A short tutorial on optical rogue waves
Institut FEMTO-ST CNRS-Université de Franche-Comté Besançon, France
Experiments in collaboration with the group of Guy Millot Institut Carnot de Bourgogne (ICB) CNRS-Université de Bourgogne, Dijon, France
John M Dudley
Large ocean waves that appear in an otherwise calm sea
• Large (~ 30 m) surface waves that represent statistical outliers
1974
1945
1995
• Measurements in 1990’s have established long-tailed statistics
C. Kharif et al. Rogue Waves in the Ocean, Springer (2009)
Oceanic rogue waves
The study of oceanic rogue waves was recognized as an important field of study, requiring new research into the ways propagating wave groups on the ocean surface can attain states of high localization Studying rogue waves in their natural environment is problematic A 2007 Nature paper made a bold proposal that analogous effects could in fact be observed in optical fiber waveguides
The 2008 scientific context
• Reliable techniques for fabricating small-core waveguides allows tailored linear guidance (dispersion) and controlled nonlinear interactions
The birth of nonlinear fiber optics
The link with light – extreme nonlinear propagation
The link with light – extreme nonlinear propagation
Numerical Model
Stable clocks
• Low noise supercontinuum generation allows the stabilisation of the carrier oscillations underneath a femtosecond laser pulse
• There is much interest in understanding these optical instabilities
History of Clocks
Deep water ocean wave groups and ultrashort envelopes in optical fibres are both described by the same propagation equation
• Ocean waves can be 1D over large scales
• Nonlinear Schrödinger equation (NLSE)
• Optical and water waves have same nonlinearity – speed depends on intensity
Origin of the optical-ocean analogy
A is surface elevation of wave group
Modelling reveals that the supercontinuum can be highly unstable
5 individual realisations, identical apart from quantum noise
Successive pulses from a laser pulse train generate significantly different spectra
We measure an artificially smooth spectrum, but the noise is still present
Stochastic simulations
J. M. Dudley, G. Genty, S. Coen, Rev. Mod. Phys. 78 1135 (2006)
Noisy supercontinuum spectra are also interesting
Experiments reveal that these instabilities yield long-tailed statistics
Stochastic simulations
Time series Histogram
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Experiments are always better than theory …
Time series Histogram
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These rare soliton events are optical rogue waves
Experiments reveal that these instabilities yield long-tailed statistics
Insight from the time-frequency domain
pulse
gate pulse variable delay gate
Spectrogram / short-time Fourier Transform
The time-frequency domain allows convenient visualisation of complex wave envelope dynamics in optics
Clarification of the rogue wave mechanism We see the emergence of localized soliton envelopes emerging from low amplitude noise on a longer input pulse
5 ps, 100 W peak power, typical supercontinuum with 1 µm zero dispersion fiber
Clarification of the rogue wave mechanism
5 ps, 100 W peak power, typical supercontinuum with 1 µm zero dispersion fiber
Identical parameters except for different quantum noise
Turbulence and « Champion Solitons »
Collisions and turbulence in optical rogue wave formation Phys. Lett. A 374 989-996 (2010)
Emergence of a champion
We have identified important links with turbulence theory
Rogue waves, rational solitons and wave turbulence theory Phys. Lett. A 375, 3149-3155 (2011)
What can we conclude? Inelastic collisions lead to the emergence of a “champion” soliton This clarifies the origin of the supercontinuum rogue waves Solitons can be observed on deep water but there have been no systematic observations in the natural environment The role of this class of soliton as an ocean rogue wave candidate remains an open question
Solitary Waves Periodic Explode-Decay Solitons or Breathers
The NLSE admits other families of soliton
Pulses on a zero background
Energy exchange between localised peaks and a background
What about the “emergence” phase?
The initial phase of propagation of an optical supercontinuum shows the appearance of these localized breather states
Spontaneous MI sidebands Supercontinuum Intermediate
(breather) regime
Analytic predictions for the spectrum are confirmed by experiments
Experimental confirmation of breather solutions
Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation Optics Express 17, 21497 (2009)
Optical technology enables experiments in “optical hydrodynamics”
Exciting the Peregrine Soliton
Optical technology enables experiments in “optical hydrodynamics”
The Peregrine soliton in nonlinear fibre optics Nature Physics 6 790 (2010)
The Peregrine soliton in a standard telecommunication fiber Optics Letters 36, 112 (2011)
Exciting the Peregrine Soliton
Optics in 2011
Raw data
The Peregrine soliton in nonlinear fibre optics Nature Physics 6 790 (2010)
The Peregrine soliton in a standard telecommunication fiber Optics Letters 36, 112 (2011)
Optics in 2011
Optical technology enables experiments in “optical hydrodynamics”
Rogue waves can split into self-similar replicas
Experiments
Erkintalo, Genty, Kibler et al. Phys Rev Lett 107 253901 (2011)
Rogue waves can split into self-similar replicas
Experiments
Erkintalo, Genty, Kibler et al. Phys Rev Lett 107 253901 (2011)
Confirms Sears et al Phys. Rev. Lett. 84 1902 (2000)
Essential Conclusions
Optical fiber propagation shows noise properties qualitatively similar to those seen in the study of wave propagation on deep water The “solitons” of the white light supercontinuum in optics may be present in deep water but there is not clear experimental evidence The coherent structures that can be excited from specific initial conditions such as the Peregrine soliton can be seen in optics and hydrodynamics The goals of MULTIWAVE are to explore this analogy in detail
