Abstract

Fiber lasers are convenient for studying extreme and rare events, such as rogue waves, thanks to the lasers’ fast dynamics. Indeed, several types of rogue wave patterns were observed in fiber lasers at different time-scales: single peak, twin peak, and triple peak. We measured the statistics of these ultrafast rogue wave patterns with a time lens and developed a numerical model proving that the patterns of the ultrafast rogue waves were generated by the non-instantaneous relaxation of the saturable absorber together with the polarization mode dispersion of the cavity. Our results indicate that the dynamics of the saturable absorber is directly related to the dynamics of ultrafast extreme events in lasers.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (9)

T. Yaron, A. Klein, H. Duadi, and M. Fridman, “Temporal superresolution based on a localization microscopy algorithm,” Appl. Opt. 56, D24–D28 (2017).
[Crossref]

A. Klein, T. Yaron, S. Shahal, G. Masri, H. Duadi, and M. Fridman, “Temporal depth imaging,” Optica 4, 502–506 (2017).
[Crossref]

J. M. Soto-Crespo, N. Devine, and N. Akhmediev, “Dissipative solitons with extreme spikes: bifurcation diagrams in the anomalous dispersion regime,” J. Opt. Soc. Am. B 34, 1542–1549 (2017).
[Crossref]

Z.-R. Cai, M. Liu, S. Hu, J. Yao, A.-P. Luo, Z.-C. Luo, and W.-C. Xu, “Graphene-decorated microfiber photonic device for generation of rogue waves in a fiber laser,” IEEE J. Sel. Top. Quantum Electron. 23, 20–25 (2017).
[Crossref]

B. C. Lima, P. I. Pincheira, E. P. Raposo, L. D. S. Menezes, C. B. de Araújo, A. S. Gomes, and R. Kashyap, “Extreme-value statistics of intensities in a cw-pumped random fiber laser,” Phys. Rev. A 96, 013834 (2017).
[Crossref]

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

S. V. Sergeyev, H. Kbashi, N. Tarasov, Y. Loiko, and S. A. Kolpakov, “Vector-resonance-multimode instability,” Phys. Rev. Lett. 118, 033904 (2017).
[Crossref]

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
[Crossref]

A. Klein, S. Shahal, G. Masri, H. Duadi, and M. Fridman, “Four wave mixing-based time lens for orthogonal polarized input signals,” IEEE Photon. J. 9, 7102707 (2017).
[Crossref]

2016 (8)

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7, 13675 (2016).
[Crossref]

O. Pottiez, R. Paez-Aguirre, J. Cruz, M. Andrés, and E. Kuzin, “Statistical characterization of the internal structure of noiselike pulses using a nonlinear optical loop mirror,” Opt. Commun. 377, 41–51 (2016).
[Crossref]

Y. Xu, X. Wei, Z. Ren, K. K. Wong, and K. K. Tsia, “Ultrafast measurements of optical spectral coherence by single-shot time-stretch interferometry,” Sci. Rep. 6, 27937 (2016).
[Crossref]

G. Herink, B. Jalali, C. Ropers, and D. Solli, “Resolving the build-up of femtosecond mode-locking with single-shot spectroscopy at 90  MHz frame rate,” Nat. Photonics 10, 321–326 (2016).
[Crossref]

P. Suret, R. El Koussaifi, A. Tikan, C. Evain, S. Randoux, C. Szwaj, and S. Bielawski, “Single-shot observation of optical rogue waves in integrable turbulence using time microscopy,” Nat. Commun. 7, 13136 (2016).
[Crossref]

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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
[Crossref]

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

J. Peng, N. Tarasov, S. Sugavanam, and D. Churkin, “Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser,” Opt. Express 24, 21256–21263 (2016).
[Crossref]

2015 (5)

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

S. Birkholz, C. Brée, A. Demircan, and G. Steinmeyer, “Predictability of rogue events,” Phys. Rev. Lett. 114, 213901 (2015).
[Crossref]

M. Fridman, Y. Okawachi, S. Clemmen, M. Ménard, M. Lipson, and A. L. Gaeta, “Waveguide-based single-shot temporal cross-correlator,” J. Opt. 17, 035501 (2015).
[Crossref]

P. Walczak, S. Randoux, and P. Suret, “Optical rogue waves in integrable turbulence,” Phys. Rev. Lett. 114, 143903 (2015).
[Crossref]

