supercontinuum to soliton

8/10/2019 supercontinuum to soliton

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John DudleyUniversit de Franche-Comt, Insti tut FEMTO-ST

CNRS UMR 6174, Besanon, France

Supercontinuum to solitons:

extreme nonlinear structures in optics


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Goery Genty

Tampere Universi ty

of Technology

Tampere, Finland

Frderic Dias

ENS Cachan France

UCD Dublin, Ireland

Nail Akhmediev

Research School of

Physics & Engineering,

ANU , Australia

Bertrand Kibler,

Christophe Finot,

Guy Millo t

Universit de

Bourgogne, France

Supercontinuum to solitons:

extreme nonlinear structures in optics


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The analysis of nonlinear guided wave propagation in optics reveals featuresmore commonly associated with oceanographic extreme events

Challenges understand the dynamics of the specific events in optics

explore different classes of nonlinear localized wave

can studies in optics really provide insight into ocean waves?

Context and introduction

Emergence of strongly localized

nonlinear structures

Long tailed probability distributionsi.e. rare events with large impact


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1974

Extreme ocean waves

19451934

Drauper 1995

Rogue Waves are large (~ 30 m) oceanic surface waves that representstatistically-rare wave height outliers

Anecdotal evidence finally confirmed through measurements in the 1990s


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There is no one unique mechanism for ocean rogue wave formation

But an important link with optics is through the (focusing) nonlinear

Schrodinger equation that describes nonlinear localization and noise

amplification through modulation instability

Cubic nonlinearity associated with an intensity-dependent wave speed

- nonlinear dispersion relation for deep water waves

- consequence of nonlinear refractive index of glass in fibers

Extreme ocean waves

NLSE


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Ocean waves can be

one-dimensional over

long and short distances

We also see importance

of understanding wave

crossing effects

We are considering how muchcan in principle be contained

in a 1D NLSE model

(Extreme ocean waves)


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Rogue waves as solitons - supercontinuum generation


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Modeling the supercontinuum requires NLSE with additional terms

Essential physics = NLSE + perturbations

Supercontinuum physics

Linear dispersion SPM, FWM, RamanSelf-steepening

Three main processesSoliton ejection

Raman shift to long

Radiation shift to short


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Modeling the supercontinuum requires NLSE with additional terms

Essential physics = NLSE + perturbations

Supercontinuum physics

Linear dispersion SPM, FWM, RamanSelf-steepening

Three main processesSoliton ejection

Raman shift to long

Radiation shift to short


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With long (> 200 fs) pulses or noise, the supercontinuum exhibits dramaticshot-to-shot fluctuations underneath an apparently smooth spectrum

Spectral instabilities

835 nm, 150 fs 10 kW, 10 cm

Stochastic simulations

5 individual realisations (different noise seeds)

Successive pulses from a laser pulse train

generate significantly different spectra

Laser repetition rates are MHz - GHz

We measure an artificially smooth spectrum


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Spectral instabilities

Stochastic simulations

Schematic

Time Series

Histograms

Initial optical rogue wave paper detected these spectral fluctuations


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Dynamics of rogue and median events is different

Differences between median and rogue evolution dynamics are clearwhen one examines the propagation characteristics numerically


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Dynamics of rogue and median events is different

Dudley, Genty, Eggleton Opt. Express 16, 3644 (2008) ; Lafargue, Dudley et al. Electronics Lett. 45 217 (2009)

Erkinatalo, Genty, Dudley Eur. Phys J. ST 185 135 (2010)

Differences between median and rogue evolution dynamics are clearwhen one examines the propagation characteristics numerically

But the rogue events are only rogue in amplitude because of the filter

Deep water propagating solitons unlikely in the ocean


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More insight from the time-frequency domain

pulse

gate

pulse variable delay gate

Spectrogram / short-time Fourier Transform

Foing, Likforman, Joffre, Migus IEEE J Quant. Electron 28 , 2285 (1992) ; Linden, Giessen, Kuhl Phys Stat. Sol. B 206, 119 (1998)

Ultrafast processes are conveniently visualized in the time-frequency domain

We intuitively see the dynamicvariation in frequency with time


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More insight from the time-frequency domain

Ultrafast processes are conveniently visualized in the time-frequency domain

pulse

gate

pulse variable delay gate

Spectrogram / short-time Fourier Transform

Foing, Likforman, Joffre, Migus IEEE J Quant. Electron 28 , 2285 (1992) ; Linden, Giessen, Kuhl Phys Stat. Sol. B 206, 119 (1998)


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Median event spectrogram

Median Event


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Rogue event spectrogram


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The extreme frequency shifting of solitons unlikely to have oceanic equivalent

BUT ... dynamics of localization and collision is common to any NLSE system

What can we conclude?

