---
title: "Microresonator Kerr Comb Interactive Lab | Sandbox Physics"
description: "When can a laser-driven microring keep a short pulse circling inside it?"
canonical_url: "https://sandboxphysics.com/labs/microresonator-kerr-comb/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/microresonator-kerr-comb/"
last_modified: "2026-10-28"
---

L34 · Driven nonlinear ring

# Microresonator Kerr Comb

**When can a laser-driven microring keep a short pulse circling inside it?** A pulse can persist when dispersion and the intensity-dependent phase shift balance, and a continuous pump replaces the energy lost each round trip. The pump frequency must also suit the heated cavity. A surviving prepared pulse does not guarantee that a frequency scan will form one.

Move the pump tuning dial and compare a surviving ring pulse with normal dispersion or no Kerr response. Inspect the captured envelope and comb spectrum.

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

The model is the normalized high-Q mean-field Lugiato–Lefever equation with a periodic boundary, second-order dispersion and an instantaneous scalar Kerr response. Negative dispersion is anomalous. Slow time is measured in field-decay times and detuning in field half-linewidths; detuning is positive when the pump sits below the cold resonance. A single thermal pole, chosen for teaching, lowers the resonance frequency: the effective detuning is the cold detuning minus the thermal shift, and the shift relaxes over ten field-decay times. The thermal coefficients are teaching values, not fitted to a material. The 100 GHz mode spacing only sets the fast-time scale, and normalized power is not in watts. The single and double presets deliberately insert approximate sech pulses on a continuous-wave background. The pattern and scan presets start instead from tiny, specified, repeatable perturbations, and a scan never inserts a pulse. Spectra are FFTs of the evolved complex field; no sech envelope is imposed on them. A peak count and a small instantaneous PDE residual are evidence of a localized stationary state, but they do not prove that the soliton is stable or that an experiment would be quiet. An ideal weak drop port samples the intracavity field with flat coupling; the plotted pump line is not a through-port interference measurement. Raman response, higher-order dispersion, avoided mode crossings, polarization, quantum noise and real heat diffusion are left out. The ring size and the intensity beads are schematic; the beads show the co-moving envelope, not photon paths. Before a record is shown, its spectral tails on the finite grid are checked.

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

## A comb emerges from one circulating field

**Background** A continuous pump can sustain localized pulses in a passive Kerr ring, with no population inversion needed.

**Why it matters** The pump never changes in time, yet the ring can hold a short pulse that keeps circling, which raises the question of what keeps it alive.

Start with the essentials

- **Focus question**: When can a pumped ring hold on to a localized pulse?
- **One-sentence intuition**: Dispersion and the Kerr phase shift shape the pulse; continuous pumping replaces the energy that leaks away.

### Core mathematical model

#### Mean-field equation around the ring

$$
\begin{aligned}\partial_\tau\psi={}&-(1+i\alpha_{\rm eff})\psi+F\\&+i\gamma|\psi|^2\psi-i\tfrac{\beta}{2}\partial_\theta^2\psi\end{aligned}
$$

In this sign convention, anomalous dispersion is negative. Because the field wraps around the ring, the equation follows many longitudinal modes and their interactions at once.

#### Single-pole heating model

$$
\begin{aligned}\dot H&=(\chi\langle|\psi|^2\rangle-H)/10\\\alpha_{\rm eff}&=\alpha_{\rm cold}-H\end{aligned}
$$

Heating lowers the resonance frequency. With the sign convention used here, that shrinks a positive, red detuning.

#### Steady continuous-wave response

$$
F^2=P\left[1+(\alpha_{\rm eff}-\gamma P)^2\right]
$$

At one pump level the response can take several values, and these give the possible backgrounds. The field around the ring still has to be evolved in full.

#### Growth of modulation sidebands

$$
\begin{aligned}\Omega_m&=-\alpha_{\rm eff}+2\gamma P+\tfrac12\beta m^2\\\lambda_m&=-1+\sqrt{(\gamma P)^2-\Omega_m^2}\end{aligned}
$$

When the growth rate has a positive real part, sidebands can grow out of the small specified perturbation.

#### An approximate starting pulse

$$
\begin{aligned}\psi&\simeq\psi_{\rm cw}+A\operatorname{sech}(b\theta)\\A&=\sqrt{2\alpha}\,e^{i\varphi}\\b&=\sqrt{2\alpha/|\beta|}\end{aligned}
$$

This shape only seeds the survival experiment. The solver then either sustains the pulse or destroys it.

#### The same field in time and frequency

$$
\begin{aligned}a_m&=\frac1{2\pi}\int_{-\pi}^{\pi}\psi e^{-im\theta}\,d\theta\\\sum_m|a_m|^2&=\langle|\psi|^2\rangle\end{aligned}
$$

Parseval's theorem ties the recorded pulse to its discrete spectrum: the comb is the Fourier transform of that same field.

### Common difficulties

#### A comb means a soliton

**Typical misconception** Any set of evenly spaced sidebands proves there is a quiet solitary pulse.

**Better mental model** Periodic patterns also produce combs. Look at the envelope in time, the residual and how the field evolves over a long run.

#### The prepared pulse formed by itself

**Typical misconception** The prepared pulse appeared on its own during the detuning scan.

**Better mental model** Prepared pulses only test survival. A scan starts from a slightly perturbed CW field and never inserts a pulse.

### Run the experiment

1. 01

   #### Test survival

   Compare Prepared single pulse and Prepared double pulse. Each selection integrates sixty decay times and captures the actual field.

   **What to observe:** Count the localized peaks, check that the residual stays small, and look at the Fourier spectrum computed from the field.

2. 02

   #### Take away what holds the pulse

   Repeat with normal dispersion, or with the Kerr strength set to zero.

   **What to observe:** The same starting pulse can decay into a continuous field.

3. 03

   #### Form a pulse by scanning

   Open Advanced controls, choose Blue-to-red scan start and use Scan to target & capture. Then vary the target, scan speed and heating.

   **What to observe:** The computed power history may show several pulses, steps, or the comb disappearing completely.

Physical conclusion

A prepared pulse that survives does not show that a scan will form one; test survival, formation and heating separately.

## Related experiments and articles

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 **Frequency combs measure both the spacing and the offset**](https://sandboxphysics.com/stories/probe-evidence/frequency-comb-self-reference/)
2. [Lab **Mode Locking** Watch random phases lock into one pulse](https://sandboxphysics.com/labs/mode-locking-frequency-comb/)
3. [Lab **Optical Frequency Comb** Check how a comb is calibrated](https://sandboxphysics.com/labs/optical-frequency-comb/)
4. [Lab **Nonlinear Frequency Conversion** See why the doubling crystal needs phase matching](https://sandboxphysics.com/labs/nonlinear-frequency-conversion/)

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)