Abstract

We introduce a general technique how to reveal in experiments of limited electrical bandwidth which is lower than the optical bandwidth of the optical signal under study, whether the statistical properties of the light source obey Gaussian distribution or mode correlations do exist. To do that one needs to perform measurements by decreasing the measurement bandwidth. We develop a simple model of bandwidth-limited measurements and predict universal laws how intensity probability density function and intensity auto-correlation function of ideal completely stochastic source of Gaussian statistics depend on limited measurement bandwidth and measurement noise level. Results of experimental investigation are in good agreement with model predictions. In particular, we reveal partial mode correlations in the radiation of quasi-CW Raman fibre laser.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
  7. C. Lecaplain, Ph. 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(23), 233901 (2012).
    [Crossref] [PubMed]
  8. M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528(2), 47–89 (2013).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [PubMed]
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    [Crossref]
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    [Crossref]
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2014 (4)

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

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542(2), 1–132 (2014).
[Crossref]

S. Randoux, P. Walczak, M. Onorato, and P. Suret, “Intermittency in integrable turbulence,” Phys. Rev. Lett. 113(11), 113902 (2014).
[Crossref] [PubMed]

I. D. Vatnik, O. A. Gorbunov, and D. V. Churkin, “Narrow-band generation and mode correlations in a short Raman fibre laser,” Laser Phys. 24(2), 025103 (2014).
[Crossref]

2013 (5)

S. V. Smirnov and D. V. Churkin, “Modeling of spectral and statistical properties of a random distributed feedback fiber laser,” Opt. Express 21(18), 21236–21241 (2013).
[Crossref] [PubMed]

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 laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013).
[Crossref]

A. E. Bednyakova, O. A. Gorbunov, M. O. Politko, S. I. Kablukov, S. V. Smirnov, D. V. Churkin, M. P. Fedoruk, and S. A. Babin, “Generation dynamics of the narrowband Yb-doped fiber laser,” Opt. Express 21(7), 8177–8182 (2013).
[Crossref] [PubMed]

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528(2), 47–89 (2013).
[Crossref]

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, “Recent progress in investigating optical rogue waves,” J. Opt. 15(6), 060201 (2013).
[Crossref]

2012 (3)

S. Randoux and P. Suret, “Experimental evidence of extreme value statistics in Raman fiber lasers,” Opt. Lett. 37(4), 500–502 (2012).
[Crossref] [PubMed]

C. Lecaplain, Ph. 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(23), 233901 (2012).
[Crossref] [PubMed]

D. V. Churkin and S. V. Smirnov, “Numerical modelling of spectral, temporal and statistical properties of Raman fiber lasers,” Opt. Commun. 285(8), 2154–2160 (2012).
[Crossref]

2011 (2)

D. V. Churkin, O. A. Gorbunov, and S. V. Smirnov, “Extreme value statistics in Raman fiber lasers,” Opt. Lett. 36(18), 3617–3619 (2011).
[Crossref] [PubMed]

B. Kibler, K. Hammani, C. Michel, C. Finot, and A. Picozzi, “Rogue waves, rational solitons and wave turbulence theory,” Phys. Lett. A 375(35), 3149–3155 (2011).
[Crossref]

2010 (1)

2009 (1)

D. Bourlaug, S. Fathpour, and B. Jalali, “Extreme Value Statistics in Silicon Photonics,” IEEE Photonics J. 1(1), 33–39 (2009).
[Crossref]

2008 (1)

2007 (2)

2005 (1)

Akhmediev, N.

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, “Recent progress in investigating optical rogue waves,” J. Opt. 15(6), 060201 (2013).
[Crossref]

C. Lecaplain, Ph. 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(23), 233901 (2012).
[Crossref] [PubMed]

Arecchi, F. T.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528(2), 47–89 (2013).
[Crossref]

Babin, S. A.

Bednyakova, A. E.

Bortolozzo, U.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528(2), 47–89 (2013).
[Crossref]

Bourlaug, D.

D. Bourlaug, S. Fathpour, and B. Jalali, “Extreme Value Statistics in Silicon Photonics,” IEEE Photonics J. 1(1), 33–39 (2009).
[Crossref]

Christodoulides, D. N.

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542(2), 1–132 (2014).
[Crossref]

Churkin, D. V.

