Abstract

We study experimentally and theoretically the dynamics of a spatially extended (along the propagation direction) oscillatory medium with coherent forcing. We observe abnormally high events, responsible for a different statistics of intensity and pulse height, in a regime where solitons and roll patterns are unstable. We focus on the formation of these high-peak events and their connection to the phase dynamics. Each abnormal event can be associated with a change in the slope of the phase time trace. Furthermore, the coexistence of ±2π phase rotations inside the cavity can be associated to the observation of abnormal events, similarly to recent predictions in bidimensional vortex turbulence.

© 2017 Optical Society of America

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  1. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
    [Crossref] [PubMed]
  2. C. Kharif, E. Pelinovsky, and A. Slunyaev, Rogue Waves in the Ocean (Advances in Geophysical and Environmental Mechanics and Mathematics) (Springer, 2009).
  3. S. Birkholz, C. Brée, I. Veselić, A. Demircan, and G. Steinmeyer, “Ocean rogue waves and their phase space dynamics in the limit of a linear interference model,” Sci. Rep. 6. 35207 (2016).
    [Crossref] [PubMed]
  4. R. Höhmann, U. Kuhl, H.-J. Stöckmann, L. Kaplan, and E. Heller, “Freak waves in the linear regime: A microwave study,” Phys. Rev. Lett. 104, 093901 (2010).
    [Crossref] [PubMed]
  5. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Rogue waves and rational solutions of the nonlinear schrödinger equation,” Phys. Rev. E 80, 026601 (2009).
    [Crossref]
  6. D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88, 013207 (2013).
    [Crossref]
  7. 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,” Nat. Phys. 6, 790–795 (2010).
    [Crossref]
  8. S. Randoux, P. Suret, and G. El, “Identification of rogue waves from scattering transform analysis of periodized waveforms,” arXiv preprint https://arXiv:1512.04707 (2015).
  9. 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] [PubMed]
  10. A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, and M. Taki, “Observation of extreme temporal events in cw-pumped supercontinuum,” Opt. Express 17, 17010–17015 (2009).
    [Crossref] [PubMed]
  11. 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).
    [Crossref] [PubMed]
  12. K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374, 3585–3589 (2010).
    [Crossref]
  13. P. Walczak, S. Randoux, and P. Suret, “Optical rogue waves in integrable turbulence,” Phys. Rev. Lett. 114, 143903 (2015).
    [Crossref] [PubMed]
  14. 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] [PubMed]
  15. M. G. Kovalsky, A. A. Hnilo, and J. R. Tredicce, “Extreme events in the ti: sapphire laser,” Opt. Lett. 36, 4449–4451 (2011).
    [Crossref] [PubMed]
  16. C. Lecaplain, P. Grelu, J. M. 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] [PubMed]
  17. F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
    [Crossref] [PubMed]
  18. S. Coulibaly, M. Clerc, F. Selmi, and S. Barbay, “Extreme events following bifurcation to spatiotemporal chaos in a spatially extended microcavity laser,” Phys. Rev. A 95, 023816 (2017).
    [Crossref]
  19. C. Rimoldi, S. Barland, F. Prati, and G. Tissoni, “Spatiotemporal extreme events in a laser with a saturable absorber,” Phys. Rev. A 95, 023841 (2017).
    [Crossref]
  20. 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] [PubMed]
  21. J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. R. Leite, C. Masoller, and J. R. Tredicce, “Rogue waves in optically injected lasers: Origin, predictability, and suppression,” Phys. Rev. A 87, 035802 (2013).
    [Crossref]
  22. J. Ahuja, D. B. Nalawade, J. Zamora-Munt, R. Vilaseca, and C. Masoller, “Rogue waves in injected semiconductor lasers with current modulation: role of the modulation phase,” Opt. Express 22, 28377–28382 (2014).
    [Crossref] [PubMed]
  23. G.-L. Oppo, A. M. Yao, and D. Cuozzo, “Self-organization, pattern formation, cavity solitons, and rogue waves in singly resonant optical parametric oscillators,” Phys. Rev. A 88, 043813 (2013).
    [Crossref]
  24. C. J. Gibson, A. M. Yao, and G.-L. Oppo, “Optical rogue waves in vortex turbulence,” Phys. Rev. Lett. 116, 043903 (2016).
    [Crossref] [PubMed]
  25. F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, B. Kelleher, B. Tykalewicz, and S. Barland, “Dissipative phase solitons in semiconductor lasers,” Phys. Rev. Lett. 115, 043902 (2015).
    [Crossref] [PubMed]
  26. F. Gustave, C. Rimoldi, P. Walczak, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Formation of phase soliton complexes in an optically injected semiconductor laser,” Eur. Phys. J. D 716, 154 (2017).
    [Crossref]
  27. F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, and S. Barland, “Phase solitons and domain dynamics in an optically injected semiconductor laser,” Phys. Rev. A 93, 063824 (2016).
    [Crossref]
  28. A. Coillet, J. Dudley, G. Genty, L. Larger, and Y. K. Chembo, “Optical rogue waves in whispering-gallery-mode resonators,” Phys. Rev. A 89, 013835 (2014).
    [Crossref]
  29. H. Chaté, A. Pikovsky, and O. Rudzick, “Forcing oscillatory media: phase kinks vs. synchronization,” Phys. D Nonlinear Phenom. 131, 17–30 (1999).
    [Crossref]
  30. S. Longhi, “Nonlinear travelling pulses in laser injection locking,” Quantum and Semiclassical Optics: J. Euro. Opt. Soc. Part B (1995–1998) 10, 617–635 (1998).
    [Crossref]
  31. P. Walczak, C. Rimoldi, F. Gustave, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Extreme events induced by collisions in a forced semiconductor laser,” Submitted to Opt. Lett. (May2017). https://arxiv.org/abs/1705.02153 .
    [Crossref]
  32. F. Gustave, “Phase dynamics and dissipative solitons in semiconductor lasers,” Ph.D. thesis, Université de Nice Sophia Antipolis (2016).
  33. S. Barland, O. Piro, M. Giudici, J. R. Tredicce, and S. Balle, “Experimental evidence of van der pol–fitzhugh–nagumo dynamics in semiconductor optical amplifiers,” Phys. Rev. E 68, 036209 (2003).
    [Crossref]
  34. L. Spinelli, G. Tissoni, L. A. Lugiato, and M. Brambilla, “Thermal effects and transverse structures in semiconductor microcavities with population inversion,” Phys. Rev. A 66, 023817 (2002).
    [Crossref]
  35. G. Tissoni, L. Spinelli, L. A. Lugiato, M. Brambilla, I. M. Perrini, and T. Maggipinto, “Spatio-temporal dynamics in semiconductor microresonators with thermal effects,” Opt. Express 10, 1009–1017 (2002).
    [Crossref] [PubMed]
  36. V. Brasch, M. Geiselmann, M. H. Pfeiffer, and T. J. Kippenberg, “Bringing short-lived dissipative kerr soliton states in microresonators into a steady state,” Opt. Express 24, 29312–29320 (2016).
    [Crossref] [PubMed]
  37. P. Coullet, L. Gil, and J. Lega, “Defect-mediated turbulence,” Phys. Rev. Lett. 62, 1619–1622 (1989).
    [Crossref] [PubMed]
  38. S. V. Fedorov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, “Effect of frequency detunings and finite relaxation rates on laser localized structures,” Phys. Rev. E 61, 5814–5824 (2000).
    [Crossref]
  39. L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
    [Crossref]

