Abstract

We present theoretical investigations including simulations and statistical analyses on the fluctuations of the temporal output power in a Brillouin erbium-doped fiber laser. The generation of even Stokes waves up to the 5th order is considered by solving coupled-mode equations including SBS and Kerr nonlinearities. It is demonstrated that by increasing the EDFA pump power and generating a few orders of Stokes waves in such a laser, there are strong power fluctuations and rogue events are expected. Transition from Gaussian-like to levy-like regime is described as the power is increased from threshold resulting in the initial Stokes wave generation to well beyond threshold generating 5 effective even Stokes waves. Accordingly, phase portraits confirm increasing fluctuations as a function of the power. It is also shown that at the SBS lasing threshold, the output signals have the maximum correlation over replicas in round trips, nevertheless by enhancing the power, the correlation diminishes, which results in a full symmetry breaking and the system radiates in a chaotic manner and exhibits random laser behavior.

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

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References

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2019 (1)

2017 (5)

V. L. Iezzi, S. Loranger, and R. Kashyap, “High sensitivity distributed temperature fiber sensor using stimulated Brillouin scattering,” Opt. Express 25(26), 32591–32596 (2017).
[Crossref]

L. Zhang, C. Wang, Z. Li, Y. Xu, B. Saxena, S. Gao, L. Chen, and X. Bao, “High-efficiency Brillouin random fiber laser using all-polarization maintaining ring cavity,” Opt. Express 25(10), 11306–11314 (2017).
[Crossref]

I. R. Roa González, B. C. Lima, P. I. R. Pincheira, A. A. Brum, A. M. S. Macêdo, G. L. Vasconcelos, L. S. Menezes, E. P. Raposo, A. S. L. Gomes, and R. Kashyap, “Turbulence hierarchy in a random fibre laser,” Nat. Commun. 8(1), 15731 (2017).
[Crossref]

B. C. Lima, P. I. R. Pincheira, E. P. Raposo, L. S. Menezes, C. B. Araújo, A. S. L. Gomes, and R. Kashyap, “Extreme-value statistics of intensities in a cw-pumped random fiber laser,” Phys. Rev. A 96(1), 013834 (2017).
[Crossref]

B. C. Lima, A. S. L. Gomes, P. I. R. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. Araújo, and R. Kashyap, “Observation of Lévy statistics in one-dimensional erbium-based random fiber laser,” J. Opt. Soc. Am. B 34(2), 293–299 (2017).
[Crossref]

2016 (2)

V. L. Iezzi, T. F. S. Büttner, A. Tehranchi, S. Loranger, I. V. Kabakova, B. J. Eggleton, and R. Kashyap, “Temporal characterization of a multi-wavelength Brillouin-erbium fiber laser,” New J. Phys. 18(5), 055003 (2016).
[Crossref]

S. Basak, A. Blanco, and C. López, “Large fluctuations at the lasing threshold of solid- and liquid-state dye lasers,” Sci. Rep. 6(1), 32134 (2016).
[Crossref]

2015 (2)

N. Ghofraniha, I. Viola, F. Di Maria, G. Barbarella, G. Gigli, L. Leuzzi, and C. Conti, “Experimental evidence of replica symmetry breaking in random lasers,” Nat. Commun. 6(1), 6058 (2015).
[Crossref]

F. Antenucci, A. Crisanti, and L. Leuzzi, “The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra,” Sci. Rep. 5(1), 16792 (2015).
[Crossref]

2014 (2)

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

2012 (2)

2011 (5)

2009 (2)

M. M. Nasir, Z. Yusoff, M. Al-Mansoori, H. A. Rashid, and P. Choudhury, “Low threshold and efficient multi-wavelength Brillouin-erbium fiber laser incorporating a fiber Bragg grating filter with intra-cavity pre-amplified Brillouin pump,” Laser Phys. Lett. 6(1), 54–58 (2009).
[Crossref]

M. H. Al-Mansoori and M. A. Mahdi, “Multiwavelength L-band Brillouin-erbium comb fiber laser utilizing nonlinear amplifying loop mirror,” J. Lightwave Technol. 27(22), 5038–5044 (2009).
[Crossref]

2008 (2)

M. M. Nasir, Z. Yusoff, M. Al-Mansoori, H. A. Rashid, and P. Choudhury, “Broadly tunable multi-wavelength Brillouin-erbium fiber laser in a Fabry-Perot cavity,” Laser Phys. Lett. 5(11), 812–816 (2008).
[Crossref]

G. Qin, H. Sotobayashi, M. Tsuchiya, A. Mori, T. Suzuki, and Y. Ohishi, “Stimulated Brillouin scattering in a single-mode tellurite fiber for amplification, lasing, and slow light generation,” J. Lightwave Technol. 26(5), 492–498 (2008).
[Crossref]

2007 (1)

S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007).
[Crossref]

2006 (1)

