# Crisis at the Origin of Deterministic Rogue Waves - PowerPoint PPT Presentation

Title: Crisis at the Origin of Deterministic Rogue Waves

1
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 DAguiar,
• J. Rios Leite, Rosero E.

2
• According to fishermen tales from a pub in
Ireland, rogue waves like solid walls of water,
higher than 30 meters, are more or less common
phenomena in deep ocean waters.

3
Is it true? Are rogue waves so common?
• 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

4
Ferry rescue after freak wave in Irish Sea
5
The freighter Riverdance was hit by a giant wave
during severe gales in the Irish Sea..
6
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!!!
• More Recent Recipe Take the probability
distribution calculate s multiply by 4
whatever.
• and if you want a BIG BIG rogue wavemultiply by
8

7
• In the WEBIt 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.

8
• Osborne, A.R. et al. Phys. Lett. A 275, 386
(2000) and PRL 96, 014503 (2006).
• Clauss, G.F. Appl. Ocean Res. 24, 147 (2002)
Dramas of the sea episodic waves and their
impact on offshore structures.
• Kharif, C. and Pelinovsky E. EJ of
Mechan.B/Fluids 22, 603 (2003).
• Petrova, P. and Guedes Soares C. Appl. Ocean
Res. 30, 144 (2008).
• Dyachenko, A. and Zakharov, V.E. JETP lett. 81,
255 (2005).

9
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)

10
Our First Experiments.
• 1) Mode Locked TiSa laser
• Hnilo et al. (Opt. Lett. November 2011)
• 2) Semiconductor Laser with Injected Signal
• Bonatto et al. (PRL, July 2011)
• 3) Laser with saturable absorber (Journal of
Optics, submitted)

11
Laser with Injected Signal
12
Probability distribution of maxima
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15
• 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

16
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?

17
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??

18
Bifurcation Diagrams
19
Experimental results
20
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)

21
Crisis of chaotic attractors
22
External crisis in a laser with mopdulated
parameter
23
Then extreme events appear after an external
crisis
24
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
25
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28
Conclusions
• External crisis produce abrupt expansion of
chaotic attractors and are at the origin of some
extreme events
• Deterministic extreme events could be predicted
with  some  anticipation
• I still do not know if we are able to control
deterministic extreme events
• BUT

29
I am always looking for the rogue waves in New
Caledonia
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Laser with saturable absorber in Q-switch regime
(to be subm. to special issue)
• With Alejandro Hnilo and Marcelo Kovalski,
• CEILAP, Villa Martelli, Argentina

53
Relevance of Spatial Effects
54
Theoretical results without spatial effects
55
Number of rogue waves in parameter space in LIS
(from J. Zamora)
56
Some bibliography to take into account
• V. Balakrishnan, C. Nicolis, and G. Nicolis
Extreme Value Distributions in Chaotic Dynamics
J. of Stat.Phys. 80, 307 1995
• C. Nicolis,V. Balakrishnan, and G. Nicolis
Extreme Events in Deterministic Dynamical
Systems PRL 97, 210602 (2006)
• P. Gaspard and X.J. Wang Sporadicity between
periodic and chaotic dynamical behaviors Proc.
Nat. Acad. Sci. USA 85, 4591 (1988).

57
Perspectives
• 1) Experiment of laser with modulation in solid
state laser (at CEILAP). Why solid state and not
semiconductor at INLN?
• 2) Experiments laser with injection large Fresnel
number (if INLN agree)
• 3) large fresnel number edge emitter lasers
(UFPE)
• 4) laser with feedback (UPC) theory
• 5) Numerical work at UNC

58
(No Transcript)
59
Conclusions
• Rogue waves appearsometimes very often!!!!
• Origin deterministic (at least in our
experiments)
• Different types of chaos without and with rogue
waves
• Simple models allow heuristic interpretation for
the generation of rogue waves

60
Université de Nice Sophia Antipolis - CNRS
I N L N
I hope you enjoyed the presentation
• If not, please .do not kill me!!
• If Yes,
• Thank you

61
Mode Locked TiSa Laser
. LB pump focusing lens R laser rod (L4mm)
M mirrors P1, 2 pair of fused silica prisms to
introduce negative GVD. The observations are done
with a fast photodiode (100 ps risetime) and a
350 MHz, 5 Gs/s digital oscilloscope with a
memory of 16 MB.
62
Results
63
Two chaotic regimes
P2
P1
64
Statistics of pulse amplitude
• (a) Experimental, regime P2, 2?AI394 9978
pulses, 237 are above the 2?AI value and 206 are
above the 4? value. Note the L-shape. Optical
rogue waves are hence observed.
• (b) Experimental, regime P1, 2?AI 417.6, 4?
256 3747 pulses, the highest one has amplitude
234? 2?AI and 4?.

65
Model based on a five dim. map
• (c) Numerical, regime P2, 2?AI 56.8 4? 3?104
pulses, 147 are above the 2?AI and 4?.
• (d) Numerical, regime P1, 2?AI 50.22, 4?
48.25 104 pulses, the highest one is 27

66
Theoretical results
(dE/dt) k ( 1 ia ) (N - 1)E I w E
Einj (dN/dt) g ( m N N E 2 )
67
About Physical Origin (PRA to be published)
68
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Crisis
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## Crisis at the Origin of Deterministic Rogue Waves

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Title: Crisis at the Origin of Deterministic Rogue Waves

1
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 DAguiar,
• J. Rios Leite, Rosero E.