2017 (3)

S. Coulibaly, M. Clerc, F. Selmi, and S. Barbay, “Extreme events following bifurcation to spatiotemporal chaos in a spatially extended microcavity laser,” Phys. Rev. A 95, 023816 (2017).
[Crossref]

C. Rimoldi, S. Barland, F. Prati, and G. Tissoni, “Spatiotemporal extreme events in a laser with a saturable absorber,” Phys. Rev. A 95, 023841 (2017).
[Crossref]

F. Gustave, C. Rimoldi, P. Walczak, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Formation of phase soliton complexes in an optically injected semiconductor laser,” Eur. Phys. J. D 716, 154 (2017).
[Crossref]

2016 (7)

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, and S. Barland, “Phase solitons and domain dynamics in an optically injected semiconductor laser,” Phys. Rev. A 93, 063824 (2016).
[Crossref]

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

V. Brasch, M. Geiselmann, M. H. Pfeiffer, and T. J. Kippenberg, “Bringing short-lived dissipative kerr soliton states in microresonators into a steady state,” Opt. Express 24, 29312–29320 (2016).
[Crossref] [PubMed]

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] [PubMed]

C. J. Gibson, A. M. Yao, and G.-L. Oppo, “Optical rogue waves in vortex turbulence,” Phys. Rev. Lett. 116, 043903 (2016).
[Crossref] [PubMed]

S. Birkholz, C. Brée, I. Veselić, A. Demircan, and G. Steinmeyer, “Ocean rogue waves and their phase space dynamics in the limit of a linear interference model,” Sci. Rep. 6. 35207 (2016).
[Crossref] [PubMed]

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] [PubMed]

2015 (2)

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

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, B. Kelleher, B. Tykalewicz, and S. Barland, “Dissipative phase solitons in semiconductor lasers,” Phys. Rev. Lett. 115, 043902 (2015).
[Crossref] [PubMed]

2014 (2)

2013 (3)

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. R. Leite, C. Masoller, and J. R. Tredicce, “Rogue waves in optically injected lasers: Origin, predictability, and suppression,” Phys. Rev. A 87, 035802 (2013).
[Crossref]

G.-L. Oppo, A. M. Yao, and D. Cuozzo, “Self-organization, pattern formation, cavity solitons, and rogue waves in singly resonant optical parametric oscillators,” Phys. Rev. A 88, 043813 (2013).
[Crossref]

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88, 013207 (2013).
[Crossref]

2012 (1)

C. Lecaplain, P. Grelu, J. M. 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] [PubMed]

2011 (2)

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] [PubMed]

M. G. Kovalsky, A. A. Hnilo, and J. R. Tredicce, “Extreme events in the ti: sapphire laser,” Opt. Lett. 36, 4449–4451 (2011).
[Crossref] [PubMed]

2010 (3)

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,” Nat. Phys. 6, 790–795 (2010).
[Crossref]

R. Höhmann, U. Kuhl, H.-J. Stöckmann, L. Kaplan, and E. Heller, “Freak waves in the linear regime: A microwave study,” Phys. Rev. Lett. 104, 093901 (2010).
[Crossref] [PubMed]

K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374, 3585–3589 (2010).
[Crossref]

2009 (3)

2007 (1)

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

2003 (1)

S. Barland, O. Piro, M. Giudici, J. R. Tredicce, and S. Balle, “Experimental evidence of van der pol–fitzhugh–nagumo dynamics in semiconductor optical amplifiers,” Phys. Rev. E 68, 036209 (2003).
[Crossref]

2002 (2)

L. Spinelli, G. Tissoni, L. A. Lugiato, and M. Brambilla, “Thermal effects and transverse structures in semiconductor microcavities with population inversion,” Phys. Rev. A 66, 023817 (2002).
[Crossref]

G. Tissoni, L. Spinelli, L. A. Lugiato, M. Brambilla, I. M. Perrini, and T. Maggipinto, “Spatio-temporal dynamics in semiconductor microresonators with thermal effects,” Opt. Express 10, 1009–1017 (2002).
[Crossref] [PubMed]

2000 (1)

S. V. Fedorov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, “Effect of frequency detunings and finite relaxation rates on laser localized structures,” Phys. Rev. E 61, 5814–5824 (2000).
[Crossref]

1999 (1)

H. Chaté, A. Pikovsky, and O. Rudzick, “Forcing oscillatory media: phase kinks vs. synchronization,” Phys. D Nonlinear Phenom. 131, 17–30 (1999).
[Crossref]

1998 (2)

S. Longhi, “Nonlinear travelling pulses in laser injection locking,” Quantum and Semiclassical Optics: J. Euro. Opt. Soc. Part B (1995–1998) 10, 617–635 (1998).
[Crossref]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[Crossref]

1989 (1)

P. Coullet, L. Gil, and J. Lega, “Defect-mediated turbulence,” Phys. Rev. Lett. 62, 1619–1622 (1989).
[Crossref] [PubMed]

Ahuja, J.