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Intrinsic intensity fluctuations in random lasers,” Phys. Rev. A 74(5), 053808 (2006).
[Crossref]

2005 (3)

2004 (1)

Y. Song, L. Zhan, S. Hu, Q. Ye, and Y. Xia, “Tunable multiwavelength Brillouin-erbium fiber laser with a polarization-maintaining fiber Sagnac loop filter,” IEEE Photonics Technol. Lett. 16(9), 2015–2017 (2004).
[Crossref]

2002 (1)

2001 (1)

B. Min, P. Kim, and N. Park, “Flat amplitude equal spacing 798-channel Rayleigh-assisted Brillouin/Raman multiwavelength comb generation in dispersion compensating fiber,” IEEE Photonics Technol. Lett. 13(12), 1352–1354 (2001).
[Crossref]

2000 (1)

H. Li and K. Ogusu, “Instability of stimulated Brillouin scattering in a fiber ring resonator,” Opt. Rev. 7(4), 303–308 (2000).
[Crossref]

1999 (1)

H. Li and K. Ogusu, “Dynamic behavior of stimulated Brillouin scattering in a single-mode optical fiber,” Jpn. J. Appl. Phys. 38(Part 1, No. 11), 6309–6315 (1999).
[Crossref]

1997 (1)

G. J. Cowle, D. Y. Stepanov, and Y. T. Chieng, “Brillouin/Erbium fiber lasers,” J. Lightwave Technol. 15(7), 1198–1204 (1997).
[Crossref]

1996 (2)

V. Lecoeuche, S. Randoux, B. Segard, and J. Zemmouri, “Dynamics of stimulated Brillouin scattering with feedback,” Quantum Semiclassical Opt. 8(6), 1109–1145 (1996).
[Crossref]

V. Lecoeuche, S. Randoux, B. Ségard, and J. Zemmouri, “Dynamics of a Brillouin fiber ring laser: Off-resonant case,” Phys. Rev. A 53(4), 2822–2828 (1996).
[Crossref]

1995 (1)

S. Randoux, V. Lecoeuche, B. Segard, and J. Zemmouri, “Dynamical behavior of a Brillouin fiber ring laser emitting two Stokes components,” Phys. Rev. A 52(3), 2327–2334 (1995).
[Crossref]

1994 (1)

R. G. Harrison, P. M. Ripley, and W. Lu, “Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback,” Phys. Rev. A 49(1), R24–R27 (1994).
[Crossref]

Abas, A. F.

Abd-Rahman, M. K.

Al-Mansoori, M.

M. M. Nasir, Z. Yusoff, M. Al-Mansoori, H. A. Rashid, and P. Choudhury, “Low threshold and efficient multi-wavelength Brillouin-erbium fiber laser incorporating a fiber Bragg grating filter with intra-cavity pre-amplified Brillouin pump,” Laser Phys. Lett. 6(1), 54–58 (2009).
[Crossref]

M. M. Nasir, Z. Yusoff, M. Al-Mansoori, H. A. Rashid, and P. Choudhury, “Broadly tunable multi-wavelength Brillouin-erbium fiber laser in a Fabry-Perot cavity,” Laser Phys. Lett. 5(11), 812–816 (2008).
[Crossref]

M. Al-Mansoori, M. K. Abd-Rahman, F. Mahamd Adikan, and M. Mahdi, “Widely tunable linear cavity multiwavelength Brillouin-Erbium fiber lasers,” Opt. Express 13(9), 3471–3476 (2005).
[Crossref]

Al-Mansoori, M. H.

Antenucci, F.

F. Antenucci, A. Crisanti, and L. Leuzzi, “The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra,” Sci. Rep. 5(1), 16792 (2015).
[Crossref]

Araújo, C. B.

B. C. Lima, A. S. L. Gomes, P. I. R. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. Araújo, and R. Kashyap, “Observation of Lévy statistics in one-dimensional erbium-based random fiber laser,” J. Opt. Soc. Am. B 34(2), 293–299 (2017).
[Crossref]

B. C. Lima, P. I. R. Pincheira, E. P. Raposo, L. S. Menezes, C. B. Araújo, A. S. L. Gomes, and R. Kashyap, “Extreme-value statistics of intensities in a cw-pumped random fiber laser,” Phys. Rev. A 96(1), 013834 (2017).
[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 laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013).
[Crossref]

Bao, X.

Barbarella, G.

N. Ghofraniha, I. Viola, F. Di Maria, G. Barbarella, G. Gigli, L. Leuzzi, and C. Conti, “Experimental evidence of replica symmetry breaking in random lasers,” Nat. Commun. 6(1), 6058 (2015).
[Crossref]

Basak, S.

S. Basak, A. Blanco, and C. López, “Large fluctuations at the lasing threshold of solid- and liquid-state dye lasers,” Sci. Rep. 6(1), 32134 (2016).
[Crossref]

Blanco, A.

