Abstract

Rogue waves, which were first described as an oceanographic phenomenon, constitute an important factor in the dynamics of many physical systems. Most of these systems were analyzed by scalar fields, while some of them, and specifically in optics, are described by a vector field. Thus, they differ from scalar systems in several crucial aspects. In this work, we study experimentally twin-peak rogue waves with a temporal imaging system capable of measuring the Stokes vectors as a function of time. We found that the two peaks in optical twin-peak rogue waves have orthogonal states of polarization and similar intensities. We observed this with two different systems, however, we do not have a theoretical explanation for this phenomena and could not explain it with current models.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  6. P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Phys. Rev. Lett. 97(9), 094501 (2006).
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  7. A. Toffoli, E. Bitner-Gregersen, A. R. Osborne, M. Serio, J. Monbaliu, and M. Onorato, “Extreme waves in random crossing seas: Laboratory experiments and numerical simulations,” Geophys. Res. Lett. 38(6), L06605 (2011).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2019 (2)

A. Klein, I. Sibony, S. Meir, S. Shahal, H. Duadi, and M. Fridman, “Overlapping time-lens array,” IEEE Photonics J. 11(3), 1–6 (2019).
[Crossref]

H. Duadi, T. Yaron, A. Klein, S. Meir, and M. Fridman, “Phase retrieval by an array of overlapping time-lenses,” Opt. Lett. 44(4), 799–802 (2019).
[Crossref]

2018 (3)

A. Klein, H. Duadi, and M. Fridman, “Full-stokes temporal imaging,” Opt. Lett. 43(8), 1651–1653 (2018).
[Crossref]

A. Klein, G. Masri, H. Duadi, K. Sulimany, O. Lib, H. Steinberg, S. A. Kolpakov, and M. Fridman, “Ultrafast rogue wave patterns in fiber lasers,” Optica 5(7), 774–778 (2018).
[Crossref]

P. Ryczkowski, M. Närhi, C. Billet, J.-M. Merolla, G. Genty, and J. Dudley, “Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser,” Nat. Photonics 12(4), 221–227 (2018).
[Crossref]

2017 (3)

A. Klein, S. Shahal, G. Masri, H. Duadi, and M. Fridman, “Four wave mixing-based time lens for orthogonal polarized input signals,” IEEE Photonics J. 9(2), 1–7 (2017).
[Crossref]

A. Klein, T. Yaron, E. Preter, H. Duadi, and M. Fridman, “Temporal depth imaging,” Optica 4(5), 502–506 (2017).
[Crossref]

A. Ankiewicz and N. Akhmediev, “Rogue wave solutions for the infinite integrable nonlinear schrödinger equation hierarchy,” Phys. Rev. E 96(1), 012219 (2017).
[Crossref]

2016 (2)

N. Akhmediev, B. Kibler, F. Baronio, M. Belić, W.-P. Zhong, Y. Zhang, W. Chang, J. M. Soto-Crespo, P. Vouzas, P. Grelu, C. Lecaplain, K. Hammani, S. Rica, A. Picozzi, M. Tlidi, K. Panajotov, A. Mussot, A. Bendahmane, P. Szriftgiser, G. Genty, J. Dudley, A. Kudlinski, A. Demircan, U. Morgner, S. Amiraranashvili, C. Bree, G. Steinmeyer, C. Masoller, N. G. R. Broderick, A. F. J. Runge, M. Erkintalo, S. Residori, U. Bortolozzo, F. T. Arecchi, S. Wabnitz, C. G. Tiofack, S. Coulibaly, and M. Taki, “Roadmap on optical rogue waves and extreme events,” J. Opt. 18(6), 063001 (2016).
[Crossref]

S. Kolpakov, H. Kbashi, and S. Sergeyev, “Dynamics of vector rogue waves in a fiber laser with a ring cavity,” Optica 3(8), 870–875 (2016).
[Crossref]

2015 (3)

A. Armaroli, C. Conti, and F. Biancalana, “Rogue solitons in optical fibers: a dynamical process in a complex energy landscape?” Optica 2(5), 497–504 (2015).
[Crossref]

Z. Yan, “Two-dimensional vector rogue wave excitations and controlling parameters in the two-component gross–pitaevskii equations with varying potentials,” Nonlinear Dyn. 79(4), 2515–2529 (2015).
[Crossref]

W.-R. Sun, B. Tian, Y. Jiang, and H.-L. Zhen, “Optical rogue waves associated with the negative coherent coupling in an isotropic medium,” Phys. Rev. E 91(2), 023205 (2015).
[Crossref]

2014 (7)

R. B. Mareeswaran, E. Charalampidis, T. Kanna, P. Kevrekidis, and D. Frantzeskakis, “Vector rogue waves and dark-bright boomeronic solitons in autonomous and nonautonomous settings,” Phys. Rev. E 90(4), 042912 (2014).
[Crossref]

W.-P. Zhong, L. Chen, M. Belić, and N. Petrović, “Controllable parabolic-cylinder optical rogue wave,” Phys. Rev. E 90(4), 043201 (2014).
[Crossref]