Akhmediev, N.

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88, 013207 (2013).
[Crossref]

C. Lecaplain, P. Grelu, J. M. 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] [PubMed]

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,” Nat. Phys. 6, 790–795 (2010).
[Crossref]

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

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).
[Crossref] [PubMed]

Ankiewicz, A.

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88, 013207 (2013).
[Crossref]

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

Balle, S.

S. Barland, O. Piro, M. Giudici, J. R. Tredicce, and S. Balle, “Experimental evidence of van der pol–fitzhugh–nagumo dynamics in semiconductor optical amplifiers,” Phys. Rev. E 68, 036209 (2003).
[Crossref]

Barbay, S.

S. Coulibaly, M. Clerc, F. Selmi, and S. Barbay, “Extreme events following bifurcation to spatiotemporal chaos in a spatially extended microcavity laser,” Phys. Rev. A 95, 023816 (2017).
[Crossref]

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Barland, S.

C. Rimoldi, S. Barland, F. Prati, and G. Tissoni, “Spatiotemporal extreme events in a laser with a saturable absorber,” Phys. Rev. A 95, 023841 (2017).
[Crossref]

F. Gustave, C. Rimoldi, P. Walczak, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Formation of phase soliton complexes in an optically injected semiconductor laser,” Eur. Phys. J. D 716, 154 (2017).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, and S. Barland, “Phase solitons and domain dynamics in an optically injected semiconductor laser,” Phys. Rev. A 93, 063824 (2016).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, B. Kelleher, B. Tykalewicz, and S. Barland, “Dissipative phase solitons in semiconductor lasers,” Phys. Rev. Lett. 115, 043902 (2015).
[Crossref] [PubMed]

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. R. Leite, C. Masoller, and J. R. Tredicce, “Rogue waves in optically injected lasers: Origin, predictability, and suppression,” Phys. Rev. A 87, 035802 (2013).
[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] [PubMed]

S. Barland, O. Piro, M. Giudici, J. R. Tredicce, and S. Balle, “Experimental evidence of van der pol–fitzhugh–nagumo dynamics in semiconductor optical amplifiers,” Phys. Rev. E 68, 036209 (2003).
[Crossref]

Beaudoin, G.

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Billet, C.

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] [PubMed]

Birkholz, S.

S. Birkholz, C. Brée, I. Veselić, A. Demircan, and G. Steinmeyer, “Ocean rogue waves and their phase space dynamics in the limit of a linear interference model,” Sci. Rep. 6. 35207 (2016).
[Crossref] [PubMed]

Bonatto, C.

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] [PubMed]

Brambilla, M.

F. Gustave, C. Rimoldi, P. Walczak, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Formation of phase soliton complexes in an optically injected semiconductor laser,” Eur. Phys. J. D 716, 154 (2017).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, and S. Barland, “Phase solitons and domain dynamics in an optically injected semiconductor laser,” Phys. Rev. A 93, 063824 (2016).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, B. Kelleher, B. Tykalewicz, and S. Barland, “Dissipative phase solitons in semiconductor lasers,” Phys. Rev. Lett. 115, 043902 (2015).
[Crossref] [PubMed]

L. Spinelli, G. Tissoni, L. A. Lugiato, and M. Brambilla, “Thermal effects and transverse structures in semiconductor microcavities with population inversion,” Phys. Rev. A 66, 023817 (2002).
[Crossref]

G. Tissoni, L. Spinelli, L. A. Lugiato, M. Brambilla, I. M. Perrini, and T. Maggipinto, “Spatio-temporal dynamics in semiconductor microresonators with thermal effects,” Opt. Express 10, 1009–1017 (2002).
[Crossref] [PubMed]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[Crossref]

Brasch, V.

Brée, C.

S. Birkholz, C. Brée, I. Veselić, A. Demircan, and G. Steinmeyer, “Ocean rogue waves and their phase space dynamics in the limit of a linear interference model,” Sci. Rep. 6. 35207 (2016).
[Crossref] [PubMed]

Chaté, H.

H. Chaté, A. Pikovsky, and O. Rudzick, “Forcing oscillatory media: phase kinks vs. synchronization,” Phys. D Nonlinear Phenom. 131, 17–30 (1999).
[Crossref]

Chembo, Y. K.

A. Coillet, J. Dudley, G. Genty, L. Larger, and Y. K. Chembo, “Optical rogue waves in whispering-gallery-mode resonators,” Phys. Rev. A 89, 013835 (2014).
[Crossref]

Clerc, M.

S. Coulibaly, M. Clerc, F. Selmi, and S. Barbay, “Extreme events following bifurcation to spatiotemporal chaos in a spatially extended microcavity laser,” Phys. Rev. A 95, 023816 (2017).
[Crossref]

Clerc, M. G.

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Coillet, A.

A. Coillet, J. Dudley, G. Genty, L. Larger, and Y. K. Chembo, “Optical rogue waves in whispering-gallery-mode resonators,” Phys. Rev. A 89, 013835 (2014).
[Crossref]

Columbo, L.

F. Gustave, C. Rimoldi, P. Walczak, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Formation of phase soliton complexes in an optically injected semiconductor laser,” Eur. Phys. J. D 716, 154 (2017).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, and S. Barland, “Phase solitons and domain dynamics in an optically injected semiconductor laser,” Phys. Rev. A 93, 063824 (2016).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, B. Kelleher, B. Tykalewicz, and S. Barland, “Dissipative phase solitons in semiconductor lasers,” Phys. Rev. Lett. 115, 043902 (2015).
[Crossref] [PubMed]

Coulibaly, S.

