Kerr Nonlinearity & Optical Bistability

Fabry-Pérot cavity with χ³ medium — input-output hysteresis & bistable switching

Cavity Transmission vs Input (S-curve)

Intracavity Field Dynamics

Phase Space (Field Amplitude)

Parameters & Theory

Lugiato-Lefever (steady state):
dE/dt = −(1+iΔ)E + i·n₂|E|²E + E_in
|E_out|² = κ|E|² (cavity transmission)
Bistability threshold:
Δ > √3: S-shaped curve, 3 steady states
Switches at fold bifurcations (saddle-node)
Intracavity |E|²
Output intensity
State
Phase shift n₂|E|²