---
title: "Laser Noise Startup Workbench Interactive Lab | Sandbox Physics"
description: "Where does the first photon in a laser cavity come from? In an unseeded cavity, spontaneous emission can put the first photon into the selected mode."
canonical_url: "https://sandboxphysics.com/labs/laser-noise-startup/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/laser-noise-startup/"
last_modified: "2026-10-28"
---

L06 · Gain and feedback

# Laser Noise Startup Workbench

**Where does the first photon in a laser cavity come from?** In an unseeded cavity, spontaneous emission can put the first photon into the selected mode. If gain exceeds all cavity losses, stimulated emission amplifies that seed; depletion then limits its growth. An injected photon can provide a seed too.

Watch a recorded laser startup from random mode seeding. Move the output mirror, compare gain with loss, and seed an exact dark state with one photon.

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

This is a hybrid single-mode rate model: spontaneous photons arrive as Poisson events and seed a classical mean photon population. The effective four-level pump works in one direction only, and the lower laser level empties instantly. The model fixes one billion active emitters, a 2 cm gain length, 1064 nm photons and a spontaneous mode fraction of 0.00000001. The cross section and lifetime are illustrative values, not fitted to a material. Loss is the logarithmic attenuation over one round trip. Transverse effects, competing modes, optical phase and quantum photon statistics are left out, and the transport markers are schematic. Each selection acquires ten microseconds. Pumping and seeding switches retain stored excitation and integrate ten more microseconds; numerical parameters prepare a fresh run. Readouts describe the record end, while replay samples the retained trajectory without adding events. The gain rod and amber event symbol are enlarged; the flash marks an accepted time, not a localized emitter. Mirror separation follows the vacuum-equivalent length with a schematic scale. Logarithmic brightness and moving markers do not count photons; uncollected rear and internal losses are not drawn separately. Only the last eighty spontaneous event times are shown; the counter includes all accepted events. Green glow follows the recorded upper fraction.

Laser foundations · Light, gain and feedback

[L01 · Compare sources](https://sandboxphysics.com/labs/laser-source-comparison/) [L02 · Count transitions](https://sandboxphysics.com/labs/light-matter-transitions/) [L03 · Build inversion](https://sandboxphysics.com/labs/population-inversion/) [L04 · Amplify once](https://sandboxphysics.com/labs/single-pass-amplifier/) [L05 · Add feedback](https://sandboxphysics.com/labs/passive-optical-resonator/) [L06 · Start from noise](https://sandboxphysics.com/labs/laser-noise-startup/) [L07 · Build and debug](https://sandboxphysics.com/labs/build-debug-laser/) [L08 · Measure and diagnose](https://sandboxphysics.com/labs/laser-diagnostic-bench/) [L09 · Select axial modes](https://sandboxphysics.com/labs/gain-longitudinal-modes/) [L10 · Confine the beam](https://sandboxphysics.com/labs/stable-resonator-geometry/) [L11 · Select spatial modes](https://sandboxphysics.com/labs/transverse-laser-modes/) [L12 · Propagate and measure](https://sandboxphysics.com/labs/gaussian-beam-quality/) [L13 · Align and match](https://sandboxphysics.com/labs/alignment-mode-matching/) [L14 · Optimize extraction](https://sandboxphysics.com/labs/output-coupler-optimization/) [L15 · Drive the dynamics](https://sandboxphysics.com/labs/laser-dynamics-relaxation/) [L16 · Store and release](https://sandboxphysics.com/labs/q-switched-giant-pulse/) [L17 · Lock phases into pulses](https://sandboxphysics.com/labs/mode-locking-frequency-comb/) [L18 · Calibrate the comb](https://sandboxphysics.com/labs/optical-frequency-comb/) [L19 · Inject carriers](https://sandboxphysics.com/labs/semiconductor-laser-diode/) [L20 · Compare gain media](https://sandboxphysics.com/labs/laser-medium-zoo/) [L21 · Distributed gain](https://sandboxphysics.com/labs/fiber-fbg-laser/) [L22 · Choose feedback](https://sandboxphysics.com/labs/laser-feedback-architectures/) [L23 · Balance ultrafast pulses](https://sandboxphysics.com/labs/ti-sapphire-oscillator/) [L24 · Stretch and compress](https://sandboxphysics.com/labs/chirped-pulse-amplification/) [L25 · Trap and extract](https://sandboxphysics.com/labs/regenerative-multipass-amplifier/) [L26 · Convert frequencies](https://sandboxphysics.com/labs/nonlinear-frequency-conversion/) [L27 · Scatter and cascade](https://sandboxphysics.com/labs/raman-brillouin-lasers/) [L28 · Synchronize a slave](https://sandboxphysics.com/labs/injection-locking/) [L29 · Lock to a reference](https://sandboxphysics.com/labs/pdh-frequency-lock/) [L30 · Measure phase noise](https://sandboxphysics.com/labs/laser-linewidth-phase-noise/) [L31 · Scatter for feedback](https://sandboxphysics.com/labs/random-laser/) [L32 · Diagnose thermal scaling](https://sandboxphysics.com/labs/thermal-lensing/) [L33 · Combine coherent fields](https://sandboxphysics.com/labs/coherent-beam-combining/) [L34 · Sustain a Kerr pulse](https://sandboxphysics.com/labs/microresonator-kerr-comb/) [L35 · Return a delayed field](https://sandboxphysics.com/labs/external-feedback-chaos/) [L36 · Scan without mode hops](https://sandboxphysics.com/labs/tunable-laser-scan/)