S. Coulibaly, M. Clerc, F. Selmi, and S. Barbay, “Extreme events following bifurcation to spatiotemporal chaos in a spatially extended microcavity laser,” Phys. Rev. A 95, 023816 (2017).
[Crossref]

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Coullet, P.

P. Coullet, L. Gil, and J. Lega, “Defect-mediated turbulence,” Phys. Rev. Lett. 62, 1619–1622 (1989).
[Crossref] [PubMed]

Cuozzo, D.

G.-L. Oppo, A. M. Yao, and D. Cuozzo, “Self-organization, pattern formation, cavity solitons, and rogue waves in singly resonant optical parametric oscillators,” Phys. Rev. A 88, 043813 (2013).
[Crossref]

Demircan, A.

S. Birkholz, C. Brée, I. Veselić, A. Demircan, and G. Steinmeyer, “Ocean rogue waves and their phase space dynamics in the limit of a linear interference model,” Sci. Rep. 6. 35207 (2016).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

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,” Nat. Phys. 6, 790–795 (2010).
[Crossref]

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).
[Crossref] [PubMed]

Douay, M.

Dudley, J.

A. Coillet, J. Dudley, G. Genty, L. Larger, and Y. K. Chembo, “Optical rogue waves in whispering-gallery-mode resonators,” Phys. Rev. A 89, 013835 (2014).
[Crossref]

Dudley, J. M.

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] [PubMed]

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,” Nat. Phys. 6, 790–795 (2010).
[Crossref]

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).
[Crossref] [PubMed]

El Koussaifi, R.

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] [PubMed]

Evain, C.

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] [PubMed]

Fatome, J.

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,” Nat. Phys. 6, 790–795 (2010).
[Crossref]

Fedorov, S. V.

S. V. Fedorov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, “Effect of frequency detunings and finite relaxation rates on laser localized structures,” Phys. Rev. E 61, 5814–5824 (2000).
[Crossref]

Feyereisen, M.

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] [PubMed]

Finot, C.

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,” Nat. Phys. 6, 790–795 (2010).
[Crossref]

K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374, 3585–3589 (2010).
[Crossref]

Garbin, B.

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. R. Leite, C. Masoller, and J. R. Tredicce, “Rogue waves in optically injected lasers: Origin, predictability, and suppression,” Phys. Rev. A 87, 035802 (2013).
[Crossref]

Geiselmann, M.

Genty, G.

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] [PubMed]

A. Coillet, J. Dudley, G. Genty, L. Larger, and Y. K. Chembo, “Optical rogue waves in whispering-gallery-mode resonators,” Phys. Rev. A 89, 013835 (2014).
[Crossref]

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,” Nat. Phys. 6, 790–795 (2010).
[Crossref]

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).
[Crossref] [PubMed]

Gibson, C. J.

C. J. Gibson, A. M. Yao, and G.-L. Oppo, “Optical rogue waves in vortex turbulence,” Phys. Rev. Lett. 116, 043903 (2016).
[Crossref] [PubMed]

Gil, L.

P. Coullet, L. Gil, and J. Lega, “Defect-mediated turbulence,” Phys. Rev. Lett. 62, 1619–1622 (1989).
[Crossref] [PubMed]

Giudici, M.

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. R. Leite, C. Masoller, and J. R. Tredicce, “Rogue waves in optically injected lasers: Origin, predictability, and suppression,” Phys. Rev. A 87, 035802 (2013).
[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] [PubMed]

S. Barland, O. Piro, M. Giudici, J. R. Tredicce, and S. Balle, “Experimental evidence of van der pol–fitzhugh–nagumo dynamics in semiconductor optical amplifiers,” Phys. Rev. E 68, 036209 (2003).
[Crossref]

Grelu, P.

C. Lecaplain, P. Grelu, J. M. 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] [PubMed]

Gustave, F.

F. Gustave, C. Rimoldi, P. Walczak, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Formation of phase soliton complexes in an optically injected semiconductor laser,” Eur. Phys. J. D 716, 154 (2017).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, and S. Barland, “Phase solitons and domain dynamics in an optically injected semiconductor laser,” Phys. Rev. A 93, 063824 (2016).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, B. Kelleher, B. Tykalewicz, and S. Barland, “Dissipative phase solitons in semiconductor lasers,” Phys. Rev. Lett. 115, 043902 (2015).
[Crossref] [PubMed]

F. Gustave, “Phase dynamics and dissipative solitons in semiconductor lasers,” Ph.D. thesis, Université de Nice Sophia Antipolis (2016).

Hammani, K.

K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374, 3585–3589 (2010).
[Crossref]

Heller, E.

R. Höhmann, U. Kuhl, H.-J. Stöckmann, L. Kaplan, and E. Heller, “Freak waves in the linear regime: A microwave study,” Phys. Rev. Lett. 104, 093901 (2010).
[Crossref] [PubMed]

Hnilo, A. A.

Höhmann, R.

R. Höhmann, U. Kuhl, H.-J. Stöckmann, L. Kaplan, and E. Heller, “Freak waves in the linear regime: A microwave study,” Phys. Rev. Lett. 104, 093901 (2010).
[Crossref] [PubMed]

Jalali, B.

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

Kaplan, L.

R. Höhmann, U. Kuhl, H.-J. Stöckmann, L. Kaplan, and E. Heller, “Freak waves in the linear regime: A microwave study,” Phys. Rev. Lett. 104, 093901 (2010).
[Crossref] [PubMed]

Kedziora, D. J.

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88, 013207 (2013).
[Crossref]

Kelleher, B.

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, B. Kelleher, B. Tykalewicz, and S. Barland, “Dissipative phase solitons in semiconductor lasers,” Phys. Rev. Lett. 115, 043902 (2015).
[Crossref] [PubMed]

Kharif, C.