2
• According to fishermen tales from a pub in
Ireland, rogue waves like solid walls of water,
higher than 30 meters, are more or less common
phenomena in deep ocean waters.

3
Is it true? Are rogue waves so common?
• 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

4
Ferry rescue after freak wave in Irish Sea
5
The freighter Riverdance was hit by a giant wave
during severe gales in the Irish Sea..
6
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!!!
• More Recent Recipe Take the probability
distribution calculate s multiply by 4
whatever.
• and if you want a BIG BIG rogue wavemultiply by
8

7
• In the WEBIt 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.

8
• Osborne, A.R. et al. Phys. Lett. A 275, 386
(2000) and PRL 96, 014503 (2006).
• Clauss, G.F. Appl. Ocean Res. 24, 147 (2002)
Dramas of the sea episodic waves and their
impact on offshore structures.
• Kharif, C. and Pelinovsky E. EJ of
Mechan.B/Fluids 22, 603 (2003).
• Petrova, P. and Guedes Soares C. Appl. Ocean
Res. 30, 144 (2008).
• Dyachenko, A. and Zakharov, V.E. JETP lett. 81,
255 (2005).

9
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)

10
Our First Experiments.
• 1) Mode Locked TiSa laser
• Hnilo et al. (Opt. Lett. November 2011)
• 2) Semiconductor Laser with Injected Signal
• Bonatto et al. (PRL, July 2011)
• 3) Laser with saturable absorber (Journal of
Optics, submitted)

11
Laser with Injected Signal
12
Probability distribution of maxima
13
(No Transcript)
14
(No Transcript)
15
• 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

16
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?

17
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??

18
Bifurcation Diagrams
19
Experimental results
20
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)

21
Crisis of chaotic attractors
22
External crisis in a laser with mopdulated
parameter
23
Then extreme events appear after an external
crisis
24
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
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
Conclusions
• External crisis produce abrupt expansion of
chaotic attractors and are at the origin of some
extreme events
• Deterministic extreme events could be predicted
with  some  anticipation
• I still do not know if we are able to control
deterministic extreme events
• BUT

29
I am always looking for the rogue waves in New
Caledonia
30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
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(No Transcript)
52
Laser with saturable absorber in Q-switch regime
(to be subm. to special issue)
• With Alejandro Hnilo and Marcelo Kovalski,
• CEILAP, Villa Martelli, Argentina

53
Relevance of Spatial Effects
54
Theoretical results without spatial effects
55
Number of rogue waves in parameter space in LIS
(from J. Zamora)
56
Some bibliography to take into account
• V. Balakrishnan, C. Nicolis, and G. Nicolis
Extreme Value Distributions in Chaotic Dynamics
J. of Stat.Phys. 80, 307 1995
• C. Nicolis,V. Balakrishnan, and G. Nicolis
Extreme Events in Deterministic Dynamical
Systems PRL 97, 210602 (2006)
• P. Gaspard and X.J. Wang Sporadicity between
periodic and chaotic dynamical behaviors Proc.
Nat. Acad. Sci. USA 85, 4591 (1988).

57
Perspectives
• 1) Experiment of laser with modulation in solid
state laser (at CEILAP). Why solid state and not
semiconductor at INLN?
• 2) Experiments laser with injection large Fresnel
number (if INLN agree)
• 3) large fresnel number edge emitter lasers
(UFPE)
• 4) laser with feedback (UPC) theory
• 5) Numerical work at UNC

58
(No Transcript)
59
Conclusions
• Rogue waves appearsometimes very often!!!!
• Origin deterministic (at least in our
experiments)
• Different types of chaos without and with rogue
waves
• Simple models allow heuristic interpretation for
the generation of rogue waves

60
Université de Nice Sophia Antipolis - CNRS
I N L N
I hope you enjoyed the presentation
• If not, please .do not kill me!!
• If Yes,
• Thank you

61
Mode Locked TiSa Laser
. LB pump focusing lens R laser rod (L4mm)
M mirrors P1, 2 pair of fused silica prisms to
introduce negative GVD. The observations are done
with a fast photodiode (100 ps risetime) and a
350 MHz, 5 Gs/s digital oscilloscope with a
memory of 16 MB.
62
Results
63
Two chaotic regimes
P2
P1
64
Statistics of pulse amplitude
• (a) Experimental, regime P2, 2?AI394 9978
pulses, 237 are above the 2?AI value and 206 are
above the 4? value. Note the L-shape. Optical
rogue waves are hence observed.
• (b) Experimental, regime P1, 2?AI 417.6, 4?
256 3747 pulses, the highest one has amplitude
234? 2?AI and 4?.

65
Model based on a five dim. map
• (c) Numerical, regime P2, 2?AI 56.8 4? 3?104
pulses, 147 are above the 2?AI and 4?.
• (d) Numerical, regime P1, 2?AI 50.22, 4?
48.25 104 pulses, the highest one is 27

66
Theoretical results
(dE/dt) k ( 1 ia ) (N - 1)E I w E
Einj (dN/dt) g ( m N N E 2 )
67
About Physical Origin (PRA to be published)
68
(No Transcript)
69
Crisis
70
(No Transcript)