Physical basis: [MIT: coherence and spectrum](https://ocw.mit.edu/courses/res-6-006-video-demonstrations-in-lasers-and-optics-spring-2008/resources/coherence-length-and-source-spectrum/) · [Rate equations](https://ocw.mit.edu/courses/6-977-ultrafast-optics-spring-2005/resources/chapter2/) · [Pumping and gain media (§7.2)](https://ocw.mit.edu/courses/6-974-fundamentals-of-photonics-quantum-electronics-spring-2006/bf3bdeb971819ddc9c68719d28bb2745_classnotes.pdf) · [Laser dynamics](https://ocw.mit.edu/courses/6-977-ultrafast-optics-spring-2005/resources/chapter4/)

Physics tutorial

## Let a mode grow from one random event

**Background** The pump stores energy in the upper laser level while the cavity keeps losing photons. A spontaneously emitted photon can land in the cavity mode; once gain beats loss, stimulated emission makes that mode grow.

**Why it matters** Because the cavity starts with almost no light, you can see how long the laser takes to turn on. Once the field grows, it drains the same stored excitation that supplied its gain.

Start with the essentials

- **Focus question**: If spontaneous emission into the mode is switched off, can a medium pumped above threshold stay exactly dark?
- **One-sentence intuition**: Gain above loss lets a seed grow; if the model omits seeding, an exactly zero photon population stays zero.

### Core mathematical model

#### Rate equations for stored excitation and cavity photons

$$
\begin{aligned}\dot n&=R(1-n)\\&\quad-\frac{n}{\tau_u}-\frac{GnS_c}{N_a}\\\dot S_c&=(Gn-\kappa)S_c\\&\quad+\frac{\beta N_a n}{\tau_u}\end{aligned}
$$

The first equation evolves the upper-state fraction; the second evolves the cavity photon population. There are one billion active emitters. Spontaneous mode seeds arrive as accepted Poisson events: each removes one excited emitter and adds one photon. Stimulated growth and losses are continuous averages.

#### Geometry, spectral overlap and loss

$$
\begin{aligned}G&=\frac{2\sigma_0N_a}{AT_R}\\&\quad\times\frac{1}{1+(\Delta\nu/\gamma)^2}\\\kappa&=-\frac{\ln R_b}{T_R}\\&\quad-\frac{\ln(1-T)}{T_R}\\&\quad-\frac{\ln(1-\ell)}{T_R}\end{aligned}
$$

In a linear cavity, light crosses the gain medium twice per round trip. The number of active emitters is fixed at one billion, so changing the mode area changes their density and their overlap with the photons. The round-trip time uses a vacuum-equivalent optical length.

#### Ideal zero-noise threshold

$$
\begin{aligned}n_{\mathrm{th}}&=\kappa/G\\n_0&=\frac{R\tau_u}{1+R\tau_u}\\R_{\mathrm{th}}&=\frac{n_{\mathrm{th}}}{\tau_u(1-n_{\mathrm{th}})}\end{aligned}
$$

If the required upper-level fraction is one or more, no finite pump rate reaches threshold. This is a zero-source steady-state reference. Finite seeding leaves a weak background below it; a single trajectory still contains discrete one-photon spontaneous jumps.