C. Kharif, E. Pelinovsky, and A. Slunyaev, Rogue Waves in the Ocean (Advances in Geophysical and Environmental Mechanics and Mathematics) (Springer, 2009).

Khodova, G. V.

S. V. Fedorov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, “Effect of frequency detunings and finite relaxation rates on laser localized structures,” Phys. Rev. E 61, 5814–5824 (2000).
[Crossref]

Kibler, B.

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,” Nat. Phys. 6, 790–795 (2010).
[Crossref]

K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374, 3585–3589 (2010).
[Crossref]

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).
[Crossref] [PubMed]

Kippenberg, T. J.

Kolobov, M.

Koonath, P.

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

Kovalsky, M. G.

Kudlinski, A.

Kuhl, U.

R. Höhmann, U. Kuhl, H.-J. Stöckmann, L. Kaplan, and E. Heller, “Freak waves in the linear regime: A microwave study,” Phys. Rev. Lett. 104, 093901 (2010).
[Crossref] [PubMed]

Larger, L.

A. Coillet, J. Dudley, G. Genty, L. Larger, and Y. K. Chembo, “Optical rogue waves in whispering-gallery-mode resonators,” Phys. Rev. A 89, 013835 (2014).
[Crossref]

Lecaplain, C.

C. Lecaplain, P. Grelu, J. M. 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] [PubMed]

Lega, J.

P. Coullet, L. Gil, and J. Lega, “Defect-mediated turbulence,” Phys. Rev. Lett. 62, 1619–1622 (1989).
[Crossref] [PubMed]

Leite, J. R. R.

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. R. Leite, C. Masoller, and J. R. Tredicce, “Rogue waves in optically injected lasers: Origin, predictability, and suppression,” Phys. Rev. A 87, 035802 (2013).
[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] [PubMed]

Loghmari, Z.

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Longhi, S.

S. Longhi, “Nonlinear travelling pulses in laser injection locking,” Quantum and Semiclassical Optics: J. Euro. Opt. Soc. Part B (1995–1998) 10, 617–635 (1998).
[Crossref]

Louvergneaux, E.

Lugiato, L. A.

G. Tissoni, L. Spinelli, L. A. Lugiato, M. Brambilla, I. M. Perrini, and T. Maggipinto, “Spatio-temporal dynamics in semiconductor microresonators with thermal effects,” Opt. Express 10, 1009–1017 (2002).
[Crossref] [PubMed]

L. Spinelli, G. Tissoni, L. A. Lugiato, and M. Brambilla, “Thermal effects and transverse structures in semiconductor microcavities with population inversion,” Phys. Rev. A 66, 023817 (2002).
[Crossref]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[Crossref]

Maggipinto, T.

Masoller, C.

J. Ahuja, D. B. Nalawade, J. Zamora-Munt, R. Vilaseca, and C. Masoller, “Rogue waves in injected semiconductor lasers with current modulation: role of the modulation phase,” Opt. Express 22, 28377–28382 (2014).
[Crossref] [PubMed]

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. R. Leite, C. Masoller, and J. R. Tredicce, “Rogue waves in optically injected lasers: Origin, predictability, and suppression,” Phys. Rev. A 87, 035802 (2013).
[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] [PubMed]

Merolla, J.-M.

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] [PubMed]

Millot, G.

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,” Nat. Phys. 6, 790–795 (2010).
[Crossref]

Morandotti, R.

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] [PubMed]

Mussot, A.

Nalawade, D. B.

Närhi, M.

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] [PubMed]

Oppo, G.-L.

C. J. Gibson, A. M. Yao, and G.-L. Oppo, “Optical rogue waves in vortex turbulence,” Phys. Rev. Lett. 116, 043903 (2016).
[Crossref] [PubMed]

G.-L. Oppo, A. M. Yao, and D. Cuozzo, “Self-organization, pattern formation, cavity solitons, and rogue waves in singly resonant optical parametric oscillators,” Phys. Rev. A 88, 043813 (2013).
[Crossref]

Pelinovsky, E.

C. Kharif, E. Pelinovsky, and A. Slunyaev, Rogue Waves in the Ocean (Advances in Geophysical and Environmental Mechanics and Mathematics) (Springer, 2009).

Perrini, I. M.

Pfeiffer, M. H.

Picozzi, A.

K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374, 3585–3589 (2010).
[Crossref]

Pikovsky, A.

H. Chaté, A. Pikovsky, and O. Rudzick, “Forcing oscillatory media: phase kinks vs. synchronization,” Phys. D Nonlinear Phenom. 131, 17–30 (1999).
[Crossref]

Piro, O.

S. Barland, O. Piro, M. Giudici, J. R. Tredicce, and S. Balle, “Experimental evidence of van der pol–fitzhugh–nagumo dynamics in semiconductor optical amplifiers,” Phys. Rev. E 68, 036209 (2003).
[Crossref]

Prati, F.

C. Rimoldi, S. Barland, F. Prati, and G. Tissoni, “Spatiotemporal extreme events in a laser with a saturable absorber,” Phys. Rev. A 95, 023841 (2017).
[Crossref]

F. Gustave, C. Rimoldi, P. Walczak, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Formation of phase soliton complexes in an optically injected semiconductor laser,” Eur. Phys. J. D 716, 154 (2017).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, and S. Barland, “Phase solitons and domain dynamics in an optically injected semiconductor laser,” Phys. Rev. A 93, 063824 (2016).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, B. Kelleher, B. Tykalewicz, and S. Barland, “Dissipative phase solitons in semiconductor lasers,” Phys. Rev. Lett. 115, 043902 (2015).
[Crossref] [PubMed]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[Crossref]

Randoux, 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).
[Crossref] [PubMed]

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

Rimoldi, C.

