---
title: "How a Laser Builds inside a Cavity Interactive Lab | Sandbox Physics"
description: "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."
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last_modified: "2026-10-27"
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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.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Resonance decides which frequencies remain in the cavity; threshold decides whether those modes grow. Satisfying one condition alone does not guarantee stable laser output.

Physics tutorial

## Laser cavities: mode selection and threshold are different jobs

**Background** A laser needs two things: a gain medium and optical feedback. Two mirrors send light back and forth through the gain medium, and only frequencies that return in phase after a round trip keep adding up.

**Why it matters** Stimulated emission only makes it possible to copy photons coherently. To get a narrow, directional, stable laser beam, the cavity must also select a mode and the pump must exceed threshold.

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 misconception** Whenever $2L=m\lambda$, strong laser light must appear.

**Better mental model** Without 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 misconception** Because the pattern does not move along, no energy propagates.

**Better mental model** The 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

1. 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.

2. 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.

3. 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.

Physical conclusion

Always ask two separate questions: which cavity modes are allowed, and which mode has net round-trip gain above one?

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)