Abstract

Semiconductor lasers with continuous-wave optical injection display a rich variety of behaviors, including stable locking, periodic or chaotic oscillations, excitable pulses, etc. Within the chaotic regime it has been shown that the laser intensity can display extreme pulses, which have been identified as optical rogue waves (RWs), and it has also been shown that such extreme pulses can be completely suppressed via direct modulation of the laser current, with appropriated modulation amplitude and frequency. Here we perform a numerical analysis of the RW statistics and show that, when RWs are not suppressed by current modulation, their probability of occurrence strongly depends on the phase of the modulation. If the modulation is slow (the modulation frequency, fmod, is below the relaxation oscillation frequency, fro), the RWs occur within a well-defined interval of values of the modulation phase, i.e., there is a “safe” window of phases where no RWs occur. The most extreme RWs occur for modulation phases that are at the boundary of the safe window. When the modulation is fast (fmod > fro), there is no safe phase window; however, the RWs are likely to occur at particular values of the modulation phase. Our findings are of interest for the study of RWs in other systems, where a similar response to external forcing could be observed, and we hope that they will motivate experimental investigations to further elucidate the role of the modulation phase in the likelihood of the occurrence of RWs.

© 2014 Optical Society of America

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References

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  1. J. R. Tredicce, F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, “Instabilities in lasers with an injected signal,” J. Opt. Soc. Am. B 2, 173–183 (1985).
    [Crossref]
  2. S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 216, 1–128 (2005).
    [Crossref]
  3. D. Lenstra, B. H. Verbeek, and A. J. den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. QE-21, 674–679 (1985).
    [Crossref]
  4. J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiments,” IEEE J. Quantum Electron. QE28, 93–108 (1992).
    [Crossref]
  5. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Phot. 4, 58–61 (2010).
    [Crossref]
  6. M. G. Kovalsky, A. Hnilo, and J. R. Tredicce, “Extreme events in the Ti:sapphire laser,” Opt. Lett. 36, 4449–4451 (2011).
    [Crossref] [PubMed]
  7. E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
    [Crossref]
  8. A. K. Dal Bosco, D. Wolfersberger, and M. Sciamanna, “Extreme events in time-delayed nonlinear optics,” Opt. Lett. 38, 703–705 (2013).
    [Crossref] [PubMed]
  9. J. A. Reinoso, J. Zamora-Munt, and C. Masoller, “Extreme intensity pulses in a semiconductor laser with a short external cavity,” Phys. Rev. E 87, 062913 (2013).
    [Crossref]
  10. K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Rare disruptive events in polarisation-resolved dynamics of optically injected 1550 nm VCSELs,” Electron. Lett. 48, 872–873 (2012).
    [Crossref]
  11. C. Bonatto, M. Feyereisen, S. Barland, M. Giudici, C. Masoller, J. R. Rios Leite, and J. R. Tredicce, “Deterministic optical rogue waves,” Phys. Rev. Lett. 107, 053901 (2011).
    [Crossref] [PubMed]
  12. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450, 1054–1057 (2007).
    [Crossref] [PubMed]
  13. J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. Rios Leite, C. Masoller, and J. R. Tredicce, “Rogue waves in optically injected lasers: Origin, predictability, and suppression,” Phys. Rev. A. 87, 035802 (2013).
    [Crossref]
  14. S. Perrone, J. Zamora-Munt, R. Vilaseca, and C. Masoller, “Controlling the likelihood of rogue waves in an optically injected semiconductor laser via direct current modulation,” Phys. Rev. A 89, 033804 (2014).
    [Crossref]

2014 (1)

S. Perrone, J. Zamora-Munt, R. Vilaseca, and C. Masoller, “Controlling the likelihood of rogue waves in an optically injected semiconductor laser via direct current modulation,” Phys. Rev. A 89, 033804 (2014).
[Crossref]

2013 (4)

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

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
[Crossref]

A. K. Dal Bosco, D. Wolfersberger, and M. Sciamanna, “Extreme events in time-delayed nonlinear optics,” Opt. Lett. 38, 703–705 (2013).
[Crossref] [PubMed]

J. A. Reinoso, J. Zamora-Munt, and C. Masoller, “Extreme intensity pulses in a semiconductor laser with a short external cavity,” Phys. Rev. E 87, 062913 (2013).
[Crossref]

2012 (1)

K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Rare disruptive events in polarisation-resolved dynamics of optically injected 1550 nm VCSELs,” Electron. Lett. 48, 872–873 (2012).
[Crossref]

2011 (2)

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

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

2010 (1)

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Phot. 4, 58–61 (2010).
[Crossref]

2007 (1)

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

2005 (1)

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 216, 1–128 (2005).
[Crossref]

1992 (1)

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiments,” IEEE J. Quantum Electron. QE28, 93–108 (1992).
[Crossref]

1985 (2)

J. R. Tredicce, F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, “Instabilities in lasers with an injected signal,” J. Opt. Soc. Am. B 2, 173–183 (1985).
[Crossref]

D. Lenstra, B. H. Verbeek, and A. J. den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. QE-21, 674–679 (1985).
[Crossref]

Adams, M. J.

