Optical cavity transmission — linear and nonlinear (thermal / free-carrier) coupled-mode simulator

Temporal coupled-mode theory with an intensity-dependent cavity frequency ω_c(|a|²). All rates in consistent arbitrary units; |a|² = intracavity photon number, |α_in|² = P_in/ħω_l = input photon flux.

Configuration

One port Two ports

Fabry–Pérot Ring

Rates

κ_i intrinsic loss

κ_e (κ_e1) external coupling, port 1

κ_e2 external coupling, port 2

Drive & nonlinearity

|α_in|² input photon flux

Nonlinear effect

Power law

g nonlinear coefficient

τ response time (thermal/carrier)

Laser sweep

Laser detuning Δ = ω_l − ω_c⁽⁰⁾ (drag)

Sweep rate dω_l/dt

Animation: seconds per sweep

Auto range to

Wavelength-like axis (red on the right)

The laser moves at the finite rate dω_l/dt and the full CMT equations are integrated in time, so the field relaxes onto whichever stable branch it is on and jumps only when that branch ends. Adiabatic following requires (dω_l/dt)·τ ≪ κ and dω_l/dt ≪ κ².

Cavity

cold resonance ω_c⁽⁰⁾hot resonance ω_c(|a|²)laser ω_l

Model

Intracavity photon number |a|² vs laser detuning

stable steady state unstable steady state linear (cold) cavity sweep toward red (ω_l ↓) sweep toward blue (ω_l ↑) current state

Output

Graphical solution at the current Δ

|α_in|² required, slope > 0 (stable) slope < 0 (unstable) actual |α_in|²