Recent developments around wave turbulence in nonlinear fiber optics Stéphane Randoux 1, Antonio...

Recent developments around wave turbulence

in nonlinear fiber optics

Stéphane Randoux1, Antonio Picozzi2, Pierre Suret1

1: Laboratoire de Physique des Lasers, Atomes et MoléculesUniversité de Lille 1, France

2: Institut Carnot de BourgogneUniversité de Bourgogne, Dijon, France

Wave turbulence in Optics

Introduction: Nonlinear optics with incoherent waves

One-dimensional (1D) optical wave turbulence

Conservative systems: Integrable wave systems (spectral broadening in optical fibers)Non-Integrable wave systems (anomalous thermalization,Supercontinuum generation)Optical wave condensation (liquid crystal)

Dissipative systems: Wave turbulence in highly multimode fiber lasers

Optical rogue waves Single-pass propagation in optical fibers (supercontinuum generation, fiber amplifier..)

Fiber lasers (connections with hydrodynamics? )

Two-dimensional (2D) optical wave turbulence

Optical wave condensation in graded-index fibers

Wave turbulence in Optics IntroductionWave turbulence in Optics

Historical viewpoint

Lasers 1960s

Nonlinear optics

2nd harmonic generation,

Stimulated Raman/Brillouin scattering …

Statistical Optics/Optical Coherence Theory

Linear Theory (degree of coherence of light)

Optical fibers 1970s

Nonlinear fiber optics Telecommunications applications(linear operation)Propagation of intense cw/pulsed

coherent light waves

Optical fibers 1995

Management of fiber dispersion

Supercontinuum generation

High power/highly multimode lasers

Incoherent nonlinear fiber optics


Incoherent nonlinear (fiber) optics Wave Turbulence (WT)

?

Use of WT theory for the understanding/description of some « standard » optical experiments (spectral broadening in fiber lasers, supercontinuum generation…)

Design of optical experiments to investigate problems from WT theory (optical wave condensation, cascades…)

Wave turbulence in Optics PEOPLEWave turbulence in Optics

Antonio PicozziDijon (France)

Theory

G. Millot, C. Finot, B. Kibler, J. Fatome

Dijon (France)Nonlinear fiber optics

Experiments

S. Randoux, P. SuretLille (France)

Fiber lasers, nonlinear fiber opticsExp/Theory

S. NazarenkoCoventry (UK)

Theory

S. Residori, U. BortolozzoNice (France)Liquid crystalExperiments

S. Turitsyn, D. ChurkinBirmingham (UK)

Fiber lasers, fiber telecommunication

Exp/Theory

S. Babin, E. PodivilovNovossibirsk (Russia)

Fiber lasersExp/theory


Hydrodynamics : Time (t) evolution of a signal/pattern

Incoherent wave Incoherent wave

Optics : Space (z) evolution of the incoherent wave

z t

˜ A (,zL)2

L

1D wave turbulence in single-mode fibers


Optical power spectra

~1 ps

A(t)2

Fiber core diameter 6-9µm

2D wave turbulence in multimode fibers

Fiber core diameter 30-100 µm

Absorption

Dispersion

Non linearity: Kerr, Raman

t

kk

kkk dtttzAtRtzA

t

ii

t

A

kiA

z

tzA'',',1

!2

),( 2

01

1


Nonlinear propagation of 1D waves in single_mode fibers

ZDW

Anomalous dispersion

Nomal dispersion

Fiber parameters (,,) are known withgood precision

Accurate numerical simulations of nonlinear propagation can

be easily performed

PCFs : the dispersion curve can be engineered


22

2

22 ,,

22

),(tzAAgtzAAi

t

AA

z

tzA

2nd order dispersion

Kerr Raman

Optical waves with narrow-bandwidth spectra

Nonlinear propagation of 1D waves in single_mode fibers

1

ATTL 202

1

DL PA

LNL 11

2

0 : Bandwidth of the optical spectrum

ATTDNL LLL In a lot of experiments :

NLLL 15and stimulated Raman scattering occurs when


Nonlinear fiber optics : how does it look like in real life?

Wave turbulence in Optics Spectral broadening in fibersWave turbulence in Optics

),(),(),(2

),(222 tztztztzi tz

Narrow-bandwidth (1nm) optical power spectrafar from zero dispersion wavelength (ZDW)

0),( znz WT theory : No change in the power spectrum of the optical wave !!

Wave turbulence in OpticsWave turbulence in Optics

),()(),(),( 1

2

2

2

112

1 tzAAAtzAtzAi tz ),()(),(),( 2

2

1

2

222

2 tzAAAtzAtzAi tz NLS equations (not integrable)

z n1(,z)1

2d1 G[J,n1]

1Kinetic equationKinetic equation

n1loc()J /2 1 (J /2)2 1 /local equilibrium spectrum

ANOMALOUS THERMALIZATION PHENOMENON

Suret et al, Phys. Rev. Lett. 104, 054101 (2010)

Non-Integrable 1D optical wave systems

Isotropic (spun) fiber1.6 meters

A1

A2

Wave turbulence in OpticsWave turbulence in Optics Non-Integrable 1D optical wave systems

B. Barviau, B. Kibler and A. PicozziPhys. Rev. A79, 063840 (2009)

Wave turbulence in OpticsWave turbulence in Optics Optical wave turbulence in 1D wave systems

U. Bortolozzo, J. Laurie, S. Nazarenko, and S. ResidoriOptical wave turbulence and the condensation of lightJ. Opt. Soc. Am. B, 26, 2280 (2009)

