Abstract

Modulation instability is thoroughly investigated and a simple analytical model for its power critically modifying the wave properties in terms of system parameters is derived and experimentally validated. The differences on the modulation instability gain spectrum in lossless and lossy optical fibers are analyzed based on theoretical models and numerical simulations. In particular the impact of background noise on the behavior of modulation instability is studied analytically and verified by measurements and simulations. The proposed analytical model is experimentally validated by monitoring the wave propagation along an optical fiber using a Brillouin optical time-domain analyzer. This way, the evolution of the optical signal traveling through optical fibers, especially, the pump depletion and the recurrence phenomenon are investigated.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref]
  51. S. A. Babin, A. E. Ismagulov, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability at propagation of narrowband 100-ns pulses in optical fibers of various types,” Laser Phys. 20(2), 334–340 (2010).
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2014 (6)

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]

S. Roy, M. Santagiustina, A. Willinger, G. Eisenstein, S. Combrié, and A. De Rossi, “Parametric gain and conversion efficiency in nanophotonic waveguides with dispersive propagation coefficients and loss,” J. Lightwave Technol. 32(6), 1177–1182 (2014).
[Crossref]

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4(1), 011054 (2014).
[Crossref]

R. Nissim, A. Pejkic, E. Myslivets, B. P. Kuo, N. Alic, and S. Radic, “Ultrafast optics. Ultrafast optical control by few photons in engineered fiber,” Science 345(6195), 417–419 (2014).
[Crossref] [PubMed]

M. Alem, M. A. Soto, and L. Thévenaz, “Modelling the depletion length induced by modulation instability in distributed optical fibre sensors,” Proc. SPIE 9157, 91575S (2014).

F. Alishahi, A. Vedadi, M. A. Shoaie, M. A. Soto, A. Denisov, K. Mehrany, L. Thévenaz, and C. S. Brès, “Power evolution along phase-sensitive parametric amplifiers: an experimental survey,” Opt. Lett. 39(21), 6114–6117 (2014).
[Crossref] [PubMed]

2013 (4)

2012 (1)

W. Chen, Z. Meng, H. J. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
[Crossref]

2011 (4)

S. M. Foaleng and L. Thévenaz, “Impact of Raman scattering and modulation instability on the performances of Brillouin sensors,” Proc. SPIE 7753, 77539V (2011).
[Crossref]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[Crossref] [PubMed]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, “Akhmediev breather evolution in optical fiber for realistic initial conditions,” Phys. Lett. A 375(19), 2029–2034 (2011).
[Crossref]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[Crossref] [PubMed]

2010 (2)

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(10), 790–795 (2010).
[Crossref]

S. A. Babin, A. E. Ismagulov, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability at propagation of narrowband 100-ns pulses in optical fibers of various types,” Laser Phys. 20(2), 334–340 (2010).
[Crossref]

2009 (3)

A. E. Ismagulov, S. A. Babin, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability of narrow-band nanosecond pulses propagating in anomalous-dispersion fibre,” Quantum Electron. 39(8), 765–769 (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(24), 21497–21508 (2009).
[Crossref] [PubMed]

Y. Dong and X. Bao, “High spatial resolution and long-distance BOTDA using differential Brillouin gain in a dispersion shifted fiber,” Proc. SPIE 7503, 750384 (2009).
[Crossref]

2008 (1)

2006 (1)

A. Kobyakov, S. A. Darmanyan, and D. Q. Chowdhury, “Exact analytical treatment of noise initiation of SBS in the presence of loss,” Opt. Commun. 260(1), 46–49 (2006).
[Crossref]

2005 (3)

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71(2), 023808 (2005).
[Crossref]

C. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13(13), 4986–5012 (2005).
[Crossref] [PubMed]

D. Alasia, M. González-Herráez, L. Abrardi, S. Martin-López, and L. Thévenaz, “Detrimental effect of modulation instability on distributed optical fiber sensors using stimulated Brillouin scattering,” Proc. SPIE 5855, 587–590 (2005).
[Crossref]

2004 (1)

2002 (2)

2001 (2)

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurements of the nonlinear coefficient of standard, SMF, DSF, and DCF fibers using a self-aligned interferometer and a Faraday mirror,” IEEE Photon. Technol. Lett. 13(12), 1337–1339 (2001).
[Crossref]

G. Van Simaeys, P. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[Crossref] [PubMed]

1997 (1)