C. Rimoldi, S. Barland, F. Prati, and G. Tissoni, “Spatiotemporal extreme events in a laser with a saturable absorber,” Phys. Rev. A 95, 023841 (2017).
[Crossref]

F. Gustave, C. Rimoldi, P. Walczak, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Formation of phase soliton complexes in an optically injected semiconductor laser,” Eur. Phys. J. D 716, 154 (2017).
[Crossref]

Ropers, C.

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

Rosanov, N. N.

S. V. Fedorov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, “Effect of frequency detunings and finite relaxation rates on laser localized structures,” Phys. Rev. E 61, 5814–5824 (2000).
[Crossref]

Rudzick, O.

H. Chaté, A. Pikovsky, and O. Rudzick, “Forcing oscillatory media: phase kinks vs. synchronization,” Phys. D Nonlinear Phenom. 131, 17–30 (1999).
[Crossref]

Sagnes, I.

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Selmi, F.

S. Coulibaly, M. Clerc, F. Selmi, and S. Barbay, “Extreme events following bifurcation to spatiotemporal chaos in a spatially extended microcavity laser,” Phys. Rev. A 95, 023816 (2017).
[Crossref]

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Slunyaev, A.

C. Kharif, E. Pelinovsky, and A. Slunyaev, Rogue Waves in the Ocean (Advances in Geophysical and Environmental Mechanics and Mathematics) (Springer, 2009).

Solli, D. R.

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

Soto-Crespo, J. M.

C. Lecaplain, P. Grelu, J. M. 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] [PubMed]

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

Spinelli, L.

L. Spinelli, G. Tissoni, L. A. Lugiato, and M. Brambilla, “Thermal effects and transverse structures in semiconductor microcavities with population inversion,” Phys. Rev. A 66, 023817 (2002).
[Crossref]

G. Tissoni, L. Spinelli, L. A. Lugiato, M. Brambilla, I. M. Perrini, and T. Maggipinto, “Spatio-temporal dynamics in semiconductor microresonators with thermal effects,” Opt. Express 10, 1009–1017 (2002).
[Crossref] [PubMed]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[Crossref]

Steinmeyer, G.

S. Birkholz, C. Brée, I. Veselić, A. Demircan, and G. Steinmeyer, “Ocean rogue waves and their phase space dynamics in the limit of a linear interference model,” Sci. Rep. 6. 35207 (2016).
[Crossref] [PubMed]

Stöckmann, H.-J.

R. Höhmann, U. Kuhl, H.-J. Stöckmann, L. Kaplan, and E. Heller, “Freak waves in the linear regime: A microwave study,” Phys. Rev. Lett. 104, 093901 (2010).
[Crossref] [PubMed]

Suret, P.

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] [PubMed]

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

Sylvestre, T.

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] [PubMed]

Szwaj, C.

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] [PubMed]

Taki, M.

Tikan, A.

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] [PubMed]

Tissoni, G.

F. Gustave, C. Rimoldi, P. Walczak, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Formation of phase soliton complexes in an optically injected semiconductor laser,” Eur. Phys. J. D 716, 154 (2017).
[Crossref]

C. Rimoldi, S. Barland, F. Prati, and G. Tissoni, “Spatiotemporal extreme events in a laser with a saturable absorber,” Phys. Rev. A 95, 023841 (2017).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, and S. Barland, “Phase solitons and domain dynamics in an optically injected semiconductor laser,” Phys. Rev. A 93, 063824 (2016).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, B. Kelleher, B. Tykalewicz, and S. Barland, “Dissipative phase solitons in semiconductor lasers,” Phys. Rev. Lett. 115, 043902 (2015).
[Crossref] [PubMed]

L. Spinelli, G. Tissoni, L. A. Lugiato, and M. Brambilla, “Thermal effects and transverse structures in semiconductor microcavities with population inversion,” Phys. Rev. A 66, 023817 (2002).
[Crossref]

G. Tissoni, L. Spinelli, L. A. Lugiato, M. Brambilla, I. M. Perrini, and T. Maggipinto, “Spatio-temporal dynamics in semiconductor microresonators with thermal effects,” Opt. Express 10, 1009–1017 (2002).
[Crossref] [PubMed]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[Crossref]

Toenger, S.

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] [PubMed]

Tredicce, J. R.

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. R. Leite, C. Masoller, and J. R. Tredicce, “Rogue waves in optically injected lasers: Origin, predictability, and suppression,” Phys. Rev. A 87, 035802 (2013).
[Crossref]

M. G. Kovalsky, A. A. Hnilo, and J. R. Tredicce, “Extreme events in the ti: sapphire laser,” Opt. Lett. 36, 4449–4451 (2011).
[Crossref] [PubMed]

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] [PubMed]

S. Barland, O. Piro, M. Giudici, J. R. Tredicce, and S. Balle, “Experimental evidence of van der pol–fitzhugh–nagumo dynamics in semiconductor optical amplifiers,” Phys. Rev. E 68, 036209 (2003).
[Crossref]

Tykalewicz, B.

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, B. Kelleher, B. Tykalewicz, and S. Barland, “Dissipative phase solitons in semiconductor lasers,” Phys. Rev. Lett. 115, 043902 (2015).
[Crossref] [PubMed]

Veselic, I.

S. Birkholz, C. Brée, I. Veselić, A. Demircan, and G. Steinmeyer, “Ocean rogue waves and their phase space dynamics in the limit of a linear interference model,” Sci. Rep. 6. 35207 (2016).
[Crossref] [PubMed]

Vilaseca, R.

Vladimirov, A. G.

S. V. Fedorov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, “Effect of frequency detunings and finite relaxation rates on laser localized structures,” Phys. Rev. E 61, 5814–5824 (2000).
[Crossref]

Walczak, P.

F. Gustave, C. Rimoldi, P. Walczak, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Formation of phase soliton complexes in an optically injected semiconductor laser,” Eur. Phys. J. D 716, 154 (2017).
[Crossref]

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

Wetzel, B.

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] [PubMed]

Yao, A. M.