S. Basak, A. Blanco, and C. López, “Large fluctuations at the lasing threshold of solid- and liquid-state dye lasers,” Sci. Rep. 6(1), 32134 (2016).
[Crossref]

Blondel, M.

Brum, A. A.

I. R. Roa González, B. C. Lima, P. I. R. Pincheira, A. A. Brum, A. M. S. Macêdo, G. L. Vasconcelos, L. S. Menezes, E. P. Raposo, A. S. L. Gomes, and R. Kashyap, “Turbulence hierarchy in a random fibre laser,” Nat. Commun. 8(1), 15731 (2017).
[Crossref]

Büttner, T. F. S.

V. L. Iezzi, T. F. S. Büttner, A. Tehranchi, S. Loranger, I. V. Kabakova, B. J. Eggleton, and R. Kashyap, “Temporal characterization of a multi-wavelength Brillouin-erbium fiber laser,” New J. Phys. 18(5), 055003 (2016).
[Crossref]

Chan, C. C. K.

C. C. K. Chan, Optical Performance Monitoring, Advanced Techniques for Next-Generation Photonic Networks (Academic Press, 2010).

Chan, E. H. W.

Chen, L.

Chen, T.

J. Tang, J. Sun, T. Chen, and Y. Zhou, “A stable optical comb with double-Brillouin-frequency spacing assisted by multiple four-wave mixing processes,” Opt. Fiber Technol. 17(6), 608–611 (2011).
[Crossref]

Chieng, Y. T.

G. J. Cowle, D. Y. Stepanov, and Y. T. Chieng, “Brillouin/Erbium fiber lasers,” J. Lightwave Technol. 15(7), 1198–1204 (1997).
[Crossref]

Choudhury, P.

M. M. Nasir, Z. Yusoff, M. Al-Mansoori, H. A. Rashid, and P. Choudhury, “Low threshold and efficient multi-wavelength Brillouin-erbium fiber laser incorporating a fiber Bragg grating filter with intra-cavity pre-amplified Brillouin pump,” Laser Phys. Lett. 6(1), 54–58 (2009).
[Crossref]

M. M. Nasir, Z. Yusoff, M. Al-Mansoori, H. A. Rashid, and P. Choudhury, “Broadly tunable multi-wavelength Brillouin-erbium fiber laser in a Fabry-Perot cavity,” Laser Phys. Lett. 5(11), 812–816 (2008).
[Crossref]

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

Conti, C.

N. Ghofraniha, I. Viola, F. Di Maria, G. Barbarella, G. Gigli, L. Leuzzi, and C. Conti, “Experimental evidence of replica symmetry breaking in random lasers,” Nat. Commun. 6(1), 6058 (2015).
[Crossref]

Cowle, G. J.

G. J. Cowle, D. Y. Stepanov, and Y. T. Chieng, “Brillouin/Erbium fiber lasers,” J. Lightwave Technol. 15(7), 1198–1204 (1997).
[Crossref]

Crisanti, A.

F. Antenucci, A. Crisanti, and L. Leuzzi, “The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra,” Sci. Rep. 5(1), 16792 (2015).
[Crossref]

Dalloz, N.

Deparis, O.

Di Maria, F.

N. Ghofraniha, I. Viola, F. Di Maria, G. Barbarella, G. Gigli, L. Leuzzi, and C. Conti, “Experimental evidence of replica symmetry breaking in random lasers,” Nat. Commun. 6(1), 6058 (2015).
[Crossref]

Eggleton, B. J.

V. L. Iezzi, T. F. S. Büttner, A. Tehranchi, S. Loranger, I. V. Kabakova, B. J. Eggleton, and R. Kashyap, “Temporal characterization of a multi-wavelength Brillouin-erbium fiber laser,” New J. Phys. 18(5), 055003 (2016).
[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]

Fotiadi, A. A.

Gagné, M.

Gao, S.

Ghatak, A.

A. Ghatak and K. Thyagarajan, An Introduction to Fiber Optics (Cambridge University, 1998).

Ghofraniha, N.

N. Ghofraniha, I. Viola, F. Di Maria, G. Barbarella, G. Gigli, L. Leuzzi, and C. Conti, “Experimental evidence of replica symmetry breaking in random lasers,” Nat. Commun. 6(1), 6058 (2015).
[Crossref]

Gigli, G.

N. Ghofraniha, I. Viola, F. Di Maria, G. Barbarella, G. Gigli, L. Leuzzi, and C. Conti, “Experimental evidence of replica symmetry breaking in random lasers,” Nat. Commun. 6(1), 6058 (2015).
[Crossref]

Gomes, A. S. L.

