dE/dt = [−κ + i(Δ − χ|E|²)] E + E_in
Optical bistability occurs when a nonlinear Kerr medium inside a Fabry-Pérot cavity produces an S-shaped input-output curve with two stable branches. As input intensity increases, the intracavity field shifts the resonance via the nonlinear refractive index n₂. The system switches abruptly between low and high transmission states — a photonic analog of a transistor. Hysteresis means the switch-up and switch-down thresholds differ. Applications: all-optical switches, optical memories, laser noise reduction, and squeezing. The critical point (cusp of the S-curve) is a pitchfork bifurcation.