S. Chen and L.-Y. Song, “Peregrine solitons and algebraic soliton pairs in kerr media considering space–time correction,” Phys. Lett. A 378(18-19), 1228–1232 (2014).
[Crossref]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nat. Photonics 8(10), 755–764 (2014).
[Crossref]

S. Chen, J. M. Soto-Crespo, and P. Grelu, “Coexisting rogue waves within the (2+ 1)-component long-wave–short-wave resonance,” Phys. Rev. E 90(3), 033203 (2014).
[Crossref]

L. Ling, B. Guo, and L.-C. Zhao, “High-order rogue waves in vector nonlinear schrödinger equations,” Phys. Rev. E 89(4), 041201 (2014).
[Crossref]

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113(3), 034101 (2014).
[Crossref]

2013 (5)

J. He, H. Zhang, L. Wang, K. Porsezian, and A. Fokas, “Generating mechanism for higher-order rogue waves,” Phys. Rev. E 87(5), 052914 (2013).
[Crossref]

W.-P. Zhong, M. R. Belić, and T. Huang, “Rogue wave solutions to the generalized nonlinear schrödinger equation with variable coefficients,” Phys. Rev. E 87(6), 065201 (2013).
[Crossref]

Y. V. Bludov, R. Driben, V. V. Konotop, and B. Malomed, “Instabilities, solitons and rogue waves in -coupled nonlinear waveguides,” J. Opt. 15(6), 064010 (2013).
[Crossref]

B.-G. Zhai, W.-G. Zhang, X.-L. Wang, and H.-Q. Zhang, “Multi-rogue waves and rational solutions of the coupled nonlinear schrödinger equations,” Nonlinear Anal.: Real World Appl. 14(1), 14–27 (2013).
[Crossref]

L.-C. Zhao and J. Liu, “Rogue-wave solutions of a three-component coupled nonlinear schrödinger equation,” Phys. Rev. E 87(1), 013201 (2013).
[Crossref]

2012 (6)

C. Lecaplain, P. Grelu, J. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108(23), 233901 (2012).
[Crossref]

C. Kumar, R. Gupta, A. Goyal, S. Loomba, T. S. Raju, and P. K. Panigrahi, “Controlled giant rogue waves in nonlinear fiber optics,” Phys. Rev. A 86(2), 025802 (2012).
[Crossref]

C.-Q. Dai, G.-Q. Zhou, and J.-F. Zhang, “Controllable optical rogue waves in the femtosecond regime,” Phys. Rev. E 85(1), 016603 (2012).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, G. Genty, B. Wetzel, N. Akhmediev, F. Dias, and J. M. Dudley, “Observation of kuznetsov-ma soliton dynamics in optical fibre,” Sci. Rep. 2(1), 463 (2012).
[Crossref]

S. El-Labany, W. Moslem, N. El-Bedwehy, R. Sabry, and H. A. El-Razek, “Rogue wave in titan’s atmosphere,” Astrophys. Space Sci. 338(1), 3–8 (2012).
[Crossref]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear schrödinger equations: evidence for deterministic rogue waves,” Phys. Rev. Lett. 109(4), 044102 (2012).
[Crossref]

2011 (4)

C. Conti and L. Leuzzi, “Complexity of waves in nonlinear disordered media,” Phys. Rev. B 83(13), 134204 (2011).
[Crossref]

Z. Yan, “Vector financial rogue waves,” Phys. Lett. A 375(48), 4274–4279 (2011).
[Crossref]

A. Ankiewicz, D. J. Kedziora, and N. Akhmediev, “Rogue wave triplets,” Phys. Lett. A 375(28-29), 2782–2785 (2011).
[Crossref]

A. Toffoli, E. Bitner-Gregersen, A. R. Osborne, M. Serio, J. Monbaliu, and M. Onorato, “Extreme waves in random crossing seas: Laboratory experiments and numerical simulations,” Geophys. Res. Lett. 38(6), L06605 (2011).
[Crossref]

2010 (2)

V. I. Shrira and V. V. Geogjaev, “What makes the peregrine soliton so special as a prototype of freak waves?” J. Eng. Math. 67(1-2), 11–22 (2010).
[Crossref]

Z. Yan, V. Konotop, and N. Akhmediev, “Three-dimensional rogue waves in nonstationary parabolic potentials,” Phys. Rev. E 82(3), 036610 (2010).
[Crossref]

2009 (4)

L. Leuzzi, C. Conti, V. Folli, L. Angelani, and G. Ruocco, “Phase diagram and complexity of mode-locked lasers: from order to disorder,” Phys. Rev. Lett. 102(8), 083901 (2009).
[Crossref]

Y. V. Bludov, V. V. Konotop, and N. Akhmediev, “Matter rogue waves,” Phys. Rev. A 80(3), 033610 (2009).
[Crossref]

N. Akhmediev, J. M. Soto-Crespo, and A. Ankiewicz, “Extreme waves that appear from nowhere: on the nature of rogue waves,” Phys. Lett. A 373(25), 2137–2145 (2009).
[Crossref]