G. M. Donovan, “Dynamics and statistics of noise-like pulses in modelocked lasers,” Physica D 309, 1–8 (2015).
[Crossref]

2014 (5)

C. Zhang, Y. Xu, X. Wei, K. K. Tsia, and K. K. Wong, “Time-stretch microscopy based on time-wavelength sequence reconstruction from wideband incoherent source,” Appl. Phys. Lett. 105, 041113 (2014).
[Crossref]

S. K. Gupta and A. K. Sarma, “Solitary waves in parity-time (PT)–symmetric Bragg grating structure and the existence of optical rogue waves,” Europhys. Lett. 105, 44001 (2014).
[Crossref]

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

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

E. Kelleher and J. Travers, “Chirped pulse formation dynamics in ultra-long mode-locked fiber lasers,” Opt. Lett. 39, 1398–1401 (2014).
[Crossref]

2013 (3)

A. Martinez and Z. Sun, “Nanotube and graphene saturable absorbers for fibre lasers,” Nat. Photonics 7, 842–845 (2013).
[Crossref]

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

K. Goda and B. Jalali, “Dispersive fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7, 102–112 (2013).
[Crossref]

2012 (10)

A. Zaviyalov, O. Egorov, R. Iliew, and F. Lederer, “Rogue waves in mode-locked fiber lasers,” Phys. Rev. A 85, 013828 (2012).
[Crossref]

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, 233901 (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, 463 (2012).
[Crossref]

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Triangular rogue wave cascades,” Phys. Rev. E 86, 056602 (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, 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, 016603 (2012).
[Crossref]

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

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, 3–8 (2012).
[Crossref]

M. Fridman, A. Farsi, Y. Okawachi, and A. L. Gaeta, “Demonstration of temporal cloaking,” Nature 481, 62–65 (2012).
[Crossref]

S. Randoux and P. Suret, “Experimental evidence of extreme value statistics in raman fiber lasers,” Opt. Lett. 37, 500–502 (2012).
[Crossref]

2011 (4)

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

A. N. Pisarchik, R. Jaimes-Reátegui, R. Sevilla-Escoboza, G. Huerta-Cuellar, and M. Taki, “Rogue waves in a multistable system,” Phys. Rev. Lett. 107, 274101 (2011).
[Crossref]

C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, J. R. R. Leite, and J. R. Tredicce, “Deterministic optical rogue waves,” Phys. Rev. Lett. 107, 053901 (2011).
[Crossref]

J. Soto-Crespo, P. Grelu, and N. Akhmediev, “Dissipative rogue waves: extreme pulses generated by passively mode-locked lasers,” Phys. Rev. E 84, 016604 (2011).
[Crossref]

2010 (3)

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. Heritage, and S. Yoo, “Real-time full-field arbitrary optical waveform measurement,” Nat. Photonics 4, 248–254 (2010).
[Crossref]

A. Zaviyalov, R. Iliew, O. Egorov, and F. Lederer, “Lumped versus distributed description of mode-locked fiber lasers,” J. Opt. Soc. Am. B 27, 2313–2321 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

2009 (6)

2008 (2)

2007 (2)

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

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

2001 (1)

A. I. Korytin, A. Y. Kryachko, and A. M. Sergeev, “Dissipative solitons in the complex ginzburg-landau equation for femtosecond lasers,” Radiophys. Quantum Electron. 44, 428–442 (2001).
[Crossref]

Akhmediev, N.