I. D. Vatnik, O. A. Gorbunov, and D. V. Churkin, “Narrow-band generation and mode correlations in a short Raman fibre laser,” Laser Phys. 24(2), 025103 (2014).
[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 laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013).
[Crossref]

A. E. Bednyakova, O. A. Gorbunov, M. O. Politko, S. I. Kablukov, S. V. Smirnov, D. V. Churkin, M. P. Fedoruk, and S. A. Babin, “Generation dynamics of the narrowband Yb-doped fiber laser,” Opt. Express 21(7), 8177–8182 (2013).
[Crossref] [PubMed]

S. V. Smirnov and D. V. Churkin, “Modeling of spectral and statistical properties of a random distributed feedback fiber laser,” Opt. Express 21(18), 21236–21241 (2013).
[Crossref] [PubMed]

D. V. Churkin and S. V. Smirnov, “Numerical modelling of spectral, temporal and statistical properties of Raman fiber lasers,” Opt. Commun. 285(8), 2154–2160 (2012).
[Crossref]

D. V. Churkin, O. A. Gorbunov, and S. V. Smirnov, “Extreme value statistics in Raman fiber lasers,” Opt. Lett. 36(18), 3617–3619 (2011).
[Crossref] [PubMed]

D. V. Churkin, S. V. Smirnov, and E. V. Podivilov, “Statistical properties of partially coherent cw fiber lasers,” Opt. Lett. 35(19), 3288–3290 (2010).
[PubMed]

S. A. Babin, D. V. Churkin, A. E. Ismagulov, S. I. Kablukov, and E. V. Podivilov, “Four-wave-mixing-induced turbulent spectral broadening in a long Raman fiber laser,” J. Opt. Soc. Am. B 24(8), 1729–1738 (2007).
[Crossref]

Coen, S.

Dias, F.

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

Dudley, J. M.

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

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, “Recent progress in investigating optical rogue waves,” J. Opt. 15(6), 060201 (2013).
[Crossref]

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16(6), 3644–3651 (2008).
[Crossref] [PubMed]

Eggleton, B. J.

Erkintalo, M.

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

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 laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013).
[Crossref]

Fathpour, S.

D. Bourlaug, S. Fathpour, and B. Jalali, “Extreme Value Statistics in Silicon Photonics,” IEEE Photonics J. 1(1), 33–39 (2009).
[Crossref]

Fedoruk, M. P.

Finot, C.

B. Kibler, K. Hammani, C. Michel, C. Finot, and A. Picozzi, “Rogue waves, rational solitons and wave turbulence theory,” Phys. Lett. A 375(35), 3149–3155 (2011).
[Crossref]

Garnier, J.

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542(2), 1–132 (2014).
[Crossref]

Genty, G.

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

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16(6), 3644–3651 (2008).
[Crossref] [PubMed]

González-Herráez, M.

Gorbunov, O. A.

Grelu, Ph.

C. Lecaplain, Ph. 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(23), 233901 (2012).
[Crossref] [PubMed]

Hammani, K.

B. Kibler, K. Hammani, C. Michel, C. Finot, and A. Picozzi, “Rogue waves, rational solitons and wave turbulence theory,” Phys. Lett. A 375(35), 3149–3155 (2011).
[Crossref]

Hansson, T.

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542(2), 1–132 (2014).
[Crossref]

Ismagulov, A. E.

Jalali, B.

D. Bourlaug, S. Fathpour, and B. Jalali, “Extreme Value Statistics in Silicon Photonics,” IEEE Photonics J. 1(1), 33–39 (2009).
[Crossref]

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

Kablukov, S. I.

Kibler, B.

B. Kibler, K. Hammani, C. Michel, C. Finot, and A. Picozzi, “Rogue waves, rational solitons and wave turbulence theory,” Phys. Lett. A 375(35), 3149–3155 (2011).
[Crossref]

Koonath, P.

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

Lecaplain, C.

C. Lecaplain, Ph. 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(23), 233901 (2012).
[Crossref] [PubMed]

Martin-Lopez, S.

Michel, C.

B. Kibler, K. Hammani, C. Michel, C. Finot, and A. Picozzi, “Rogue waves, rational solitons and wave turbulence theory,” Phys. Lett. A 375(35), 3149–3155 (2011).
[Crossref]

Millot, G.

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542(2), 1–132 (2014).
[Crossref]

Montina, A.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528(2), 47–89 (2013).
[Crossref]

Onorato, M.

