Group Delay Dispersion Calculator

Analyze ultrafast pulse stretching by calculating dispersion over length and wavelength range. Choose fiber parameter or phase model, then download clear reports instantly here.

Calculator

Pick the parameterization you have available.
Total propagation length.
Second-order dispersion coefficient (sign matters).
ps/(nm·km)
Commonly used for telecom fibers near 1550 nm.
Used to convert D into β2.
Use this if you already have spectral phase curvature.
Enables a quick broadening estimate.
Reset Results appear above this form after submission.

Formula used

Group delay dispersion is the second derivative of spectral phase with respect to angular frequency: GDD = d²φ/dω².

For propagation in a uniform medium or fiber, the accumulated dispersion is: GDD = β2 · L, where β2 = d²β/dω² and L is length.

When using the dispersion parameter D (often in ps/(nm·km)): β2 = - (λ² / (2πc)) · D, with wavelength λ and speed of light c.

How to use

  1. Select the calculation mode that matches your available data.
  2. Enter length for β2 or D modes; use consistent units.
  3. Provide β2 directly, or enter D and wavelength to convert.
  4. Optionally enter pulse FWHM to estimate dispersion broadening.
  5. Click Compute, then download CSV or PDF for reporting.

Example data table

Case Mode Inputs Expected sign Typical magnitude
Telecom fiber D D = 17 ps/(nm·km), λ = 1550 nm, L = 10 km Negative β2, negative GDD ~ -2.2×103 ps²
Short fiber patch β2 β2 = -21.7 ps²/km, L = 2 m Negative ~ -4.34×10-2 ps²
Compressor setting Phase φ2 = -12000 fs² Negative ~ 104 fs²
Stretcher Phase φ2 = 1.2×106 fs² Positive ~ 106 fs²
Waveguide section β2 β2 = 0.08 fs²/mm, L = 50 mm Positive ~ 4 fs²

Values are illustrative; use your device specifications for accurate results.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.