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

J. M. Soto-Crespo, N. Devine, and N. Akhmediev, “Dissipative solitons with extreme spikes: bifurcation diagrams in the anomalous dispersion regime,” J. Opt. Soc. Am. B 34, 1542–1549 (2017).
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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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
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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, 463 (2012).
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D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Triangular rogue wave cascades,” Phys. Rev. E 86, 056602 (2012).
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J. Soto-Crespo, P. Grelu, and N. Akhmediev, “Dissipative rogue waves: extreme pulses generated by passively mode-locked lasers,” Phys. Rev. E 84, 016604 (2011).
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A. Ankiewicz, D. J. Kedziora, and N. Akhmediev, “Rogue wave triplets,” Phys. Lett. A 375, 2782–2785 (2011).
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Y. V. Bludov, V. V. Konotop, and N. Akhmediev, “Matter rogue waves,” Phys. Rev. A 80, 033610 (2009).
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J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).
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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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
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O. Pottiez, R. Paez-Aguirre, J. Cruz, M. Andrés, and E. Kuzin, “Statistical characterization of the internal structure of noiselike pulses using a nonlinear optical loop mirror,” Opt. Commun. 377, 41–51 (2016).
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A. Ankiewicz, D. J. Kedziora, and N. Akhmediev, “Rogue wave triplets,” Phys. Lett. A 375, 2782–2785 (2011).
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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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
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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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
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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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
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W.-P. Zhong, L. Chen, M. Belić, and N. Petrović, “Controllable parabolic-cylinder optical rogue wave,” Phys. Rev. E 90, 043201 (2014).
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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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
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Bielawski, S.

P. Suret, R. El Koussaifi, A. Tikan, C. Evain, S. Randoux, C. Szwaj, and S. Bielawski, “Single-shot observation of optical rogue waves in integrable turbulence using time microscopy,” Nat. Commun. 7, 13136 (2016).
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M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7, 13675 (2016).
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S. Birkholz, C. Brée, A. Demircan, and G. Steinmeyer, “Predictability of rogue events,” Phys. Rev. Lett. 114, 213901 (2015).
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Y. V. Bludov, V. V. Konotop, and N. Akhmediev, “Matter rogue waves,” Phys. Rev. A 80, 033610 (2009).
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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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
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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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
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S. Birkholz, C. Brée, A. Demircan, and G. Steinmeyer, “Predictability of rogue events,” Phys. Rev. Lett. 114, 213901 (2015).
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A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
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N. Broderick, M. Erkintalo, and G. Donovan, “Dynamics and statistics of noise-like pulses and rogue waves,” in Advanced Photonics (Optical Society of America, 2014), paper NTH1A.6.

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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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
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W.-P. Zhong, L. Chen, M. Belić, and N. Petrović, “Controllable parabolic-cylinder optical rogue wave,” Phys. Rev. E 90, 043201 (2014).
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Churkin, D. V.

A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
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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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
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O. Pottiez, R. Paez-Aguirre, J. Cruz, M. Andrés, and E. Kuzin, “Statistical characterization of the internal structure of noiselike pulses using a nonlinear optical loop mirror,” Opt. Commun. 377, 41–51 (2016).
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B. C. Lima, P. I. Pincheira, E. P. Raposo, L. D. S. Menezes, C. B. de Araújo, A. S. Gomes, and R. Kashyap, “Extreme-value statistics of intensities in a cw-pumped random fiber laser,” Phys. Rev. A 96, 013834 (2017).
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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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
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S. Birkholz, C. Brée, A. Demircan, and G. Steinmeyer, “Predictability of rogue events,” Phys. Rev. Lett. 114, 213901 (2015).
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Dias, F.

M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7, 13675 (2016).
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J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nat. Photonics 8, 755–764 (2014).
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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, 463 (2012).
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J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).
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N. Broderick, M. Erkintalo, and G. Donovan, “Dynamics and statistics of noise-like pulses and rogue waves,” in Advanced Photonics (Optical Society of America, 2014), paper NTH1A.6.

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P. Ryczkowski, M. Närhi, C. Billet, G. Genty, and J. Dudley, “Real-time measurements of dissipative solitons in a mode-locked fiber laser,” arXiv: 1706.08571 (2017).

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M. Närhi, B. Wetzel, C. Billet, S. Toenger, T. Sylvestre, J.-M. Merolla, R. Morandotti, F. Dias, G. Genty, and J. M. Dudley, “Real-time measurements of spontaneous breathers and rogue wave events in optical fibre modulation instability,” Nat. Commun. 7, 13675 (2016).
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J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation,” Opt. Express 17, 21497–21508 (2009).
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J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nat. Photonics 8, 755–764 (2014).
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M. Anderson, Y. Wang, F. Leo, S. Coen, M. Erkintalo, and S. Murdoch, “Super cavity solitons and the coexistence of multiple nonlinear states in a tristable passive kerr resonator,” arXiv: 1702.00782 (2017).

N. Broderick, M. Erkintalo, and G. Donovan, “Dynamics and statistics of noise-like pulses and rogue waves,” in Advanced Photonics (Optical Society of America, 2014), paper NTH1A.6.

