A short tutorial on optical rogue waves John M Dudley 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 Oceanic rogue waves Large ocean waves that appear in an otherwise calm sea • Large (~ 30 m) surface waves that represent statistical outliers • Measurements in 1990’s have established long-tailed statistics 1995 1945 1974 C. Kherif et al. Rogue Waves in the Ocean, Springer (2009) Rogue waves are large and unexpected The long tailed statistics reflects the unexpected nature of large waves The 2008 scientific context 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 birth of nonlinear fiber optics • Reliable techniques for fabricating small-core waveguides allows tailored linear guidance (dispersion) and controlled nonlinear interactions The link with light – extreme nonlinear propagation There was immediate interest and impact Pulsed lasers generate a frequency ruler or frequency comb An octave-spanning spectrum allows pump carrier-envelope phase and the comb position to be readily stabilized Example: precision spectroscopy Molecular fingerprinting S. Diddams et al. Nature 445, 627 (2007) Human breath analysis M. J. Thorpe et al. Opt. Express 16, 2387 (2008) Example: planetary discovery Periodic Doppler shift of stellar spectral lines is perturbed by planetary motion Who would have predicted this ? The link with light – extreme nonlinear propagation Numerical Model Noisy supercontinuum spectra are also interesting Modelling reveals that the supercontinuum can be highly unstable Stochastic simulations 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 J. M. Dudley, G. Genty, S. Coen, Rev. Mod. Phys. 78 1135 (2006) Experiments are always better than theory … Experiments reveal that these instabilities yield long-tailed statistics Stochastic simulations Time series Histogram Power Frequency Time Power These rare soliton events are optical rogue waves Experiments reveal that these instabilities yield long-tailed statistics Time series Histogram Power Frequency Time Power Origin of the optical-ocean analogy 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) A is surface elevation of wave group • Optical and water waves have same nonlinearity – speed depends on intensity Wave breaking imposes a limit Analogy is valid for moderate nonlinear strengths before wave breaking H < λ /7 Insight from the time-frequency domain The time-frequency domain allows convenient visualisation of complex wave envelope dynamics in optics Spectrogram / short-time Fourier Transform gate pulse variable delay gate pulse Gabor and the time-frequency domain J. IEE (London), 93(III):429-457 (1946) 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 Identical parameters except for different quantum noise 5 ps, 100 W peak power, typical supercontinuum with 1 µm zero dispersion fiber The NLSE admits other families of soliton Solitary Waves Pulses on a zero background Periodic Explode-Decay Solitons or Breathers Energy exchange between localised peaks and a background Experiments Optical technology enables experiments in “optical hydrodynamics” Where do the waves come from? Frequency The initial phase of propagation of an optical supercontinuum shows the appearance of these localized breather states Time Spectral structure agrees with theory The spectral wings seen in experiment correspond to the theoretical prediction for the shortest temporal pulses Specific forms of rogue waves can also be stimulated The Peregrine soliton is an explode-decay rogue wave prototype, measured in optics 20 years after its prediction in hydrodynamics Kibler et al. Nature Phys. 6 790 (2010) Hammani et al Opt. Lett. 36 112 (2011) New analysis of an old instability Wetzel et al. SPIE Newsroom (2011) Rogue Waves in a Water Tank Chabchoub et al. Phys. Rev. Lett. 106 204502 (2011) Raw data 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 in 2011 Optics Letters 36, 112 (2011) 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 Confirms Sears et al Phys. Rev. Lett. 84 1902 (2000) Erkintalo, Genty, Kibler et al. Phys Rev Lett 107 253901 (2011) Why is the control of optical rogue waves interesting? Essential Conclusions Optical fiber propagation shows noise properties qualitatively similar to those seen in the study of wave propagation on deep water 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 .