Presets
Playback
Pulse, beam and chain
Compressed-pulse energy, duration, beam radius and repetition rate give the same peak power, fluence, intensity and average power as the 3D page. The stretcher lengthens the pulse so the amplifier sees a much lower intensity and a small nonlinear phase.
Model checks
The science
What is modelled
Chirped-pulse amplification stretches a short pulse in time with a dispersive grating pair, amplifies it while its peak intensity is low, and recompresses it with the opposite dispersion. The page computes the beam relations of the 3D page, a dispersion-based stretch, the energy gain of a saturating amplifier and the nonlinear phase (B-integral) that limits how intense the stretched pulse may be.
Equations
P = E/τ,F = E/(π r²),I = P/A = F/τ,Pavg = E f.- Gaussian stretch:
τout = τ √(1 + (4 ln2 · GDD/τ²)²). - Frantz-Nodvik:
Fout = Fsat ln[1 + G0(eFin/Fsat - 1)]. - B-integral:
B = (2π/λ) n2 I L.
Checks run in the page
- The beam relations computed by two routes.
- A numerical FFT stretch against the closed form.
- Recompression with the opposite GDD.
- RK4 gain saturation against the Frantz-Nodvik formula.
Honest simplifications
Gaussian pulses with a pure quadratic spectral phase (no higher-order dispersion), one amplifier crystal with a single small-signal gain standing in for several passes, a uniform circular beam, a constant illustrative damage fluence and Ti:sapphire-like constants, and no gain narrowing, pump depletion or thermal effects. The check FFT uses a scaled-down stretch factor so it fits its time grid. An educational model, not a laser design.
What to try
- Press Weak stretch (50 ps) and compare its B-integral with the default 400 ps.
- Press Small beam: the fluence bar goes past the damage limit.
- Raise the seed energy and see how the required small-signal gain drops.