A. Carena, V. Curri, R. Guadino, P. Poggiolini, and S. Benedetto, “New analytical results on fiber parametric gain and its effects on ASE noise,” IEEE Photon. Technol. Lett. 9(4), 535–537 (1997).
[Crossref]

1995 (2)

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering: optical fiber sensors,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[Crossref]

M. Karlsson, “Modulational instability in lossy optical fibers,” J. Opt. Soc. Am. B 12(11), 2071–2077 (1995).

1991 (2)

1990 (2)

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78(2), 137–142 (1990).
[Crossref]

J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A 42(1), 682–685 (1990).
[Crossref] [PubMed]

1989 (5)

Y. Chen and A. W. Snyder, “Four-photon parametric mixing in optical fibers: effect of pump depletion,” Opt. Lett. 14(1), 87–89 (1989).
[Crossref] [PubMed]

H. Itoh, G. M. Davis, and S. Sudo, “Continuous-wave-pumped modulational instablity in an optical fiber,” Opt. Lett. 14(24), 1368–1370 (1989).
[Crossref] [PubMed]

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Modulation instability induced by cross-phase modulation in optical fibers,” Phys. Rev. A 39(7), 3406–3413 (1989).
[Crossref] [PubMed]

A. Hasegawa and K. Tai, “Effects of modulational instability on coherent transmission systems,” Opt. Lett. 14(10), 512–513 (1989).
[Crossref] [PubMed]

T. Horiguchi and M. Tateda, “BOTDA-Nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989).
[Crossref]

1987 (1)

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987).
[Crossref] [PubMed]

1986 (3)

K. Tajima, “Self-amplitude modulation in PSK coherent optical transmission systems,” J. Lightwave Technol. 4(7), 900–904 (1986).
[Crossref]

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236 (1986).
[Crossref]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[Crossref] [PubMed]

1984 (3)

1980 (1)

A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. 16(7), 694–697 (1980).
[Crossref]

1972 (1)

Abrardi, L.

D. Alasia, M. González-Herráez, L. Abrardi, S. Martin-López, and L. Thévenaz, “Detrimental effect of modulation instability on distributed optical fiber sensors using stimulated Brillouin scattering,” Proc. SPIE 5855, 587–590 (2005).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Modulation instability induced by cross-phase modulation in optical fibers,” Phys. Rev. A 39(7), 3406–3413 (1989).
[Crossref] [PubMed]

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59(8), 880–883 (1987).
[Crossref] [PubMed]

Akhmediev, N.

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4(1), 011054 (2014).
[Crossref]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[Crossref] [PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[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(10), 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(24), 21497–21508 (2009).
[Crossref] [PubMed]

Alahbabi, M. N.

Alasia, D.

D. Alasia, M. González-Herráez, L. Abrardi, S. Martin-López, and L. Thévenaz, “Detrimental effect of modulation instability on distributed optical fiber sensors using stimulated Brillouin scattering,” Proc. SPIE 5855, 587–590 (2005).
[Crossref]

Alem, M.

M. Alem, M. A. Soto, and L. Thévenaz, “Modelling the depletion length induced by modulation instability in distributed optical fibre sensors,” Proc. SPIE 9157, 91575S (2014).

M. A. Soto, M. Alem, W. Chen, and L. Thévenaz, “Mitigating modulation instability in Brillouin distributed fibre sensors,” Proc. SPIE 8794, 87943J (2013).
[Crossref]

Alfano, R. R.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Modulation instability induced by cross-phase modulation in optical fibers,” Phys. Rev. A 39(7), 3406–3413 (1989).
[Crossref] [PubMed]

Alic, N.

R. Nissim, A. Pejkic, E. Myslivets, B. P. Kuo, N. Alic, and S. Radic, “Ultrafast optics. Ultrafast optical control by few photons in engineered fiber,” Science 345(6195), 417–419 (2014).
[Crossref] [PubMed]

Alishahi, F.

Amans, D.

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71(2), 023808 (2005).
[Crossref]

Anderson, D.

Babin, S. A.

S. A. Babin, A. E. Ismagulov, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability at propagation of narrowband 100-ns pulses in optical fibers of various types,” Laser Phys. 20(2), 334–340 (2010).
[Crossref]

A. E. Ismagulov, S. A. Babin, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability of narrow-band nanosecond pulses propagating in anomalous-dispersion fibre,” Quantum Electron. 39(8), 765–769 (2009).
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G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Modulation instability induced by cross-phase modulation in optical fibers,” Phys. Rev. A 39(7), 3406–3413 (1989).
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Bao, X.