MI


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Early stage localization

The initial stage of breakup arises from modulation instability (MI)

A periodic perturbation on a plane wave is amplified with nonlinear transfer ofenergy from the background

MI was later linked to exact dynamical breather solutions to the NLSE

Whitham, Bespalov-Talanov, Lighthill, Benjamin-Feir (1965-1969)

Akhmediev-Korneev Theor. Math. Phys 69 189 (1986)


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Experiments

Spontaneous MI is the initial phase of CW supercontinuum generation

1 ns pulses at 1064 nm with large anomalous GVD

allow the study of quasi-CW MI dynamics

Power-dependence of spectral structure illustratesthree main dynamical regimes

Spontaneous

MI sidebandsSupercontinuum

Intermediate

(breather) regime

Dudley et al Opt. Exp. 17, 21497-21508 (2009)


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Breather spectrum explains the log triangular wings seen in noise-induced MI

Comparing supercontinuum and analytic breather spectrum


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The Peregrine Soliton

Particular limit of the Akhmediev Breather in the limit of a 1/2

The breather breathes once, growing over a single growth-return cycle and

having maximum contrast between peak and background

Emergence from nowhere of a steep wave spike

Polynomial form1938

-2007


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Two closely spaced lasers generate a low amplitude beat signal that evolvesfollowing the expected analytic evolution

By adjusting the modulation frequency we can approach the Peregrine soliton

Under induced conditions we excite the Peregrine soliton


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Experiments can reach a = 0.45, and the key aspects of the Peregrine solitonare observed non zero background and phase jump in the wings

Temporal localisation

Nature Physics 6 , 790795 (2010) ; Optics Letters 36, 112-114 (2011)


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Spectral dynamics

Signal to noise ratio allows measurements of a large number of modes


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Collisions in the MI-phase can also lead to localized field enhancement

Such collisions lead to extended tails in the probability distributions

Controlled collision experiments suggest experimental observation may bepossible through enhanced dispersive wave radiation generation

Early-stage collisions

TimeDistance

Single breather

2 breather collisions

3 breather

collisions


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Other systems

Capillary rogue waves

Shats et al. PRL (2010)

Financial Rogue Waves

Yan Comm. Theor. Phys. (2010)

Matter rogue waves

Bludov et al. PRA (2010)Resonant freak microwaves

De Aguiar et al. PLA (2011)

Statistics of filamentation

Lushnikov et al. OL (2010)Optical turbulence in

a nonlinear optical cavity

Montina et al. PRL (2009)


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Analysis of nonlinear guided wave propagation in optics reveals features morecommonly associated with oceanographic extreme events

Solitons on the long wavelength edge of a supercontinuum have been termed

optical rogue waves but are unlikely to have an oceanographic counterpart

The soliton propagation dynamics nonetheless reveal the importance of

collisions, but can we identify the champion soliton in advance?

Studying the emergence of solitons from initial MI has led to a re-appreciation

of earlier studies of analytic breathers

Spontaneous spectra, Peregrine soliton, sideband evolution etc

Many links with other systems governed by NLSE dynamics

Conclusions and Challenges


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Tsunami vs Rogue Wave

Tsunami Rogue Wave


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Tsunami vs Rogue Wave

Tsunami Rogue Wave


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Real interdisciplinary interest


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Without cutting the fiber we can study the longitudinal localisation bychanging effective nonlinear length

Characterized in terms of the autocorrelation function

Longitudinal localisation


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Localisation properties can be readily examined in experiments as a

function of frequency a

Define localisation measures in terms of temporal width to period and

longitudinal width to period

Temporal

Longitudinal

determined numerically

More on localisation


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Localisation properties as a function of frequency a can be readily

examined in experiments



Temporal Spatial Spatio-temporal

Under induced conditions we enter Peregrine soliton regime


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Localisation properties as a function of frequency a can be readily

examined in experiments



Temporal Spatial Spatio-temporal

R d i d t i i t k l li ti

Under induced conditions we enter Peregrine soliton regime

supercontinuum to soliton

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