N. Akhmediev, A. Ankiewicz, and J. Soto-Crespo, “Rogue waves and rational solutions of the nonlinear schrödinger equation,” Phys. Rev. E 80(2), 026601 (2009).
[Crossref]

2008 (1)

K. Dysthe, H. E. Krogstad, and P. Müller, “Oceanic rogue waves,” Annu. Rev. Fluid Mech. 40(1), 287–310 (2008).
[Crossref]

2007 (2)

D. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[Crossref]

D.-I. Yeom and B. J. Eggleton, “Photonics: rogue waves surface in light,” Nature 450(7172), 953–954 (2007).
[Crossref]

2006 (2)

M. Onorato, A. R. Osborne, and M. Serio, “Modulational instability in crossing sea states: A possible mechanism for the formation of freak waves,” Phys. Rev. Lett. 96(1), 014503 (2006).
[Crossref]

P. K. Shukla, I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Phys. Rev. Lett. 97(9), 094501 (2006).
[Crossref]

2005 (1)

C. Conti, “Complex light: Dynamic phase transitions of a light beam in a nonlinear nonlocal disordered medium,” Phys. Rev. E 72(6), 066620 (2005).
[Crossref]

2001 (1)

M. Onorato, A. R. Osborne, M. Serio, and S. Bertone, “Freak waves in random oceanic sea states,” Phys. Rev. Lett. 86(25), 5831–5834 (2001).
[Crossref]

1999 (2)

K. Henderson, D. Peregrine, and J. Dold, “Unsteady water wave modulations: fully nonlinear solutions and comparison with the nonlinear schrödinger equation,” Wave Motion 29(4), 341–361 (1999).
[Crossref]

K. B. Dysthe and K. Trulsen, “Note on breather type solutions of the nls as models for freak-waves,” Phys. Scr. T82(1), 48 (1999).
[Crossref]

1983 (1)

D. Peregrine, “Water waves, nonlinear schrödinger equations and their solutions,” J. Aust. Math. Soc. Series B, Appl. Math 25(1), 16–43 (1983).
[Crossref]

1976 (1)

G. Roskes, “Nonlinear multiphase deep-water wavetrains,” Phys. Fluids (1958-1988) 19(8), 1253–1254 (1976).
[Crossref]

Akhmediev, N.

A. Ankiewicz and N. Akhmediev, “Rogue wave solutions for the infinite integrable nonlinear schrödinger equation hierarchy,” Phys. Rev. E 96(1), 012219 (2017).
[Crossref]

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Phys. Scr. (1)

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Y. Ohta and J. Yang, “General high-order rogue waves and their dynamics in the nonlinear schrödinger equation,” in Proc. R. Soc. A, vol. 468 (The Royal Society, 2012), pp. 1716–1740.

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A. Klein, S. Shahal, H. D. S. Meir, K. Sulimany, O. Lib, H. Steinberg, S. A. Kolpakov, and M. Fridman, “Findingdoublepeaks_auto_3_good.m,” figshare (2019) [retrieved 30 September 2019], https://doi.org/10.6084/m9.figshare.9916508 .

A. Klein, S. Shahal, H. D. S. Meir, K. Sulimany, O. Lib, H. Steinberg, S. A. Kolpakov, and M. Fridman, “scopee1.mat,” figshare (2019) [retrieved 30 September 2019], https://doi.org/10.6084/m9.figshare.9916502 .

A. Klein, S. Shahal, H. D. S. Meir, K. Sulimany, O. Lib, H. Steinberg, S. A. Kolpakov, and M. Fridman, “calculatingrw.m,” figshare (2019) [retrieved 30 September 2019], https://doi.org/10.6084/m9.figshare.9916505 .

Supplementary Material (3)

NameDescription
» Code 1       This code finds 6 peaks in the data. Assuming that every two peaks are measured with a different time-lens
» Dataset 1       A sample of the data - for more data please contact the author
» Dataset 2       This code calculates the resulting state of polarization after finding all the rogue waves

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Figures (1)

Fig. 1.
Fig. 1. (a) Rogue wave measurement scheme with a full Stokes temporal imaging. GSA - graphene saturable absorber, OC - output coupler, EDF - erbium doped fiber, PC - polarization controller, FSTI - Full Stokes temporal imaging. (b) Histogram of the peak intensities showing a large tail that deviates from the exponential distribution expected by stochastic models (red dashed curve). (c) The magnified output of three time-lenses, each projects on a different state of polarization. (d) Polarization measurement of the two magnified peaks in the twin-peak rogue wave, showing that the two peaks have orthogonal states of polarization. (e) Probability distribution for the relative state of polarization of the two peaks, as $S_1 \cdot S_2$ where $S_1$ and $S_2$ are the Stokes vectors of the two peaks, respectively. Typical states of polarization of the two peaks are presented when the two peaks have similar states of polarization and when the two peaks have orthogonal states of polarization. (f) Probability distribution for the peaks intensity ratio in twin-peak rogue waves. The x-axis denote the intensity ratio between the peaks. Typical twin-peak rogue waves with relative intensity ratio of 0.5 and 1 are presented at the insets where $I_H$ denotes the intensity of the higher peak and $I_L$ denotes the intensity of the lower peak.

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