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Harnessing and control of optical rogue waves in supercontinuum generation

John. M. Dudley, Goëry Genty, and Benjamin J. Eggleton

Open Access Open Access

Abstract

We present a numerical study of the evolution dynamics of “optical rogue waves”, statistically-rare extreme red-shifted soliton pulses arising from supercontinuum generation in photonic crystal fiber [D. R. Solli et al. Nature 450, 1054–1058 (2007)]. Our specific aim is to use nonlinear Schrödinger equation simulations to identify ways in which the rogue wave dynamics can be actively controlled, and we demonstrate that rogue wave generation can be enhanced by an order of magnitude through a small modulation across the input pulse envelope and effectively suppressed through the use of a sliding frequency filter.

©2008 Optical Society of America

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Figures (4)
Fig. 1.
Fig. 1. (a) Results showing 1000 individual spectra (gray curves). The mean spectrum is shown as the solid black line. (b) Expanded view above 1210 nm. (c) Histogram of the peak power frequency distribution using 25 W bins. We plot normalized frequency such that bar height represents the proportion of data in each bin. The inset plots the results on a log-log scale, and also shows the fitted Weibull distribution (solid line) [24].

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Fig. 2.
Fig. 2. Density plots of spectral and temporal evolution for: (a) a rare event leading to a rogue soliton (RS) and (b) a result close to the distribution median.

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Fig. 3.
Fig. 3. (a) MI gain curve and (b) density plot of output spectra with a 4% envelope modulation at the frequency indicated. Subfigures (i)–(iii) show spectra at the frequencies indicated.

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Fig. 4.
Fig. 4. Results for (a) an induced modulation at 5.8 THz and (b) a sliding frequency filter. The left panels show individual spectra (gray curves) and the corresponding mean spectrum (solid line) and the middle panels shows expanded views of the long wavelength edge. The right panels show the normalized frequency distribution of the peak power after spectral filtering with the insets plotting results on a log-log scale. These histograms should be compared with Fig. 1(c) to emphasize the relative rogue wave enhancement and suppression.

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Equations (1)

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∂ A ∂ z − ∑ k ≥ 2 i k + 1 k ! β k ∂ k A ∂ t k = i γ ( 1 + i τ shock ∂ ∂ t ) ( A ( z , t ) ∫ − ∞ + ∞ R ( t ′ ) ∣ A ( z , t − t ′ ) ∣ 2 d t ′ ) .
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