C. J. Gibson, A. M. Yao, and G.-L. Oppo, “Optical rogue waves in vortex turbulence,” Phys. Rev. Lett. 116, 043903 (2016).
[Crossref] [PubMed]

G.-L. Oppo, A. M. Yao, and D. Cuozzo, “Self-organization, pattern formation, cavity solitons, and rogue waves in singly resonant optical parametric oscillators,” Phys. Rev. A 88, 043813 (2013).
[Crossref]

Zamora-Munt, J.

J. Ahuja, D. B. Nalawade, J. Zamora-Munt, R. Vilaseca, and C. Masoller, “Rogue waves in injected semiconductor lasers with current modulation: role of the modulation phase,” Opt. Express 22, 28377–28382 (2014).
[Crossref] [PubMed]

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. R. Leite, C. Masoller, and J. R. Tredicce, “Rogue waves in optically injected lasers: Origin, predictability, and suppression,” Phys. Rev. A 87, 035802 (2013).
[Crossref]

Eur. Phys. J. D (1)

F. Gustave, C. Rimoldi, P. Walczak, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Formation of phase soliton complexes in an optically injected semiconductor laser,” Eur. Phys. J. D 716, 154 (2017).
[Crossref]

Nat. Commun. (2)

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] [PubMed]

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] [PubMed]

Nat. Phys. (1)

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,” Nat. Phys. 6, 790–795 (2010).
[Crossref]

Nature (1)

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

Opt. Express (5)

Opt. Lett. (1)

Phys. D Nonlinear Phenom. (1)

H. Chaté, A. Pikovsky, and O. Rudzick, “Forcing oscillatory media: phase kinks vs. synchronization,” Phys. D Nonlinear Phenom. 131, 17–30 (1999).
[Crossref]

Phys. Lett. A (1)

K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374, 3585–3589 (2010).
[Crossref]

Phys. Rev. A (8)

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. R. Leite, C. Masoller, and J. R. Tredicce, “Rogue waves in optically injected lasers: Origin, predictability, and suppression,” Phys. Rev. A 87, 035802 (2013).
[Crossref]

G.-L. Oppo, A. M. Yao, and D. Cuozzo, “Self-organization, pattern formation, cavity solitons, and rogue waves in singly resonant optical parametric oscillators,” Phys. Rev. A 88, 043813 (2013).
[Crossref]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, and S. Barland, “Phase solitons and domain dynamics in an optically injected semiconductor laser,” Phys. Rev. A 93, 063824 (2016).
[Crossref]

A. Coillet, J. Dudley, G. Genty, L. Larger, and Y. K. Chembo, “Optical rogue waves in whispering-gallery-mode resonators,” Phys. Rev. A 89, 013835 (2014).
[Crossref]

S. Coulibaly, M. Clerc, F. Selmi, and S. Barbay, “Extreme events following bifurcation to spatiotemporal chaos in a spatially extended microcavity laser,” Phys. Rev. A 95, 023816 (2017).
[Crossref]

C. Rimoldi, S. Barland, F. Prati, and G. Tissoni, “Spatiotemporal extreme events in a laser with a saturable absorber,” Phys. Rev. A 95, 023841 (2017).
[Crossref]

L. Spinelli, G. Tissoni, L. A. Lugiato, and M. Brambilla, “Thermal effects and transverse structures in semiconductor microcavities with population inversion,” Phys. Rev. A 66, 023817 (2002).
[Crossref]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[Crossref]

Phys. Rev. E (4)

S. Barland, O. Piro, M. Giudici, J. R. Tredicce, and S. Balle, “Experimental evidence of van der pol–fitzhugh–nagumo dynamics in semiconductor optical amplifiers,” Phys. Rev. E 68, 036209 (2003).
[Crossref]

S. V. Fedorov, A. G. Vladimirov, G. V. Khodova, and N. N. Rosanov, “Effect of frequency detunings and finite relaxation rates on laser localized structures,” Phys. Rev. E 61, 5814–5824 (2000).
[Crossref]

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

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88, 013207 (2013).
[Crossref]

Phys. Rev. Lett. (8)

R. Höhmann, U. Kuhl, H.-J. Stöckmann, L. Kaplan, and E. Heller, “Freak waves in the linear regime: A microwave study,” Phys. Rev. Lett. 104, 093901 (2010).
[Crossref] [PubMed]

C. J. Gibson, A. M. Yao, and G.-L. Oppo, “Optical rogue waves in vortex turbulence,” Phys. Rev. Lett. 116, 043903 (2016).
[Crossref] [PubMed]

F. Gustave, L. Columbo, G. Tissoni, M. Brambilla, F. Prati, B. Kelleher, B. Tykalewicz, and S. Barland, “Dissipative phase solitons in semiconductor lasers,” Phys. Rev. Lett. 115, 043902 (2015).
[Crossref] [PubMed]

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

C. Lecaplain, P. Grelu, J. M. 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] [PubMed]

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

P. Coullet, L. Gil, and J. Lega, “Defect-mediated turbulence,” Phys. Rev. Lett. 62, 1619–1622 (1989).
[Crossref] [PubMed]

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] [PubMed]

Quantum and Semiclassical Optics: J. Euro. Opt. Soc. Part B (1995–1998) (1)

S. Longhi, “Nonlinear travelling pulses in laser injection locking,” Quantum and Semiclassical Optics: J. Euro. Opt. Soc. Part B (1995–1998) 10, 617–635 (1998).
[Crossref]

Sci. Rep. (1)

S. Birkholz, C. Brée, I. Veselić, A. Demircan, and G. Steinmeyer, “Ocean rogue waves and their phase space dynamics in the limit of a linear interference model,” Sci. Rep. 6. 35207 (2016).
[Crossref] [PubMed]

Other (4)

C. Kharif, E. Pelinovsky, and A. Slunyaev, Rogue Waves in the Ocean (Advances in Geophysical and Environmental Mechanics and Mathematics) (Springer, 2009).