Y. Dong and X. Bao, “High spatial resolution and long-distance BOTDA using differential Brillouin gain in a dispersion shifted fiber,” Proc. SPIE 7503, 750384 (2009).
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A. Carena, V. Curri, R. Guadino, P. Poggiolini, and S. Benedetto, “New analytical results on fiber parametric gain and its effects on ASE noise,” IEEE Photon. Technol. Lett. 9(4), 535–537 (1997).
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Brainis, E.

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71(2), 023808 (2005).
[Crossref]

Brès, C. S.

Brinkman, W. F.

A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. 16(7), 694–697 (1980).
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Cappellini, G.

Carena, A.

A. Carena, V. Curri, R. Guadino, P. Poggiolini, and S. Benedetto, “New analytical results on fiber parametric gain and its effects on ASE noise,” IEEE Photon. Technol. Lett. 9(4), 535–537 (1997).
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Chen, W.

M. A. Soto, M. Alem, W. Chen, and L. Thévenaz, “Mitigating modulation instability in Brillouin distributed fibre sensors,” Proc. SPIE 8794, 87943J (2013).
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W. Chen, Z. Meng, H. J. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
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Chen, Y.

Cho, Y. T.

Chowdhury, D. Q.

A. Kobyakov, S. A. Darmanyan, and D. Q. Chowdhury, “Exact analytical treatment of noise initiation of SBS in the presence of loss,” Opt. Commun. 260(1), 46–49 (2006).
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Combrié, S.

Corredera, P.

Curri, V.

A. Carena, V. Curri, R. Guadino, P. Poggiolini, and S. Benedetto, “New analytical results on fiber parametric gain and its effects on ASE noise,” IEEE Photon. Technol. Lett. 9(4), 535–537 (1997).
[Crossref]

M. E. Marhic, V. Curri, and L. G. Kazovsky, “Bessel function solution for the gain of one-pump fiber optical parametric amplifier,” in Proceedings of IEEE Conference on Nonlinear Optics (IEEE, 1998), pp. 221–223.
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Darmanyan, S. A.

A. Kobyakov, S. A. Darmanyan, and D. Q. Chowdhury, “Exact analytical treatment of noise initiation of SBS in the presence of loss,” Opt. Commun. 260(1), 46–49 (2006).
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Davis, G. M.

De Rossi, A.

Denisov, A.

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).
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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(10), 790–795 (2010).
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J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express 17(24), 21497–21508 (2009).
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Dong, Y.

Y. Dong and X. Bao, “High spatial resolution and long-distance BOTDA using differential Brillouin gain in a dispersion shifted fiber,” Proc. SPIE 7503, 750384 (2009).
[Crossref]

Droques, M.

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4(1), 011054 (2014).
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Drummond, P. D.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78(2), 137–142 (1990).
[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).
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M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, “Akhmediev breather evolution in optical fiber for realistic initial conditions,” Phys. Lett. A 375(19), 2029–2034 (2011).
[Crossref]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
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K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
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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(10), 790–795 (2010).
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J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, “Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation,” Opt. Express 17(24), 21497–21508 (2009).
[Crossref] [PubMed]

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78(2), 137–142 (1990).
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Eisenstein, G.

Emplit, P.

G. Van Simaeys, P. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B 19(3), 477–486 (2002).
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G. Van Simaeys, P. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[Crossref] [PubMed]

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]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, “Akhmediev breather evolution in optical fiber for realistic initial conditions,” Phys. Lett. A 375(19), 2029–2034 (2011).
[Crossref]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
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Evans, A. F.

Fatome, J.

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[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(10), 790–795 (2010).
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Fedoruk, M. P.

S. A. Babin, A. E. Ismagulov, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability at propagation of narrowband 100-ns pulses in optical fibers of various types,” Laser Phys. 20(2), 334–340 (2010).
[Crossref]

A. E. Ismagulov, S. A. Babin, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability of narrow-band nanosecond pulses propagating in anomalous-dispersion fibre,” Quantum Electron. 39(8), 765–769 (2009).
[Crossref]

Finot, C.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[Crossref] [PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[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(10), 790–795 (2010).
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Foaleng, S. M.

