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Laser physics · stimulated emission

Laser Resonant Cavity

Two mirrors select longitudinal modes while a gain medium replaces round-trip loss. Standing wave, round-trip phase, gain profile, and allowed modes update together.

Interactive modelLaser Resonant Cavity
Nearest mode mm12
Round-trip detuning0.00 rad
Threshold gthLg_{\mathrm{th}}L1.00
Intracavity power0.0 a.u.
Cavity stateBuilding

Physics tutorial

Laser cavities: mode selection and threshold are different jobs

BackgroundA laser combines an optical gain medium with feedback. Mirrors send light repeatedly through the gain while preserving only frequencies whose round trips return with self-consistent phase.

Why it mattersStimulated emission only makes coherent photon copying possible. Narrow, directional, stable laser output additionally requires cavity mode selection and pump above threshold.

Start with the essentials

Focus question
Why can an integer half-wave cavity still produce no laser, while strong pumping can 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=mλ,νm=mc2L2L=m\lambda,\qquad \nu_m=\frac{mc}{2L}

A round trip must accumulate an integer 2π2\pi phase, and adjacent modes are separated by the free spectral range c/(2L)c/(2L).

Round-trip threshold

e2gLR1R2≥1e^{2gL}R_1R_2\ge 1

Gain must replace mirror and intracavity loss before the field stops decaying; saturation later limits steady power.

Common difficulties

Resonance is not laser oscillation

Typical misconceptionWhenever 2L=mλ2L=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 translate, no energy propagates.

Better mental modelOpposite traveling waves form the standing pattern, while the output coupler still releases a propagating laser beam.

Run the experiment

  1. 01

    Isolate threshold

    Choose On resonance and raise pump slowly through 1.

    What to observe: Mode position stays fixed, but intracavity power builds only after crossing threshold.
  2. 02

    Isolate phase

    Keep pump above threshold and tune cavity length continuously.

    What to observe: Leaving the integer half-wave condition causes round-trip phase mismatch and a sharp power drop.
  3. 03

    Change reflectivity

    Increase mirror reflectivity and inspect the resonance.

    What to observe: Photon lifetime and buildup rise, while the allowed resonance narrows and becomes more detuning-sensitive.