B. C. Lima, P. I. R. Pincheira, E. P. Raposo, L. S. Menezes, C. B. Araújo, A. S. L. Gomes, and R. Kashyap, “Extreme-value statistics of intensities in a cw-pumped random fiber laser,” Phys. Rev. A 96(1), 013834 (2017).
[Crossref]

I. R. Roa González, B. C. Lima, P. I. R. Pincheira, A. A. Brum, A. M. S. Macêdo, G. L. Vasconcelos, L. S. Menezes, E. P. Raposo, A. S. L. Gomes, and R. Kashyap, “Turbulence hierarchy in a random fibre laser,” Nat. Commun. 8(1), 15731 (2017).
[Crossref]

B. C. Lima, A. S. L. Gomes, P. I. R. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. Araújo, and R. Kashyap, “Observation of Lévy statistics in one-dimensional erbium-based random fiber laser,” J. Opt. Soc. Am. B 34(2), 293–299 (2017).
[Crossref]

Gorbunov, O. A.

Han, Y. G.

Harrison, R. G.

R. G. Harrison, P. M. Ripley, and W. Lu, “Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback,” Phys. Rev. A 49(1), R24–R27 (1994).
[Crossref]

Hitam, S.

Hu, S.

Y. Song, L. Zhan, S. Hu, Q. Ye, and Y. Xia, “Tunable multiwavelength Brillouin-erbium fiber laser with a polarization-maintaining fiber Sagnac loop filter,” IEEE Photonics Technol. Lett. 16(9), 2015–2017 (2004).
[Crossref]

Iezzi, V. L.

Ismail, A.

Ji, J. H.

Kabakova, I. V.

V. L. Iezzi, T. F. S. Büttner, A. Tehranchi, S. Loranger, I. V. Kabakova, B. J. Eggleton, and R. Kashyap, “Temporal characterization of a multi-wavelength Brillouin-erbium fiber laser,” New J. Phys. 18(5), 055003 (2016).
[Crossref]

Kashyap, R.

A. Tehranchi, V. L. Iezzi, and R. Kashyap, “Power Fluctuations and Random Lasing in Multiwavelength Brillouin Erbium-Doped Fiber Lasers,” J. Lightwave Technol. 37(17), 4439–4444 (2019).
[Crossref]

V. L. Iezzi, S. Loranger, and R. Kashyap, “High sensitivity distributed temperature fiber sensor using stimulated Brillouin scattering,” Opt. Express 25(26), 32591–32596 (2017).
[Crossref]

B. C. Lima, P. I. R. Pincheira, E. P. Raposo, L. S. Menezes, C. B. Araújo, A. S. L. Gomes, and R. Kashyap, “Extreme-value statistics of intensities in a cw-pumped random fiber laser,” Phys. Rev. A 96(1), 013834 (2017).
[Crossref]

I. R. Roa González, B. C. Lima, P. I. R. Pincheira, A. A. Brum, A. M. S. Macêdo, G. L. Vasconcelos, L. S. Menezes, E. P. Raposo, A. S. L. Gomes, and R. Kashyap, “Turbulence hierarchy in a random fibre laser,” Nat. Commun. 8(1), 15731 (2017).
[Crossref]

B. C. Lima, A. S. L. Gomes, P. I. R. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. Araújo, and R. Kashyap, “Observation of Lévy statistics in one-dimensional erbium-based random fiber laser,” J. Opt. Soc. Am. B 34(2), 293–299 (2017).
[Crossref]

V. L. Iezzi, T. F. S. Büttner, A. Tehranchi, S. Loranger, I. V. Kabakova, B. J. Eggleton, and R. Kashyap, “Temporal characterization of a multi-wavelength Brillouin-erbium fiber laser,” New J. Phys. 18(5), 055003 (2016).
[Crossref]

S. Loranger, V. L. Iezzi, and R. Kashyap, “Demonstration of an ultra-high frequency picosecond pulse generator using an SBS frequency comb and self-phase-locking,” Opt. Express 20(17), 19455–19462 (2012).
[Crossref]

A. Tehranchi, V. L. Iezzi, and R. Kashyap, “Temporal Instability and Random Lasing in a Brillouin Fiber laser,” in Nonlinear Optics (NLO), OSA Technical Digest paper NW3B.4 (2019).

Kim, P.

B. Min, P. Kim, and N. Park, “Flat amplitude equal spacing 798-channel Rayleigh-assisted Brillouin/Raman multiwavelength comb generation in dispersion compensating fiber,” IEEE Photonics Technol. Lett. 13(12), 1352–1354 (2001).
[Crossref]

Kim, S. H.

Kiyan, R.

Lagendijk, A.

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Intrinsic intensity fluctuations in random lasers,” Phys. Rev. A 74(5), 053808 (2006).
[Crossref]

Lecoeuche, V.

V. Lecoeuche, S. Randoux, B. Segard, and J. Zemmouri, “Dynamics of stimulated Brillouin scattering with feedback,” Quantum Semiclassical Opt. 8(6), 1109–1145 (1996).
[Crossref]

V. Lecoeuche, S. Randoux, B. Ségard, and J. Zemmouri, “Dynamics of a Brillouin fiber ring laser: Off-resonant case,” Phys. Rev. A 53(4), 2822–2828 (1996).
[Crossref]

S. Randoux, V. Lecoeuche, B. Segard, and J. Zemmouri, “Dynamical behavior of a Brillouin fiber ring laser emitting two Stokes components,” Phys. Rev. A 52(3), 2327–2334 (1995).
[Crossref]

Lee, S. B.

