Optical Fiber Chromatic Dispersion — Pulse Broadening Simulator

Fiber & Pulse Parameters

Fiber length L 50 km

Dispersion parameter D 17.0 ps/nm·km

Input pulse width (FWHM) 10.0 ps

Carrier wavelength λ 1550 nm

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Output width T₁(L)

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Broadening T₁/T₀

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Dispersion length L_D

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GVD β₂

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Regime

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How it works

An optical pulse is never a single wavelength — a pulse of duration T has a spectral bandwidth Δλ ≈ 0.44λ²/(cT) set by the Fourier time–bandwidth limit. In a real fiber, the refractive index depends on wavelength, so each spectral component travels at a slightly different group velocity — group-velocity dispersion (GVD). Components that started overlapped in time drift apart as they propagate, stretching the pulse in time even though no energy is lost.

Group-velocity dispersion:  β₂ = − D·λ² / (2πc)   [ps²/km]
Dispersion length:          L_D = T₀² / |β₂|        [km]
Gaussian pulse broadening:  T₁(z) = T₀ · √(1 + (z/L_D)²)
Peak power (energy conserved): P₁ = P₀ / (T₁/T₀)

T₀ is the 1/e half-width, T₀ = T_FWHM / 1.6651.
D > 0 (anomalous dispersion, typical of standard single-mode fiber above ~1310 nm) — longer wavelengths travel faster. D < 0 (normal dispersion) — shorter wavelengths travel faster. At D = 0 (the zero-dispersion wavelength) a Gaussian pulse does not broaden to first order.
The particle cloud represents individual spectral components of the same pulse, each carrying a random frequency detuning Δω drawn from the pulse's own bandwidth; its accumulated timing offset at distance z is β₂·z·Δω, exactly the mechanism above. Its spreading radius reproduces T₁(z) numerically, not just qualitatively.
The translucent envelope traces T₁(z) analytically across the whole fiber, independent of where the animated pulse currently is.
This is the dominant pulse-spreading mechanism engineers combat with dispersion-compensating fiber and Bragg gratings in every long-haul telecom link.

Spectral component (color = wavelength offset) Fiber core Cone spread = accumulated timing spread, not physical space

Intensity vs. time

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