Evain, C.

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Y. Xu, X. Wei, Z. Ren, K. K. Wong, and K. K. Tsia, “Ultrafast measurements of optical spectral coherence by single-shot time-stretch interferometry,” Sci. Rep. 6, 27937 (2016).
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A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
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Y. Xu, X. Wei, Z. Ren, K. K. Wong, and K. K. Tsia, “Ultrafast measurements of optical spectral coherence by single-shot time-stretch interferometry,” Sci. Rep. 6, 27937 (2016).
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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. Picoxxi, M. Tlidi, K. Panajotov, A. Mussor, 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, 063001 (2016).
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A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11, 341–351 (2017).
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Phys. Rev. A (5)

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P. Ryczkowski, M. Närhi, C. Billet, G. Genty, and J. Dudley, “Real-time measurements of dissipative solitons in a mode-locked fiber laser,” arXiv: 1706.08571 (2017).

N. Broderick, M. Erkintalo, and G. Donovan, “Dynamics and statistics of noise-like pulses and rogue waves,” in Advanced Photonics (Optical Society of America, 2014), paper NTH1A.6.

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Figures (7)

Fig. 1.
Fig. 1. Rogue wave measurement scheme with 350 × temporal magnification. Insets (a) and (b) show the laser spectrum and measured pulse width of 1 ps during operation under stable conditions, respectively. The red curve shows the measured low-resolution output under unstable conditions, which reveals the generation of a rogue wave from the intensity noise. GSA, graphene saturable absorber; OC, output coupler; EDF, erbium-doped fiber; PC, polarization controller.
Fig. 2.
Fig. 2. Histogram of the peak intensities; the large tail deviates from the exponential distribution predicted by stochastic models (red dashed curve). SWH: significant wave height. Inset: high-resolution measurement of the laser output noise showing three rogue waves.
Fig. 3.
Fig. 3. Probability of rogue waves as a function of the laser pump power for single-peak, twin-peak, and triple-peak patterns. Insets show typical measured results of each rogue wave pattern.
Fig. 4.
Fig. 4. Measured separation between peaks as a function of the number of round trips in the cavity for two cases: stable separation, indicating a twin-peak pattern (circles), and increasing separation, indicating two separate single-peak rogue waves. Inset illustrates the stable twin-peak rogue wave.
Fig. 5.
Fig. 5. Calculated vector field envelope as a function of the number of round trips in the fiber laser for different PMD values. (a) Low PMD, showing the same chaotic behavior as a scalar model. (b) Increased PMD, showing fewer pulses. (c) Realistic value of PMD, showing rogue waves every few hundred round trips. L smf = 10 , L edf = 0.22 , D 2 = 0.735 , Γ 2 = 3 , g 0 = 4 , β 2 = 0.008 , Q sat = 8 , T r = 0.7 , T 0 = 0.9 , Δ T = 0.1 , I sat = 0.6 , κ = 0.2 , ϕ 1 = 0 , and ϕ 2 = 0.1 .
Fig. 6.
Fig. 6. (a) Probability of multipeak rogue waves as a function of the cutoff frequency of the low-pass filter. (b) and (c) Typical calculated twin-peak and triple-peak rogue waves, respectively.
Fig. 7.
Fig. 7. (e) Calculated likelihood of rogue waves in the simulation as a function of Q sat . (a) Typical output as a function of time for Q sat = 3 , (b) typical output as a function of time for Q sat = 8 , (c) peak height histogram for Q sat = 8 , which deviates from an exponential distribution (dashed line), and (d) peak height histogram for Q sat = 13 , which shows an exponential distribution (dashed line).

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

i ψ z + D 2 ψ t t + | ψ | 2 ψ = 0 ,
i ψ z + D 2 2 ψ t t + Γ 2 | ψ | 2 ψ = i g 0 1 + Q / Q sat ( ψ + β 2 ψ t t ) ,
Q = | ψ | 2 d t .
T ( t ) = T 0 + Δ T I ( t ) I sat + I ( t ) ,
ψ out = [ ( 1 κ ) e i ϕ 1 κ e i ϕ 2 κ e i ϕ 2 ( 1 κ ) e i ϕ 1 ] ψ in ,

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