---
title: "Chirped Pulse Amplification Interactive Lab | Sandbox Physics"
description: "Can a short pulse be amplified without its peak power getting dangerously high? It can, if you stretch the pulse first."
canonical_url: "https://sandboxphysics.com/labs/chirped-pulse-amplification/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/chirped-pulse-amplification/"
last_modified: "2026-10-28"
---

L24 · Stretch, amplify, compress

# Chirped Pulse Amplification

**Can a short pulse be amplified without its peak power getting dangerously high?** It can, if you stretch the pulse first. Dispersion spreads it out in time: same energy, much lower peak power. The amplifier can then add energy without the peak getting dangerously high, and a compressor afterwards undoes the stretch to give back a short, intense pulse.

Follow one complex pulse through four probe planes as it is stretched, amplified and compressed. Record its energy and peak power, then spoil the compression with leftover dispersion or a narrow spectral acceptance.

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

A scalar 800-nanometre Gaussian seed passes through an ideal phase-only stretcher, a broadband Frantz–Nodvik saturated-gain map, a gain-weighted Gaussian spectral acceptance filter, an effective nonlinear plate and a phase-only compressor. The spectral acceptance is a separate lossy step that stands in for gain narrowing; it is not a joint frequency-dependent inversion or Maxwell–Bloch solution. Rejected energy is reported separately. The amplifier uses the cumulative pulse energy and a saturation energy and initial log gain that you set; the pump does not replenish the gain during the pulse. A uniform beam area converts energy and power into fluence and intensity. Changing the area keeps the saturation energy fixed, so it does not model a fixed material cross-section. The effective plate at the output plane has a one-centimetre path and an illustrative nonlinear index; its phase is not the nonlinear phase integrated through the real gain medium. Turning the plate off gives a linear comparison. Damage thresholds, thermal fracture, ASE, compressor throughput, diffraction and spatial hot spots are not simulated. Stretching keeps the incident energy and fluence while lowering the peak power; it does not guarantee that a real optic escapes damage. The 32768-point Fourier grid spans 65.536 picoseconds with two-femtosecond spacing. Edge fractions show when the pulse is cut off in time or strains the frequency grid. The main-peak FWHM does not capture all the satellite pulses. Capturing the four planes copies the computed fields; it is not hardware detector data. The dashed output curve is an ideal pulse with zero spectral phase built from the output spectrum, not a reconstruction of the captured pulse. The dispersive blocks are schematic and do not trace rays through grating angles.

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

## Carry energy through a lower peak

**Background** Chirped pulse amplification stretches a short pulse, amplifies it and compresses it again. Here one complex pulse goes through every step, and a probe can look at it at a physical plane after each one.

**Why it matters** Because every step acts on the same complex pulse and each one can be checked at a physical plane, you can see where the peak drops, where the energy grows and where the phase is removed.

Start with the essentials

- **Focus question**: Can a short pulse be amplified without its peak power getting dangerously high?
- **One-sentence intuition**: Stretching lowers the peak intensity, amplification adds energy, and compression removes the spectral phase again.

### Core mathematical model

#### Phase-only stretching

$$
\widetilde A_s(\Omega)=\widetilde A_0(\Omega)\exp(-i\phi_{2,s}\Omega^2/2)
$$

The Fourier transform uses a negative exponent, and the carrier uses the positive sign convention. With positive group-delay dispersion, frequencies above the carrier arrive later.

#### Analytic stretching of a Gaussian pulse

$$
\tau_s=\tau_0\sqrt{1+\left(\frac{4\ln 2\,\phi_{2,s}}{\tau_0^2}\right)^2}
$$

The Lab checks the propagated field against this analytic intensity FWHM. Stretching leaves the energy and the spectral magnitude unchanged.

#### Broadband saturated amplification

$$
E_{\rm out}(t)=E_s\ln\!\left[1+e^{g_0}\left(e^{E_{\rm in}(t)/E_s}-1\right)\right]
$$

The Frantz–Nodvik map is applied to each time bin using the energy that has already passed. The energy taken from the initial reservoir can never exceed the saturation energy times the log gain.

#### Spectral acceptance filter

$$
\widetilde A_a\longmapsto\widetilde A_a\exp\!\left[-2g_0\ln 2\left(\frac{\nu}{B}\right)^2\right]
$$

This lossy step narrows the spectrum that gets through. It stands in for gain narrowing as a separate step in the chain and does not resolve inversion depletion by frequency. The rejected energy is reported.

#### Compression and residual phase

$$
\begin{aligned}\phi_{2,c}&=-\phi_{2,s}+\Delta\phi_2\\ \widetilde A_c&=\widetilde A_a\exp\!\left[-i\left(\frac{\phi_{2,c}\Omega^2}{2}+\frac{\phi_3\Omega^3}{6}\right)\right]\end{aligned}
$$

Cancelling the second-order dispersion leaves any third-order or nonlinear phase in place, and it cannot bring back spectral energy that was already rejected.

#### Peak intensity is different from fluence

$$
\begin{aligned}F&=E/A\\ I_{\rm peak}&=P_{\rm peak}/A\\ B_{\rm plate}&=\eta_{\rm NL}\frac{2\pi n_2L}{\lambda_0}I_{\rm peak}\end{aligned}
$$

Stretching lowers the peak intensity but not the incident fluence. The phase in the effective plate is a teaching diagnostic: it does not certify that an optic survives, and it is not integrated along the amplifier path.

### Common difficulties

#### A short main peak is not the whole story

**Typical misconception** If the main peak is short, the pulse must be good.

**Better mental model** Also check the satellite pulses, the RMS duration, the energy near the edges of the numerical grid and the separate ideal reference.

### Run the experiment

1. 01

   #### Record every plane

   Choose Matched CPA and move Physical probe plane through the four positions. All four fields are recorded automatically.

   **What to observe:** The stretcher and the compressor each pass on all the energy they receive.

2. 02

   #### Skip the stretcher

   Compare the Matched CPA and Bypass stretcher presets.

   **What to observe:** The amplifier holds about the same stored energy in both cases, but the peak intensity and the plate phase are very different.

3. 03

   #### Spoil the compression

   Drag the compressor dial, then compare Dispersion mismatch, Cubic phase and Narrow acceptance. Check the short output pulse against its dashed ideal reference below.

   **What to observe:** Cancelling one order of dispersion is not enough to restore the pulse fully.

Physical conclusion

Check the recorded field and its spectrum, and know where the model's approximations stop holding.

## 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 **Chirped pulse amplification separates energy gain from peak power**](https://sandboxphysics.com/stories/probe-evidence/cpa-stretch-amplify-compress/)
2. [Lab **Nonlinear Light Shapes Its Own Medium** Watch a beam write its own waveguide](https://sandboxphysics.com/labs/nonlinear-light-shapes-its-own-medium/)
3. [Lab **Q-Switched Giant Pulse** Store energy in the gain medium before a burst](https://sandboxphysics.com/labs/q-switched-giant-pulse/)

Probes and measurement · Reading path

### Molecules, forces and ultrafast dynamics

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

1. [Article **Attosecond pulses: how electrons timed the shortest flashes of light**](https://sandboxphysics.com/stories/probe-evidence/attosecond-pulses-and-metrology/)
2. [Lab **Attosecond RABBIT Metrology** Retrieve pulse-train phases with RABBIT](https://sandboxphysics.com/labs/attosecond-rabbitt-metrology/)

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)