BSC arises in a self-adaptive way without necessity to tune the material parameters. The absence of the superposition principle in that nonlinear system gives rise to coupling of the BSC with injected light, resulting in a novel transmission resonance.