Supercontinuum Generation in Photonic-Crystal Fiber

Pump Pulse & Fiber

Soliton order N 3.5

Third-order dispersion δ₃ 0.020

Pulse duration T₀ (fs) 50

Propagation

Distance ξ = z / L_D 0.00

Live Readouts

Spectral width Δλ

0 nm

Peak power (norm.)

1.00

Physical distance z

0.0 mm

Soliton order N

3.5

Output Spectrum |û(Ω)|²

How it works

A short pump pulse launched into a photonic-crystal fiber's tiny (≈2 μm) silica core experiences both group-velocity dispersion (GVD) and an intensity-dependent Kerr nonlinearity. In normalized retarded time τ = t/T₀ and distance ξ = z/L_D (with L_D = T₀²/|β₂|), the pulse envelope u(ξ,τ) obeys a generalized nonlinear Schrödinger equation:

∂u/∂ξ = i/2 ∂²u/∂τ² − δ₃ ∂³u/∂τ³ + i N² |u|² u

N² = γ P₀ T₀² / |β₂|     (soliton order)
δ₃  = β₃ / (6 T₀ |β₂|)    (third-order dispersion)

This simulator solves that equation numerically with the split-step Fourier method: alternate a nonlinear phase kick in the time domain with a dispersive phase rotation applied to the FFT of the field, once per propagation step.

N (soliton order) — for integer N>1 in an ideal (δ₃=0) fiber, the pulse is a higher-order soliton that breathes periodically without changing shape. Real photonic-crystal fibers always carry some higher-order dispersion, which breaks that periodicity.
δ₃ (third-order dispersion) — triggers soliton fission: the higher-order soliton splits into N individual fundamental solitons of different amplitude and width, each red-shifting via the Raman-like group-velocity walk-off encoded here, plus a blue-shifted dispersive wave. Their spectra spread out and overlap into a broadband supercontinuum.
ξ (propagation distance) — scrub or press Play to watch the spectrum widen from a narrow pump line into a continuum as ξ increases; bar color encodes each time slice's local instantaneous frequency (chirp).
T₀ (pulse duration) — only rescales the physical distance readout (via a fixed representative PCF dispersion β₂ = −11 fs²/mm near an 800 nm Ti:sapphire pump); shorter pulses need a physically shorter fiber to reach the same normalized ξ.

Real-world relevance: this is the mechanism (Ranka et al. 2000; reviewed by Dudley, Genty & Coen, Rev. Mod. Phys. 2006) that makes photonic-crystal fiber supercontinuum sources — octave-spanning white light from a single near-IR laser — the workhorse light source for optical coherence tomography, frequency combs and hyperspectral microscopy.

Pulse envelope |u(τ)|² Bar hue = instantaneous frequency

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