1D light propagation in a Liquid Crystal (LC) cell



WT treatment

5/1kNk

Intensity spectrum


Single mode optical fiber

Ytterbium

fiber laser

λs

λp

L~500 m

R~99% R~80%

Wavelength (nm)

FBG

rflectiv

ity

R1(λ)

R2(λ)

Opica

l pow

er

spectru

m

300 GHz

(iii)

Fibre Bragg Grating (FBG) mirrors

P. Suret and S. Randoux, Opt. Comm. 237, 201 (2004)

Cavity Free Spectral Range ~ 100 kHz

Laser linewidth ~ 100 GHz

~ 106 cavity modes

1100 nm 1160 nm

Raman fiber lasers

Wave turbulence theoryWave turbulence theory

Mean field approximation

FBGs mirrors parabolic losses in frequency space

2nd order dispersion from cavity fiber

Four-wave-mixing-induced turbulent spectral broadening in a long Raman fiber laser

S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, E. V. PodivilovJOSA B 24, 1729 (2007)


Numerical simulations (Mean field approximation)Numerical simulations (Mean field approximation)

Influence of the sign of 2nd order dispersion (2)

Turitsyna et al, Phys. Rev. A 80, 031804(R) (2010)

Formation of the optical power spectrum inRaman fiber lasers

Changes in the shape of the laser spectrum NOT described from WT theory

PCF

Diffraction grating

IR laser 200 fs

Source : University of Bath

Wave turbulence in Optics Optical rogue wavesWave turbulence in Optics

Supercontinuum generation in Photonic Crystal fibers

Pump

Supercontinuum

Wavelength (nm)Ref: Ranka etal, Opt. Lett 25, 25 (2000)


D. R. Solli, C. Ropers, P. Koonath, B. JalaliNature 450, 1054 (2007)

Rogue waves in optical supercontinuum


J. M. Dudley, G. Genty, and B. J. EggletonOptics Express 16, 3644 (2008)

Raman fiber amplifier: K. Hammani, C. Finot, J. M. Dudley, G. Millot; Opt. Express 16, 16467 (2008)

Parametric fiber amplifier: K. Hammani, C. Finot, G. Millot; Opt. Lett 34, 1138 (2009)

Rogue waves in optical supercontinuum


Granularity and inhomogeneity are joint generators of optical rogue wavesF. T. Arrechi, U. Bortolozzo, A. Montina, and S. ResidoriPhys. Rev. Lett. 106, 153901 (2011)

Optical rogue waves


Non gaussian statistics and extreme waves in a nonlinear optical cavityA. Montina, U. Bortolozzo, S. Residori and F. T. ArrechiPhys. Rev. Lett. 103, 173901 (2009)

Optical rogue waves


Narrow-bandwidthElectrical filter Central frequency : 6HzBandwidth : 1Hz

Extreme-type statistics in hydrodynamic experiments

P. Dennissenko, S. Lukaschuck, S. NazarenkoPhys. Rev. Lett. 99, 014501 (2007)

Wave turbulence in OpticsWave turbulence in Optics Extreme-type statistics in RamanFiber lasers

Slicing/Filtering of the intracavity Stokes spectrum in a Raman fiber laser

Single mode optical fiber

Ytterbium

fiber laser

λs

λp

L~500 m

R~99% R~80%

1100 nm 1160 nm

300 GHz Bandwidth of the optical filter: 5GHz

S. Randoux and P. Suret, Opt. Lett. 37, 500 (2012)


Raman fiber laser

Extreme-type statistics in RamanFiber lasers

Slicing/Filtering of the intracavity Stokes spectrum in a Raman fiber laser

Narrow-bandwidth optical filter

Optical power spectra transmitted bythe narrow-bandwidth (5GHz-2pm) optical filter


300 GHz

Extreme-type statistics in RamanFiber lasers


Dynamics and Statistics at the output of the narrow-bandwidth optical filter

Centeredfilter

Off-centeredfilter

Wave turbulence in OpticsWave turbulence in Optics Extreme-type statistics in RamanFiber lasers


Wave turbulence in OpticsWave turbulence in Optics Optical wave condensation

Dyachenko et. al, Physica Dyachenko et. al, Physica D (1992)D (1992)Connaughton et. al, PRL Connaughton et. al, PRL (2005)(2005)Düring et. al, Physica D Düring et. al, Physica D (2009)(2009)

kkxx kkyy

00 00

n(kn(kxx,k,kyy))

χχ(3)(3)

xx

yy

zz

kkxx kkyy

00 00

n(kn(kxx,k,kyy))

corecore

Optical claddingOptical cladding

n(r)n(r)

rr

nn00

nn11Core refractive index Core refractive index

cœurcœur


V(r)V(r)

rraa

VV00


Some theoretical works

-Condensation and thermalization of classical optical waves in a waveguideP. Aschieri, J. Garnier, C. Michel, V. Doya, and A. PicozziPhys. Rev. A 83, 033838 (2011)

-Wave turbulence in Bose-Einstein CondensatesY. Lvov, S. Nazarenko, R. WestPhysica D 184, 333 (2003)

But still an experimentalchallenge !!

Recent developments around wave turbulence

in nonlinear fiber optics

Stéphane Randoux1, Antonio Picozzi2, Pierre Suret1

1: Laboratoire de Physique des Lasers, Atomes et MoléculesUniversité de Lille 1, France

2: Institut Carnot de BourgogneUniversité de Bourgogne, Dijon, France

Recent developments around wave turbulence in nonlinear fiber optics Stéphane Randoux 1, Antonio...

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