Transcript Rogue waves in laser systems

Crisis at the Origin of
Deterministic Rogue Waves
PPME, Universite de la Nouvelle Caledonie
C. Metayer, A. Serres, J. Tredicce
INLN, UMR 6618 UNS-CNRS France
S. Barland, M. Giudici
CEILAP - CITEDEF – Argentina
A. Hnilo, M. Kovalski
Univ. Politecn. Cataluna, Spain
Masoller, C.
Univ. Fed Pernambuco, Recife, PE Brazil
W. Barbosa, F. Menezes D’Aguiar,
J. Rios Leite, Rosero E.
 Are rogue waves just tales of fishermen into an
Irish Pub?
Or are rogue waves a common
feature of a complex dynamical
systems?
 This fact is in contradiction with the Gaussian models
used to describe fluctuations of the wave height in the
sea*.
* M. S. Longuet-Higgins, Phil. Trans. Roy. Soc. A 249
321 (1957).
S. Aberg and G. Lindgren, Height distribution of
stochastic Lagrange ocean waves, Prob. Eng. Mech.
23, 359 (2008)
HOWEVER……
Ferry rescue after freak wave in Irish
Sea
The freighter Riverdance was hit
by a giant wave during severe
gales in the Irish Sea…..
But….What is the definition of a
rogue wave?
 Old Recipe: Take the 1/3 biggest amplitude
waves; calculate their average value;
multiply by 2….whatever amplitude exceeds
such value is a rogue wave!!!
 Or another Recipe: Take the probability
distribution; calculate s ; multiply by 4;
whatever….;
and if you want a BIG BIG rogue
wave…multiply by 8
 In the WEB:
It is probably sufficient to say that
any wave so large that it is
unexpected based on current
conditions can be counted as a
rogue.
There are very few photographs of rogue
waves. For centuries, the best evidence for
their existence was anecdotal -- the countless
stories told by sailors who had survived one.
How was that “Opticians” got
interested on Rogue Waves?
 A “NONLINEAR OPTICS PHYSICIST” WENT TO
THE IRISH PUB….and then some papers appear
in Nature or other “GO..O..D” Journals
D. R. Solli, C. Ropers et al, Optical rogue waves,
Nature 450 1054 (2007).
B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G.
Genty, N. Akhmediev and J. M. Dudley, The
Peregrine soliton in nonlinear fibre optics Nature
Phys. 6, 790 (2010).
A. Montina, U. Bortolozzo, S. Residori, F.T. Arecchi,
Phys. Rev. Lett. 103, 173901 (2009)
For us, the story begins with..
 “Critical slowing down at a bifurcation” JRT,
Lippi ; Mandel; and B. Charasse ; A.
Chevalier; B. Picque: American Journal of
Physics Vol 72 Jun 2004
 Cited by a series of papers on Anticipating
Critical Transitions
Scheffer, M.et al. SCIENCE 338 (2012)
Dakos,V. et al. PLOS ONE 7 (2012)
Scheffer, M.; et al. NATURE 461 (2009)
Our Experiments o, ….
1) Mode Locked Ti:Sa laser
Hnilo et al. (Opt. Lett. November 2011)
2) Semiconductor Laser with Injected Signal
Bonatto et al. (PRL, July 2011); Zamora-Munt
et al. (PRA, March 2013).
3) Laser with saturable absorber Hnilo et al.
(Journal of Optics, June 2013).
Probability distribution of maxima
Our Already Published
Conclusions
 1) Extreme Events are rare but they can be
much more probable than in Gaussian
models when the dynamical behavior is
“Deterministically” Chaotic
 2) There is “chaos” without rogue waves and
chaos with rogue waves
Some questions:
 How? What is the dynamical process the
laser use to generate “extreme events”?
 Can we predict deterministic extreme events
in optical systems?
 Can we control them?
How?
a) Intermittency ….
P Gaspard and X Wang, PNAS 1988
Nicolis et al., Journal of Statistical physics 1995
b) By abrupt expansion of a chaotic attractor??
Bifurcation Diagrams
Experimental results
Laser with Modulated parameter
Remembering very old « times »:
H.G. Solari J, E. Eschenazi, R. Gilmore et al., Opt.
Commun. 64, 49 (1987)
on
“Crisis of chaotic attractors”
Two ingredients: 1) chaos
2) Enough low dissipation in order to have
“generalized” multistability (several stable
dynamical solutions for the same parameter
values)
Crisis of chaotic attractors
External crisis in a laser with
mopdulated parameter
Then extreme events appear
after an external crisis
Predicting “Rogue waves”?
In a deterministic system, the time of “prediction” equals the
inverse of the maximum positive Lyapunov exponent
But in the laser with injected signal, the prediction time is
much larger, and just looking one variable: the intensity
Conclusions
1) External crisis produce abrupt expansion of
chaotic attractors and are at the origin of
some extreme events
2) Deterministic extreme events could be
predicted with « some » anticipation
3) I still do not know if we are able to control
deterministic extreme events
BUT
I am always looking for the rogue
waves in New Caledonia