Stretched pulse calculator

Stretched duration of a transform-limited Gaussian pulse for a given GDD, plus a converter between GDD (fs²) and dispersion (ps/nm).

Pulse stretching

Central wavelength λ₀

Spectral width Δλ (intensity FWHM)

Group delay dispersion (GDD)

Transform-limited duration τ₀: –
Stretched duration τ (exact): –
Stretched duration (large-stretch approx.): –
Stretch factor τ / τ₀: –

GDD ↔ ps/nm converter

Central wavelength λ₀

GDD

fs²

Dispersion D = dτ/dλ

ps/nm

Edit either box and the other updates. Sign convention: D = −2πc·GDD / λ₀², so positive GDD (normal dispersion, red leads blue) gives negative ps/nm. The magnitude is what sets the stretched duration.

Formulas and assumptions

τ₀ = 2 ln2 · λ₀² / (π c Δλ) ≈ 0.441 λ₀² / (c Δλ)

τ = τ₀ · √( 1 + (4 ln2 · GDD / τ₀²)² )

τ ≈ |GDD| · 2π c Δλ / λ₀² (τ ≫ τ₀)

D = dτ/dλ = −2π c · GDD / λ₀²

The input pulse is transform-limited with a Gaussian spectrum (time-bandwidth product 0.441).
Δλ and all durations are intensity FWHM. Mixing in amplitude or 1/e² widths causes factor-of-√2 and ln2 errors.
Only second-order dispersion is included. Third and higher orders, and nonlinear effects such as SPM, are ignored.
The ps/nm conversion is evaluated at the central wavelength and assumes GDD is constant across the bandwidth.
Constants: c = 299.792458 nm/fs.