#### Gain clamping and envelope output

$$
\begin{aligned}n_{\mathrm{ss}}&\simeq n_{\mathrm{th}}\\\frac{\kappa S_{c,\mathrm{ss}}}{N_a}&\simeq R(1-n_{\mathrm{th}})\\&\quad-\frac{n_{\mathrm{th}}}{\tau_u}\\P_{\mathrm{out}}&=h\nu\kappa_{\mathrm{out}}S_c\end{aligned}
$$

The first two relations ignore the small spontaneous source above threshold. The output loss rate is the logarithmic attenuation at the output mirror divided by the round-trip time, and the displayed power is an average taken from the envelope.

### Common difficulties

#### Only the seeding is random

**Typical misconception** The photon-number trace is an exact quantum simulation that counts every photon.

**Better mental model** The spontaneous events in the mode are discrete, but stimulated growth and loss follow a classical envelope that stays positive. The model does not compute photon correlations, phase diffusion or linewidth.

#### Positive gain is not enough

**Typical misconception** Any positive inversion is enough to make the laser oscillate.

**Better mental model** The unsaturated gain has to beat all the losses in one trip around the cavity. Strong output coupling, internal loss or a mode far from the gain line can put threshold out of reach.

### Run the experiment

1. 01

   #### Tell noise from lasing

   Compare Below threshold and Above threshold. Each selection automatically acquires ten microseconds. Read the event count and the output, even when the light is weak.

   **What to observe:** Below threshold, spontaneous photons leak out of the cavity, but they never build a macroscopic population in the mode. Above threshold, the mode grows and uses up the stored inversion.

2. 02

   #### Start from exact darkness

   Choose Exact dark state, then use Inject one photon and evolve. The one-photon intermediate sample is retained before ten more microseconds are integrated.

   **What to observe:** With no noise source, a classical photon population of exactly zero stays at zero. One injected photon provides the missing seed.

3. 03

   #### Watch relaxation oscillations

   Choose Relaxation oscillation. Compare the acquired upper fraction with the loss threshold; Logarithmic photon trace in Advanced controls changes only the display scale.

   **What to observe:** Stored population, photon buildup and depletion produce an overshoot, followed by a damped exchange of energy between the atoms and the photons. Photon decay and upper-level recovery happen on different timescales.

4. 04

   #### Move the mode off the gain line

   Choose Above threshold and increase the mode offset. Return to Above threshold, switch Pump on off, and inspect the continued record.

   **What to observe:** Detuning reduces gain without changing mirror loss. Numerical parameters prepare a new run. Switching pumping or seeding keeps the stored state and integrates ten more microseconds, so the subsequent decay remains in the same record.

Physical conclusion

A random first photon, feedback from the mirrors and depletion of the stored excitation act together as one causal loop. The rate model covers startup and relaxation; it does not describe optical phase or competition between modes.

## Related experiments and articles

Continue exploring

### From a seed to laser light

Does a smooth startup curve describe what happens in every individual run?

1. [Lab **Laser Startup from Noise** Follow the mean start-up of many modes and see one win.](https://sandboxphysics.com/labs/laser-startup-from-noise/)
2. [You are here **Laser Noise Startup Workbench** Repeat stochastic seeding and inspect the recorded photon history.](https://sandboxphysics.com/labs/laser-noise-startup/)

Probes and measurement · Reading path

### Controlled light and precision measurement

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **How an ammonia beam became a microwave oscillator**](https://sandboxphysics.com/stories/probe-evidence/maser-inversion-and-feedback/)
2. [Lab **Absorption, Spontaneous & Stimulated Emission** Watch a probe beam grow, then fade, in a prepared gas](https://sandboxphysics.com/labs/absorption-spontaneous-stimulated-emission/)
3. [Lab **Pumping & Population Inversion** Pump three gases with one lamp and see which one amplifies](https://sandboxphysics.com/labs/pumping-population-inversion/)
4. [Lab **Passive Optical Resonator** Compare stored light with self-sustained oscillation](https://sandboxphysics.com/labs/passive-optical-resonator/)
5. [Lab **Stable Resonator & Transverse Modes** Curve two mirrors and size an iris until one beam shape is left](https://sandboxphysics.com/labs/stable-resonator-transverse-modes/)
6. [Lab **Build & Debug Your First Laser** Test gain against cavity loss](https://sandboxphysics.com/labs/build-debug-laser/)
7. [Lab **Laser Startup from Noise** Watch many cavity frequencies compete for one gain](https://sandboxphysics.com/labs/laser-startup-from-noise/)

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)