Leuzzi, L.

N. Ghofraniha, I. Viola, F. Di Maria, G. Barbarella, G. Gigli, L. Leuzzi, and C. Conti, “Experimental evidence of replica symmetry breaking in random lasers,” Nat. Commun. 6(1), 6058 (2015).
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F. Antenucci, A. Crisanti, and L. Leuzzi, “The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra,” Sci. Rep. 5(1), 16792 (2015).
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H. Li and K. Ogusu, “Instability of stimulated Brillouin scattering in a fiber ring resonator,” Opt. Rev. 7(4), 303–308 (2000).
[Crossref]

H. Li and K. Ogusu, “Dynamic behavior of stimulated Brillouin scattering in a single-mode optical fiber,” Jpn. J. Appl. Phys. 38(Part 1, No. 11), 6309–6315 (1999).
[Crossref]

Li, Z.

Lima, B. C.

I. R. Roa González, B. C. Lima, P. I. R. Pincheira, A. A. Brum, A. M. S. Macêdo, G. L. Vasconcelos, L. S. Menezes, E. P. Raposo, A. S. L. Gomes, and R. Kashyap, “Turbulence hierarchy in a random fibre laser,” Nat. Commun. 8(1), 15731 (2017).
[Crossref]

B. C. Lima, P. I. R. Pincheira, E. P. Raposo, L. S. Menezes, C. B. Araújo, A. S. L. Gomes, and R. Kashyap, “Extreme-value statistics of intensities in a cw-pumped random fiber laser,” Phys. Rev. A 96(1), 013834 (2017).
[Crossref]

B. C. Lima, A. S. L. Gomes, P. I. R. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. Araújo, and R. Kashyap, “Observation of Lévy statistics in one-dimensional erbium-based random fiber laser,” J. Opt. Soc. Am. B 34(2), 293–299 (2017).
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S. Basak, A. Blanco, and C. López, “Large fluctuations at the lasing threshold of solid- and liquid-state dye lasers,” Sci. Rep. 6(1), 32134 (2016).
[Crossref]

Loranger, S.

Lu, W.

R. G. Harrison, P. M. Ripley, and W. Lu, “Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback,” Phys. Rev. A 49(1), R24–R27 (1994).
[Crossref]

Macêdo, A. M. S.

I. R. Roa González, B. C. Lima, P. I. R. Pincheira, A. A. Brum, A. M. S. Macêdo, G. L. Vasconcelos, L. S. Menezes, E. P. Raposo, A. S. L. Gomes, and R. Kashyap, “Turbulence hierarchy in a random fibre laser,” Nat. Commun. 8(1), 15731 (2017).
[Crossref]

Mahamd Adikan, F.

Mahdi, M.

Mahdi, M. A.

Mégret, P.

Menezes, L. S.

I. R. Roa González, B. C. Lima, P. I. R. Pincheira, A. A. Brum, A. M. S. Macêdo, G. L. Vasconcelos, L. S. Menezes, E. P. Raposo, A. S. L. Gomes, and R. Kashyap, “Turbulence hierarchy in a random fibre laser,” Nat. Commun. 8(1), 15731 (2017).
[Crossref]

B. C. Lima, P. I. R. Pincheira, E. P. Raposo, L. S. Menezes, C. B. Araújo, A. S. L. Gomes, and R. Kashyap, “Extreme-value statistics of intensities in a cw-pumped random fiber laser,” Phys. Rev. A 96(1), 013834 (2017).
[Crossref]

Min, B.

B. Min, P. Kim, and N. Park, “Flat amplitude equal spacing 798-channel Rayleigh-assisted Brillouin/Raman multiwavelength comb generation in dispersion compensating fiber,” IEEE Photonics Technol. Lett. 13(12), 1352–1354 (2001).
[Crossref]

Minasian, R. A.

Mori, A.

Mosk, A. P.

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Intrinsic intensity fluctuations in random lasers,” Phys. Rev. A 74(5), 053808 (2006).
[Crossref]

Moura, A. L.

Mujumdar, S.

S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007).
[Crossref]

Munk, W. H.

H. U. Sverdrup and W. H. Munk, Wind, sea and swell. Theory of relations for forecasting. US navy Hydrographic Office Pub. 601 (1947).

Nasir, M. M.

M. M. Nasir, Z. Yusoff, M. Al-Mansoori, H. A. Rashid, and P. Choudhury, “Low threshold and efficient multi-wavelength Brillouin-erbium fiber laser incorporating a fiber Bragg grating filter with intra-cavity pre-amplified Brillouin pump,” Laser Phys. Lett. 6(1), 54–58 (2009).
[Crossref]

M. M. Nasir, Z. Yusoff, M. Al-Mansoori, H. A. Rashid, and P. Choudhury, “Broadly tunable multi-wavelength Brillouin-erbium fiber laser in a Fabry-Perot cavity,” Laser Phys. Lett. 5(11), 812–816 (2008).
[Crossref]

Ogusu, K.