S. Randoux, P. Suret, and G. El, “Identification of rogue waves from scattering transform analysis of periodized waveforms,” arXiv preprint https://arXiv:1512.04707 (2015).

P. Walczak, C. Rimoldi, F. Gustave, L. Columbo, M. Brambilla, F. Prati, G. Tissoni, and S. Barland, “Extreme events induced by collisions in a forced semiconductor laser,” Submitted to Opt. Lett. (May2017). https://arxiv.org/abs/1705.02153 .
[Crossref]

F. Gustave, “Phase dynamics and dissipative solitons in semiconductor lasers,” Ph.D. thesis, Université de Nice Sophia Antipolis (2016).

Supplementary Material (2)

NameDescription
» Visualization 1       Spatio-temporal diagram and phase dynamics of the experimental data, as reported also in Fig. 3.
» Visualization 2       Spatio-temporal diagram and phase dynamics of the same simulation as in Fig. 7. Please note that extreme events are not present in the shown interval.

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Figures (13)

Fig. 1
Fig. 1

Scheme of the experimental setup. SOA semiconductor optical amplifier, M mirrors, BS beam splitters, OI optical isolator, Piezo piezoelectric actuator. See text for details.

Fig. 2
Fig. 2

Dynamical and statistical properties of abnormal events. (a) Spatio-temporal diagram of the optical power along 1500 roundtrips, (b) logarithm of the probability density function of the total power and (c) distribution of the peak amplitudes. Both (b) and (c) are computed on long time traces of length ≃ 27 000 × τc (5 × 106 points)

Fig. 3
Fig. 3

Power and phase dynamics around the formation of an abnormal event. (a) spatio-temporal diagram focused on one event, taken around roundtrip 1000 of Fig. 2(a), (b) Power profiles corresponding to roundtrip 40, 83, 95 and 120 and depicted by red horizontal lines in (a), (d) phase trajectory in the Argand plane before the abnormal event (roundtrip 40) and (c) at the maximum peak power of the event (roundtrip 83). (See also Visualization 1 in supplementary materials).

Fig. 4
Fig. 4

Evolution of the phase when approaching the abnormal event. Left : 100 ns long time trace of the phase centered on the maximum of an abnormal event showing the acquisition of positive phase rotations. Right : zoom of the same time trace at the beginning of the change of slope. The initial phase is arbitrarily set to zero.

Fig. 5
Fig. 5

(a) Stationary homogenous solution of Eqs. (1)(2) as indicated in Eq. (3) for the parameters µ = 1.1, and θ = −3.04 (see the text for the other parameters). Points A, B and C represent the three injection locked solutions corresponding to the value of injection used in the simulations y = 0.004, highlighted by the red dashed vertical line. (b) Instability domains in the (I, n) plane for the model described in Eqs. (1)(2) (in green) and for the pure rate equation model with d = 0 (in blue).

Fig. 6
Fig. 6

Spatiotemporal diagrams in (a) the experimental reference frame at fixed z and (b) in the numerical reference frame, where the diagram is built through the stacking of the full cavity spatial profiles acquired each roundtrip.

Fig. 7
Fig. 7

Zoom (b) of the spatio-temporal diagram centered on an event of high intensity (3) and intensity time traces (a) at fixed roundtrip corresponding to the horizontal cuts highlighted on the diagram. (For the phase dynamics see Visualization 2 in supplementary materials).

Fig. 8
Fig. 8

PDF of the temporal peak heights (in black), computed over 2.1×106 roundtrips (a), the green dashed line corresponds to a Gaussian fit of the initial slope. PDF (in black) of all the values explored by the intensity (b), computed over 2.1×105 roundtrips. The green and red dashed lines correspond to two negative exponential fits highlighting the change of the slopes in the tail of the distribution. The data in dark yellow shows the corresponding PDFs for a set of data simulated with the same parameters but a different θ = −3.049.

Fig. 9
Fig. 9

Histogram of the values assumed by the electric field in the complex plane (Re(E), Im(E)) in the experimental case (a), computed over 104 roundtrips, and in the numerical case (b), computed over 105 roundtrips, in order to mantain the same number of events associated to the bounded state.

Fig. 10
Fig. 10

Evolution of the phase when approaching an abnormally high event: the high-peak event (occurring at the time indicated by the red vertical dashed line) is to be associated with a change in the slope of the phase. In particular in this case we notice an initially balanced situation between the number of positive and negative chiral charges that breaks when the negative chiral charge disappears. A little later an abnormal event takes place.

Fig. 11
Fig. 11

Total evolution of the phase during 2×104 roundtrips. The red vertical dashed lines correspond to five different abnormal events occurring during this time interval.

Fig. 12
Fig. 12

Phase portrait in the (Re(E), Im(E)) plane (a) and in the (D, I) plane (b) of the trajectory of the system at fixed roundtrip in the time region close to an abnormal event highlighted in Fig. 7. A, B and C represent the injection locked solutions highlighted in Fig. 5. The red (blue) cross indicates a complete counterclockwise (clockwise) phase rotation, which starts from the point highlighted by the red (blue) circle. As for the dashed red line/circle see text.

Fig. 13
Fig. 13

Spatio-temporal diagram of the intensity I of the electric field (a) and of the carrier population D (b). The light blue (orange) line corresponds to clockwise (counterclockwise) phase rotations, the abnormal event has been highlighted by the green circle.

Equations (8)

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E z + E t d 2 E z 2 = T [ ( 1 + i θ ) E + y + ( 1 i α ) E D ]
D t = b [ μ D ( 1 + | E | 2 ) ]
y 2 = ρ s 2 [ ( 1 D s ) 2 + ( θ + α D s ) 2 ]
ϕ s = arctan ( θ + α D s D s 1 )
D s = μ 1 + ρ s 2
ρ z + ρ t = T [ ( D 1 ) ρ + y cos ϕ ]
ϕ z + ϕ t = T [ θ + α D + y ρ sin ϕ ]
D t = b [ μ D ( 1 + ρ 2 ) ] ,

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