Optical Fiber Chromatic Dispersion — Pulse Broadening Simulator (2D)

Fiber, Pulse & Link 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

Bit rate 10 Gb/s

Live Readouts

Spectral width Δλ

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Output width Δt(L)

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Broadening factor

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Bit period T_b

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ISI severity @ L

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Max error-free L

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Regime at current L

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How it works

A pulse of finite duration Δt is never a single wavelength: the Fourier time–bandwidth limit forces it to carry a spectral width Δλ ≈ 0.441·λ²/(c·Δt). In a real fiber the group velocity depends on wavelength (chromatic dispersion, parameter D, ps/nm/km), so each spectral component drifts in time at a different rate as it travels distance L. The result is quantitative pulse broadening:

Spectral width (transform limit):  Δλ ≈ 0.441 · λ² / (c · Δt₀)
Pulse broadening (quadrature sum): Δt(L) = √( Δt₀² + (D·L·Δλ)² )
Bit period at rate B:              T_b = 1 / B

The pulse train (top of the canvas) shows the real, energy-conserving Gaussian intensity profile of every "1" bit at the current propagation distance z — peak power scales as Δt₀/Δt(z) so total pulse energy stays constant as it spreads.
Once Δt(z) grows past the bit period T_b, neighboring "1" bits visibly bleed into each other and into "0" slots — real inter-symbol interference (ISI).
The eye diagram (bottom of the canvas) overlays every 2·T_b window of the received waveform on one time axis, the standard way engineers judge a link: a wide open eye is decodable, a closed eye is not.
ISI severity = 1 − (eye opening at the decision instant, normalized to an undispersed pulse's peak power) — 0% is a fully open eye, 100% is fully closed.
Max error-free distance is root-found numerically (bisection on Δt(L)) for the distance where Δt(L) first exceeds a quarter of the bit period, Δt(L) = T_b/4 — a common conservative ISI design margin. Beyond it, dispersion (not attenuation) is what caps the link.
D > 0 (anomalous, typical of standard single-mode fiber above ~1310 nm) and D < 0 (normal dispersion) broaden a Gaussian pulse identically here, since only |D| enters the quadrature sum — sign matters for compensation techniques (Bragg gratings, DCF), not for this broadening magnitude.

Received optical power p(t) Bit-slot boundary Bottom panel: live eye diagram (2·T_b window)