K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Rare disruptive events in polarisation-resolved dynamics of optically injected 1550 nm VCSELs,” Electron. Lett. 48, 872–873 (2012).
[Crossref]

Arecchi, F. T.

Aviad, Y.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Phot. 4, 58–61 (2010).
[Crossref]

Babin, S. A.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
[Crossref]

Barland, S.

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. Rios 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. Rios Leite, and J. R. Tredicce, “Deterministic optical rogue waves,” Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

Bonatto, C.

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

Churkin, D. V.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
[Crossref]

Cohen, E.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Phot. 4, 58–61 (2010).
[Crossref]

Dal Bosco, A. K.

den Boef, A. J.

D. Lenstra, B. H. Verbeek, and A. J. den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. QE-21, 674–679 (1985).
[Crossref]

Falkovich, G.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
[Crossref]

Feyereisen, M.

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

Garbin, B.

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

Giudici, M.

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. Rios 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. Rios Leite, and J. R. Tredicce, “Deterministic optical rogue waves,” Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

Henning, I. D.

K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Rare disruptive events in polarisation-resolved dynamics of optically injected 1550 nm VCSELs,” Electron. Lett. 48, 872–873 (2012).
[Crossref]

Hnilo, A.

Hurtado, A.

K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Rare disruptive events in polarisation-resolved dynamics of optically injected 1550 nm VCSELs,” Electron. Lett. 48, 872–873 (2012).
[Crossref]

Jalali, B.

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

Kanter, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Phot. 4, 58–61 (2010).
[Crossref]

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.

Krauskopf, B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 216, 1–128 (2005).
[Crossref]

Lenstra, D.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 216, 1–128 (2005).
[Crossref]

D. Lenstra, B. H. Verbeek, and A. J. den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. QE-21, 674–679 (1985).
[Crossref]

Lippi, G. L.

Mark, J.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiments,” IEEE J. Quantum Electron. QE28, 93–108 (1992).
[Crossref]

Masoller, C.

S. Perrone, J. Zamora-Munt, R. Vilaseca, and C. Masoller, “Controlling the likelihood of rogue waves in an optically injected semiconductor laser via direct current modulation,” Phys. Rev. A 89, 033804 (2014).
[Crossref]

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

J. A. Reinoso, J. Zamora-Munt, and C. Masoller, “Extreme intensity pulses in a semiconductor laser with a short external cavity,” Phys. Rev. E 87, 062913 (2013).
[Crossref]

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

Mork, J.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiments,” IEEE J. Quantum Electron. QE28, 93–108 (1992).
[Crossref]

Perrone, S.

S. Perrone, J. Zamora-Munt, R. Vilaseca, and C. Masoller, “Controlling the likelihood of rogue waves in an optically injected semiconductor laser via direct current modulation,” Phys. Rev. A 89, 033804 (2014).
[Crossref]

Podivilov, E. V.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
[Crossref]

Puccioni, G. P.

Reidler, I.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Phot. 4, 58–61 (2010).
[Crossref]

Reinoso, J. A.

J. A. Reinoso, J. Zamora-Munt, and C. Masoller, “Extreme intensity pulses in a semiconductor laser with a short external cavity,” Phys. Rev. E 87, 062913 (2013).
[Crossref]

Rios Leite, J. R.

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. Rios 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. Rios Leite, and J. R. Tredicce, “Deterministic optical rogue waves,” Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

Ropers, C.

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

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Phot. 4, 58–61 (2010).
[Crossref]

Schires, K.

K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Rare disruptive events in polarisation-resolved dynamics of optically injected 1550 nm VCSELs,” Electron. Lett. 48, 872–873 (2012).
[Crossref]

Sciamanna, M.

Shu, X.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
[Crossref]

Simpson, T. B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 216, 1–128 (2005).
[Crossref]

Smirnov, S. V.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
[Crossref]

Solli, D. R.

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

Sugavanam, S.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
[Crossref]

Tarasov, N.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
[Crossref]

Tredicce, J. R.

J. Zamora-Munt, B. Garbin, S. Barland, M. Giudici, J. R. Rios 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. 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. Rios Leite, and J. R. Tredicce, “Deterministic optical rogue waves,” Phys. Rev. Lett. 107, 053901 (2011).
[Crossref] [PubMed]

J. R. Tredicce, F. T. Arecchi, G. L. Lippi, and G. P. Puccioni, “Instabilities in lasers with an injected signal,” J. Opt. Soc. Am. B 2, 173–183 (1985).
[Crossref]

Tromborg, B.

