Laser physics · stimulated emission

Laser Resonant Cavity

Which waves return between two mirrors and keep growing? Only modes that come back in phase after a round trip and gain more than they lose on the way. Matching the phase is not enough if the gain stays below threshold, and no amount of pumping helps a mode the cavity does not support.

Two mirrors pick out longitudinal modes, and a gain medium makes up the loss on each round trip. Change the cavity length, mirror reflectivity and pump, and watch the standing wave, round-trip phase, gain profile and allowed modes change together.

Nearest mode

m

Round-trip detuning0.00 rad

Threshold

g_{\mathrm{th}}L

1.00

Intracavity power0.0 a.u.

Cavity stateBuilding

Start with the essentials

Focus question: Why can a cavity that fits a whole number of half wavelengths still give no laser light, and why can strong pumping fail when the cavity is detuned?
One-sentence intuition: The phase condition asks which mode returns in phase; the threshold condition asks whether that mode grows or decays after each round trip. Both must hold.

Core mathematical model

Longitudinal modes

2L=m\lambda,\qquad \nu_m=\frac{mc}{2L}

The phase gained in one round trip must be a whole-number multiple of $2\pi$ . Neighboring modes are spaced by the free spectral range $c/(2L)$ .

Round-trip threshold

e^{2gL}R_1R_2\ge 1

Gain must make up for the mirror and intracavity losses, or the field shrinks on every round trip. Gain saturation then limits the steady power.

Common difficulties

Resonance is not laser oscillation

Typical misconceptionWhenever $2L=m\lambda$ , strong laser light must appear.

Better mental modelWithout enough population inversion, the cavity is only a passive Fabry-Perot filter and its field still decays.

A standing wave is not motionless light

Typical misconceptionBecause the pattern does not move along, no energy propagates.

Better mental modelThe standing pattern is made of two waves traveling in opposite directions. The output coupler still lets part of the energy out as a traveling laser beam.

Run the experiment

01
Look at threshold alone
Choose On resonance and slowly raise the pump from below 1 to above 1.
What to observe: The mode stays where it is, but the intracavity power builds up only after the pump crosses threshold.
02
Look at phase alone
Keep the pump above threshold and tune the cavity length continuously.
What to observe: Once the length no longer fits a whole number of half wavelengths, the round-trip phase stops matching and the power drops sharply.
03
Change reflectivity
Raise the mirror reflectivity and watch the resonance peak.
What to observe: Photons stay longer in the cavity and the field builds higher. The resonance also narrows, so a small detuning matters more.