S. Randoux, P. Walczak, M. Onorato, and P. Suret, “Intermittency in integrable turbulence,” Phys. Rev. Lett. 113(11), 113902 (2014).
[Crossref] [PubMed]

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528(2), 47–89 (2013).
[Crossref]

Picozzi, A.

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542(2), 1–132 (2014).
[Crossref]

B. Kibler, K. Hammani, C. Michel, C. Finot, and A. Picozzi, “Rogue waves, rational solitons and wave turbulence theory,” Phys. Lett. A 375(35), 3149–3155 (2011).
[Crossref]

Podivilov, E. V.

Politko, M. O.

Randoux, S.

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542(2), 1–132 (2014).
[Crossref]

S. Randoux, P. Walczak, M. Onorato, and P. Suret, “Intermittency in integrable turbulence,” Phys. Rev. Lett. 113(11), 113902 (2014).
[Crossref] [PubMed]

S. Randoux and P. Suret, “Experimental evidence of extreme value statistics in Raman fiber lasers,” Opt. Lett. 37(4), 500–502 (2012).
[Crossref] [PubMed]

Residori, S.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528(2), 47–89 (2013).
[Crossref]

Ropers, C.

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

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 laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013).
[Crossref]

Smirnov, S. V.

Solli, D. R.

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, “Recent progress in investigating optical rogue waves,” J. Opt. 15(6), 060201 (2013).
[Crossref]

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

Soto-Crespo, J. M.

C. Lecaplain, Ph. 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(23), 233901 (2012).
[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 laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013).
[Crossref]

Suret, P.

S. Randoux, P. Walczak, M. Onorato, and P. Suret, “Intermittency in integrable turbulence,” Phys. Rev. Lett. 113(11), 113902 (2014).
[Crossref] [PubMed]

A. Picozzi, J. Garnier, T. Hansson, P. Suret, S. Randoux, G. Millot, and D. N. Christodoulides, “Optical wave turbulence: Toward a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics,” Phys. Rep. 542(2), 1–132 (2014).
[Crossref]

S. Randoux and P. Suret, “Experimental evidence of extreme value statistics in Raman fiber lasers,” Opt. Lett. 37(4), 500–502 (2012).
[Crossref] [PubMed]

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 laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013).
[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 laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013).
[Crossref]

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, “Recent progress in investigating optical rogue waves,” J. Opt. 15(6), 060201 (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 laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013).
[Crossref]

Vanholsbeeck, F.

Vatnik, I. D.

I. D. Vatnik, O. A. Gorbunov, and D. V. Churkin, “Narrow-band generation and mode correlations in a short Raman fibre laser,” Laser Phys. 24(2), 025103 (2014).
[Crossref]

Walczak, P.

S. Randoux, P. Walczak, M. Onorato, and P. Suret, “Intermittency in integrable turbulence,” Phys. Rev. Lett. 113(11), 113902 (2014).
[Crossref] [PubMed]

IEEE Photonics J. (1)

D. Bourlaug, S. Fathpour, and B. Jalali, “Extreme Value Statistics in Silicon Photonics,” IEEE Photonics J. 1(1), 33–39 (2009).
[Crossref]

J. Opt. (1)

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, “Recent progress in investigating optical rogue waves,” J. Opt. 15(6), 060201 (2013).
[Crossref]

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

Laser Phys. (1)

I. D. Vatnik, O. A. Gorbunov, and D. V. Churkin, “Narrow-band generation and mode correlations in a short Raman fibre laser,” Laser Phys. 24(2), 025103 (2014).
[Crossref]

Nat. Photonics (2)

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

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Figures (5)

Fig. 1
Fig. 1 (a) Temporal dynamics (b) intensity PDFs and (c) intensity ACFs measured with different bandwidths.
Fig. 2
Fig. 2 Modelled (a) optical spectrum, (b) intensity dynamics, and (c) intensity PDF. At insert – intensity ACF.
Fig. 3
Fig. 3 Noise limitations. (a) Intensity PDFs (at insert – PDF of the noise), (b) Left slope of the intensity PDF and (c) Intensity ACFs (at insert - ACF background level) for different values of the noise power.
Fig. 4
Fig. 4 Bandwidth limitations. (a) Intensity time dynamics, (b) Intensity PDFs and (c) Intensity ACFs for different values the bandwidth.
Fig. 5
Fig. 5 Experimentally measured and numerically calculated (a) intensity PDF’ slope and (b) intensity ACF background level as function of electrical to spectral bandwidth ratio.

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