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiments,” IEEE J. Quantum Electron. QE28, 93–108 (1992).
[Crossref]

Turitsyn, S. K.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
[Crossref]

Turitsyna, E. G.

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
[Crossref]

Verbeek, B. H.

D. Lenstra, B. H. Verbeek, and A. J. den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. QE-21, 674–679 (1985).
[Crossref]

Vilaseca, R.

S. Perrone, J. Zamora-Munt, R. Vilaseca, and C. Masoller, “Controlling the likelihood of rogue waves in an optically injected semiconductor laser via direct current modulation,” Phys. Rev. A 89, 033804 (2014).
[Crossref]

Wieczorek, S.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 216, 1–128 (2005).
[Crossref]

Wolfersberger, D.

Zamora-Munt, J.

S. Perrone, J. Zamora-Munt, R. Vilaseca, and C. Masoller, “Controlling the likelihood of rogue waves in an optically injected semiconductor laser via direct current modulation,” Phys. Rev. A 89, 033804 (2014).
[Crossref]

J. A. Reinoso, J. Zamora-Munt, and C. Masoller, “Extreme intensity pulses in a semiconductor laser with a short external cavity,” Phys. Rev. E 87, 062913 (2013).
[Crossref]

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

Electron. Lett. (1)

K. Schires, A. Hurtado, I. D. Henning, and M. J. Adams, “Rare disruptive events in polarisation-resolved dynamics of optically injected 1550 nm VCSELs,” Electron. Lett. 48, 872–873 (2012).
[Crossref]

IEEE J. Quantum Electron. (2)

D. Lenstra, B. H. Verbeek, and A. J. den Boef, “Coherence collapse in single-mode semiconductor lasers due to optical feedback,” IEEE J. Quantum Electron. QE-21, 674–679 (1985).
[Crossref]

J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiments,” IEEE J. Quantum Electron. QE28, 93–108 (1992).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Phot (1)

E. G. Turitsyna, S. V. Smirnov, S. Sugavanam, N. Tarasov, X. Shu, S. A. Babin, E. V. Podivilov, D. V. Churkin, G. Falkovich, and S. K. Turitsyn, “The laminarturbulent transition in a fibre laser,” Nat. Phot 7, 783–786 (2013).
[Crossref]

Nat. Phot. (1)

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Phot. 4, 58–61 (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. Lett. (2)

Phys. Rep. (1)

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 216, 1–128 (2005).
[Crossref]

Phys. Rev. A (1)

S. Perrone, J. Zamora-Munt, R. Vilaseca, and C. Masoller, “Controlling the likelihood of rogue waves in an optically injected semiconductor laser via direct current modulation,” Phys. Rev. A 89, 033804 (2014).
[Crossref]

Phys. Rev. A. (1)

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

Phys. Rev. E (1)

J. A. Reinoso, J. Zamora-Munt, and C. Masoller, “Extreme intensity pulses in a semiconductor laser with a short external cavity,” Phys. Rev. E 87, 062913 (2013).
[Crossref]

Phys. Rev. Lett. (1)

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

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Figures (4)

Fig. 1
Fig. 1

(a) Number of detected RWs as a function of the phase of the modulation, Φ. (b) Mean RW amplitude as a function of Φ. The error bars indicate the standard deviation of the distribution of RW amplitudes. The parameters are: Δν = 0.22 GHz (Point A), Amod = 0.2, fmod = 3.5 GHz, D = 10−3 ns−1, other parameters are as indicated in the text.

Fig. 2
Fig. 2

(a) Number of detected RWs vs the modulation phase when the noise strength is D = 10−4 ns−1 (black) and D = 5 × 10−3 ns−1 (red). (b) Total number of RWs vs the noise strength without modulation (Amod = 0, circles) and with modulation (Amod = 0.2, triangles). Other parameters are as in Fig. 1.

Fig. 3
Fig. 3

Influence of the modulation frequency. Number of detected RWs vs the modulation phase for (a) fmod = 2 GHz, (b) 3 GHz and (c) 5 GHz. Panel (d) displays a detail of (c). Note that the vertical scale in (a) and (b) is logarithmic, but a linear scale is used in (c) and (d) in order to better display the “quantized” character of the modulation phases when RWs occur. All other parameters are as in Fig. 1.

Fig. 4
Fig. 4

(a) Number of detected RWs and (b) mean RW height as a function of the modulation phase. Δν = −0.24 GHz (Point B), fmod = 3.5 GHz and other parameters are as in Fig. 1. (c) as panel (a) but for fmod = 5 GHz.

Equations (2)

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d E d t = κ ( 1 + i α ) ( N 1 ) E + i Δ ω E + P inj + D ξ ( t )
d N d t = γ N ( μ ( t ) N | E | 2 )

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