H. Li and K. Ogusu, “Instability of stimulated Brillouin scattering in a fiber ring resonator,” Opt. Rev. 7(4), 303–308 (2000).
[Crossref]

H. Li and K. Ogusu, “Dynamic behavior of stimulated Brillouin scattering in a single-mode optical fiber,” Jpn. J. Appl. Phys. 38(Part 1, No. 11), 6309–6315 (1999).
[Crossref]

Ohishi, Y.

Pagani, M.

Park, N.

B. Min, P. Kim, and N. Park, “Flat amplitude equal spacing 798-channel Rayleigh-assisted Brillouin/Raman multiwavelength comb generation in dispersion compensating fiber,” IEEE Photonics Technol. Lett. 13(12), 1352–1354 (2001).
[Crossref]

Pincheira, P. I. R.

B. C. Lima, A. S. L. Gomes, P. I. R. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. Araújo, and R. Kashyap, “Observation of Lévy statistics in one-dimensional erbium-based random fiber laser,” J. Opt. Soc. Am. B 34(2), 293–299 (2017).
[Crossref]

I. R. Roa González, B. C. Lima, P. I. R. Pincheira, A. A. Brum, A. M. S. Macêdo, G. L. Vasconcelos, L. S. Menezes, E. P. Raposo, A. S. L. Gomes, and R. Kashyap, “Turbulence hierarchy in a random fibre laser,” Nat. Commun. 8(1), 15731 (2017).
[Crossref]

B. C. Lima, P. I. R. Pincheira, E. P. Raposo, L. S. Menezes, C. B. Araújo, A. S. L. Gomes, and R. Kashyap, “Extreme-value statistics of intensities in a cw-pumped random fiber laser,” Phys. Rev. A 96(1), 013834 (2017).
[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 laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013).
[Crossref]

Qin, G.

Rahman, Z. A.

Randoux, S.

S. Randoux and P. Suret, “Experimental evidence of extreme value statistics in Raman fiber lasers,” Opt. Lett. 37(4), 500–502 (2012).
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S. Randoux, N. Dalloz, and P. Suret, “Intracavity changes in the field statistics of Raman fiber lasers,” Opt. Lett. 36(6), 790–792 (2011).
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V. Lecoeuche, S. Randoux, B. Ségard, and J. Zemmouri, “Dynamics of a Brillouin fiber ring laser: Off-resonant case,” Phys. Rev. A 53(4), 2822–2828 (1996).
[Crossref]

V. Lecoeuche, S. Randoux, B. Segard, and J. Zemmouri, “Dynamics of stimulated Brillouin scattering with feedback,” Quantum Semiclassical Opt. 8(6), 1109–1145 (1996).
[Crossref]

S. Randoux, V. Lecoeuche, B. Segard, and J. Zemmouri, “Dynamical behavior of a Brillouin fiber ring laser emitting two Stokes components,” Phys. Rev. A 52(3), 2327–2334 (1995).
[Crossref]

Raposo, E. P.

I. R. Roa González, B. C. Lima, P. I. R. Pincheira, A. A. Brum, A. M. S. Macêdo, G. L. Vasconcelos, L. S. Menezes, E. P. Raposo, A. S. L. Gomes, and R. Kashyap, “Turbulence hierarchy in a random fibre laser,” Nat. Commun. 8(1), 15731 (2017).
[Crossref]

B. C. Lima, P. I. R. Pincheira, E. P. Raposo, L. S. Menezes, C. B. Araújo, A. S. L. Gomes, and R. Kashyap, “Extreme-value statistics of intensities in a cw-pumped random fiber laser,” Phys. Rev. A 96(1), 013834 (2017).
[Crossref]

B. C. Lima, A. S. L. Gomes, P. I. R. Pincheira, A. L. Moura, M. Gagné, E. P. Raposo, C. B. Araújo, and R. Kashyap, “Observation of Lévy statistics in one-dimensional erbium-based random fiber laser,” J. Opt. Soc. Am. B 34(2), 293–299 (2017).
[Crossref]

Rashid, H. A.

M. M. Nasir, Z. Yusoff, M. Al-Mansoori, H. A. Rashid, and P. Choudhury, “Low threshold and efficient multi-wavelength Brillouin-erbium fiber laser incorporating a fiber Bragg grating filter with intra-cavity pre-amplified Brillouin pump,” Laser Phys. Lett. 6(1), 54–58 (2009).
[Crossref]

M. M. Nasir, Z. Yusoff, M. Al-Mansoori, H. A. Rashid, and P. Choudhury, “Broadly tunable multi-wavelength Brillouin-erbium fiber laser in a Fabry-Perot cavity,” Laser Phys. Lett. 5(11), 812–816 (2008).
[Crossref]

Ripley, P. M.

