Laser Cavity Threshold Lab (2D)

Pump & Gain

Pump rate (P) 0.0090

Cavity Mirrors

Rear mirror R₁ (HR) 99.90%

Output coupler R₂ 95.0%

Internal loss (α) 0.0050

Cavity length (L) 0.30 m

Live Readout

Round trips

Threshold pump P_th

–

Inversion n

0.00

Photon number φ

0.00

Status

Below threshold — spontaneous emission only

How it works

This is a real four-level laser rate-equation model, integrated with RK4, not a canned animation. Photons make round trips between a highly-reflective rear mirror (R₁) and a partially-transmissive output coupler (R₂), gaining energy each pass through a pumped gain medium and losing some each pass to mirror transmission and internal scattering/absorption (α):

dn/dt  = P − n/τ − g₀·n·φ/(1+φ/φsat)
dφ/dt  = g₀·n·φ/(1+φ/φsat) − γ·φ + β·n/τ

γ = −ln(R₁·R₂) + 2·α·L    (loss per round trip)
n_th = γ / g₀              (gain-clamped inversion)
P_th = n_th / τ            (lasing threshold pump rate)

Below threshold the inversion n rises roughly linearly with pump P while the photon number φ stays pinned near the small spontaneous-emission seed (β term). Once P crosses P_th, stimulated emission clamps n at n_th (gain = loss) and any extra pump instead drives φ up sharply — the classic lasing "kink" in the input–output curve. Raising R₂ or lowering α reduces γ and pulls the threshold down; a leakier cavity raises it.

Gain medium bar — brightness tracks inversion n relative to n_th.
Bouncing pulses — visual density and glow track photon number φ (log-compressed).
Graph — n(t) and φ(t) over the last few seconds, auto-scaled, with the threshold n_th marked.

Inversion n(t) Photons φ(t) Threshold n_th