Laser Threshold: Population Inversion
Four-level rate equations — gain vs loss, threshold behavior
dN₂/dt = R
p
− N₂/τ − g·φ·N₂ | dφ/dt = g·φ·N₂ − φ/τ
c
+ β·N₂/τ
Threshold: g·N₂
th
= 1/τ
c
| P
out
∝ (R
p
− R
th
) for R
p
> R
th
Pump rate R
p
(× R
th
) =
1.5
Cavity loss κ (ns⁻¹) =
1.0
Stimulated emission gain g =
2.0
Spontaneous emission β =
0.001
—
Threshold R
th
—
N₂ (ss)
—
Photon density φ