R. G. Harrison, P. M. Ripley, and W. Lu, “Observation and characterization of deterministic chaos in stimulated Brillouin scattering with weak feedback,” Phys. Rev. A 49(1), R24–R27 (1994).
[Crossref]

Roa González, I. R.

I. R. Roa González, B. C. Lima, P. I. R. Pincheira, A. A. Brum, A. M. S. Macêdo, G. L. Vasconcelos, L. S. Menezes, E. P. Raposo, A. S. L. Gomes, and R. Kashyap, “Turbulence hierarchy in a random fibre laser,” Nat. Commun. 8(1), 15731 (2017).
[Crossref]

Saxena, B.

Segard, B.

V. Lecoeuche, S. Randoux, B. Segard, and J. Zemmouri, “Dynamics of stimulated Brillouin scattering with feedback,” Quantum Semiclassical Opt. 8(6), 1109–1145 (1996).
[Crossref]

S. Randoux, V. Lecoeuche, B. Segard, and J. Zemmouri, “Dynamical behavior of a Brillouin fiber ring laser emitting two Stokes components,” Phys. Rev. A 52(3), 2327–2334 (1995).
[Crossref]

Ségard, B.

V. Lecoeuche, S. Randoux, B. Ségard, and J. Zemmouri, “Dynamics of a Brillouin fiber ring laser: Off-resonant case,” Phys. Rev. A 53(4), 2822–2828 (1996).
[Crossref]

Shee, Y. G.

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.

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).
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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]

Song, Y.

Y. Song, L. Zhan, S. Hu, Q. Ye, and Y. Xia, “Tunable multiwavelength Brillouin-erbium fiber laser with a polarization-maintaining fiber Sagnac loop filter,” IEEE Photonics Technol. Lett. 16(9), 2015–2017 (2004).
[Crossref]

Song, Y. J.

Sotobayashi, H.

Stepanov, D. Y.

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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]

Sun, J.

J. Tang, J. Sun, T. Chen, and Y. Zhou, “A stable optical comb with double-Brillouin-frequency spacing assisted by multiple four-wave mixing processes,” Opt. Fiber Technol. 17(6), 608–611 (2011).
[Crossref]

Suret, P.

Suzuki, T.

Sverdrup, H. U.

H. U. Sverdrup and W. H. Munk, Wind, sea and swell. Theory of relations for forecasting. US navy Hydrographic Office Pub. 601 (1947).

Tang, J.

J. Tang, J. Sun, T. Chen, and Y. Zhou, “A stable optical comb with double-Brillouin-frequency spacing assisted by multiple four-wave mixing processes,” Opt. Fiber Technol. 17(6), 608–611 (2011).
[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 laminar–turbulent transition in a fibre laser,” Nat. Photonics 7(10), 783–786 (2013).
[Crossref]

Tehranchi, A.

A. Tehranchi, V. L. Iezzi, and R. Kashyap, “Power Fluctuations and Random Lasing in Multiwavelength Brillouin Erbium-Doped Fiber Lasers,” J. Lightwave Technol. 37(17), 4439–4444 (2019).
[Crossref]

V. L. Iezzi, T. F. S. Büttner, A. Tehranchi, S. Loranger, I. V. Kabakova, B. J. Eggleton, and R. Kashyap, “Temporal characterization of a multi-wavelength Brillouin-erbium fiber laser,” New J. Phys. 18(5), 055003 (2016).
[Crossref]

A. Tehranchi, V. L. Iezzi, and R. Kashyap, “Temporal Instability and Random Lasing in a Brillouin Fiber laser,” in Nonlinear Optics (NLO), OSA Technical Digest paper NW3B.4 (2019).

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A. Ghatak and K. Thyagarajan, An Introduction to Fiber Optics (Cambridge University, 1998).

Torre, R.

S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007).
[Crossref]

Tran, T. V. A.

Tsuchiya, M.

Türck, V.

S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007).
[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]

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]

van der Molen, K. L.

K. L. van der Molen, A. P. Mosk, and A. Lagendijk, “Intrinsic intensity fluctuations in random lasers,” Phys. Rev. A 74(5), 053808 (2006).
[Crossref]

Vasconcelos, G. L.

I. R. Roa González, B. C. Lima, P. I. R. Pincheira, A. A. Brum, A. M. S. Macêdo, G. L. Vasconcelos, L. S. Menezes, E. P. Raposo, A. S. L. Gomes, and R. Kashyap, “Turbulence hierarchy in a random fibre laser,” Nat. Commun. 8(1), 15731 (2017).
[Crossref]

Viola, I.

N. Ghofraniha, I. Viola, F. Di Maria, G. Barbarella, G. Gigli, L. Leuzzi, and C. Conti, “Experimental evidence of replica symmetry breaking in random lasers,” Nat. Commun. 6(1), 6058 (2015).
[Crossref]

Wabnitz, S.

Wang, C.

Wiersma, D. S.

S. Mujumdar, V. Türck, R. Torre, and D. S. Wiersma, “Chaotic behavior of a random laser with static disorder,” Phys. Rev. A 76(3), 033807 (2007).
[Crossref]

Xia, Y.

Y. Song, L. Zhan, S. Hu, Q. Ye, and Y. Xia, “Tunable multiwavelength Brillouin-erbium fiber laser with a polarization-maintaining fiber Sagnac loop filter,” IEEE Photonics Technol. Lett. 16(9), 2015–2017 (2004).
[Crossref]

Xia, Y. X.

Xu, Y.

Ye, Q.

Y. Song, L. Zhan, S. Hu, Q. Ye, and Y. Xia, “Tunable multiwavelength Brillouin-erbium fiber laser with a polarization-maintaining fiber Sagnac loop filter,” IEEE Photonics Technol. Lett. 16(9), 2015–2017 (2004).
[Crossref]

Ye, Q. H.

Yusoff, Z.

M. M. Nasir, Z. Yusoff, M. Al-Mansoori, H. A. Rashid, and P. Choudhury, “Low threshold and efficient multi-wavelength Brillouin-erbium fiber laser incorporating a fiber Bragg grating filter with intra-cavity pre-amplified Brillouin pump,” Laser Phys. Lett. 6(1), 54–58 (2009).
[Crossref]

M. M. Nasir, Z. Yusoff, M. Al-Mansoori, H. A. Rashid, and P. Choudhury, “Broadly tunable multi-wavelength Brillouin-erbium fiber laser in a Fabry-Perot cavity,” Laser Phys. Lett. 5(11), 812–816 (2008).
[Crossref]

Zemmouri, J.

V. Lecoeuche, S. Randoux, B. Segard, and J. Zemmouri, “Dynamics of stimulated Brillouin scattering with feedback,” Quantum Semiclassical Opt. 8(6), 1109–1145 (1996).
[Crossref]

V. Lecoeuche, S. Randoux, B. Ségard, and J. Zemmouri, “Dynamics of a Brillouin fiber ring laser: Off-resonant case,” Phys. Rev. A 53(4), 2822–2828 (1996).
[Crossref]

S. Randoux, V. Lecoeuche, B. Segard, and J. Zemmouri, “Dynamical behavior of a Brillouin fiber ring laser emitting two Stokes components,” Phys. Rev. A 52(3), 2327–2334 (1995).
[Crossref]

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Y. J. Song, L. Zhan, J. H. Ji, Y. Su, Q. H. Ye, and Y. X. Xia, “Self-seeded multiwavelength Brillouin-erbium fiber laser,” Opt. Lett. 30(5), 486–488 (2005).
[Crossref]

Y. Song, L. Zhan, S. Hu, Q. Ye, and Y. Xia, “Tunable multiwavelength Brillouin-erbium fiber laser with a polarization-maintaining fiber Sagnac loop filter,” IEEE Photonics Technol. Lett. 16(9), 2015–2017 (2004).
[Crossref]

Zhang, L.

Zhou, Y.

J. Tang, J. Sun, T. Chen, and Y. Zhou, “A stable optical comb with double-Brillouin-frequency spacing assisted by multiple four-wave mixing processes,” Opt. Fiber Technol. 17(6), 608–611 (2011).
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Figures (5)

Fig. 1.
Fig. 1. Set-up of an MWBEFL.
Fig. 2.
Fig. 2. Power fluctuations versus time over 2 ms for the EDFA pump power of (a) 20 mW, (b) 30 mW and (c) 2000mW. The spikes reaching unity in (c) are probably rogue events.
Fig. 3.
Fig. 3. PDFs of power, f(P) obtained for a pump power of (a) 20 mW, (b) 30 mW and (c) 2000 mW. For low-pump power near and above threshold (20 & 30 mW) a Gaussian-like PDF fits a histogram. For pump power much beyond threshold (2000 mW) a levy-like PDF can be fitted. The insets show the CDFs of power, F(P).
Fig. 4.
Fig. 4. Phase portraits achieved for a pump power of (a) 20 mW, (b) 30 mW and (c) 2000 mW. For the highest pump power (2000 mW) more distributed bars with increased density, and consequently more pronounced temporal power fluctuations are expected.
Fig. 5.
Fig. 5. Histograms calculated using Eq. (3) for a pump power of

Tables (1)

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Table 1. Fit parameters for stable distribution of power histogram.

Equations (3)

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f ( x ) = 1 2 π + P ¯ ( k ) e i k x d x ,
P ¯ ( k ) = e x p { | γ k | α [ 1 i β sgn ( k ) Φ ] + i δ k } ,
q a b = τ = 1 M Δ a ( τ ) Δ b ( τ ) τ = 1 M Δ a ( τ ) 2 τ = 1 M Δ b ( τ ) 2 ,

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