S. M. Foaleng and L. Thévenaz, “Impact of Raman scattering and modulation instability on the performances of Brillouin sensors,” Proc. SPIE 7753, 77539V (2011).
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Frazão, O.

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]

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, “Akhmediev breather evolution in optical fiber for realistic initial conditions,” Phys. Lett. A 375(19), 2029–2034 (2011).
[Crossref]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[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(10), 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(24), 21497–21508 (2009).
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C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurements of the nonlinear coefficient of standard, SMF, DSF, and DCF fibers using a self-aligned interferometer and a Faraday mirror,” IEEE Photon. Technol. Lett. 13(12), 1337–1339 (2001).
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H. F. Martins, S. Martin-Lopez, P. Corredera, P. Salgado, O. Frazão, and M. González-Herráez, “Modulation instability-induced fading in phase-sensitive optical time-domain reflectometry,” Opt. Lett. 38(6), 872–874 (2013).
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A. Carena, V. Curri, R. Guadino, P. Poggiolini, and S. Benedetto, “New analytical results on fiber parametric gain and its effects on ASE noise,” IEEE Photon. Technol. Lett. 9(4), 535–537 (1997).
[Crossref]

Haelterman, M.

G. Van Simaeys, P. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B 19(3), 477–486 (2002).
[Crossref]

G. Van Simaeys, P. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[Crossref] [PubMed]

Hammani, K.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[Crossref] [PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[Crossref] [PubMed]

Hartog, A. H.

Harvey, J. D.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78(2), 137–142 (1990).
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A. Hasegawa and K. Tai, “Effects of modulational instability on coherent transmission systems,” Opt. Lett. 14(10), 512–513 (1989).
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K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236 (1986).
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A. Hasegawa, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Opt. Lett. 9(7), 288–290 (1984).
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A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. 16(7), 694–697 (1980).
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Hermansson, B.

B. Hermansson and D. Yevick, “Modulational instability effects in PSK modulated coherent fiber systems and their reduction by optical loss,” Opt. Commun. 52(2), 99–102 (1984).
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T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering: optical fiber sensors,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
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T. Horiguchi and M. Tateda, “BOTDA-Nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989).
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Ismagulov, A. E.

S. A. Babin, A. E. Ismagulov, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability at propagation of narrowband 100-ns pulses in optical fibers of various types,” Laser Phys. 20(2), 334–340 (2010).
[Crossref]

A. E. Ismagulov, S. A. Babin, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability of narrow-band nanosecond pulses propagating in anomalous-dispersion fibre,” Quantum Electron. 39(8), 765–769 (2009).
[Crossref]

Itoh, H.

Jewell, J. L.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236 (1986).
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Karlsson, M.

Kazovsky, L. G.

M. E. Marhic, V. Curri, and L. G. Kazovsky, “Bessel function solution for the gain of one-pump fiber optical parametric amplifier,” in Proceedings of IEEE Conference on Nonlinear Optics (IEEE, 1998), pp. 221–223.
[Crossref]

Kennedy, T. A. B.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78(2), 137–142 (1990).
[Crossref]

Kibler, B.

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
[Crossref] [PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[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(10), 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(24), 21497–21508 (2009).
[Crossref] [PubMed]

Kobtsev, S. M.

Kobyakov, A.

A. Kobyakov, S. A. Darmanyan, and D. Q. Chowdhury, “Exact analytical treatment of noise initiation of SBS in the presence of loss,” Opt. Commun. 260(1), 46–49 (2006).
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A. Kobyakov, M. Mehendale, M. Vasilyev, S. Tsuda, and A. F. Evans, “Stimulated Brillouin scattering in Raman-pumped fibers: a theoretical approach,” J. Lightwave Technol. 20(8), 1635–1643 (2002).
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Koyamada, Y.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering: optical fiber sensors,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
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Kudlinski, A.

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4(1), 011054 (2014).
[Crossref]

Kuo, B. P.

R. Nissim, A. Pejkic, E. Myslivets, B. P. Kuo, N. Alic, and S. Radic, “Ultrafast optics. Ultrafast optical control by few photons in engineered fiber,” Science 345(6195), 417–419 (2014).
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Kurashima, T.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering: optical fiber sensors,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
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Leonhardt, R.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78(2), 137–142 (1990).
[Crossref]

Lin, J.

Lisak, M.

Luo, H.

W. Chen, Z. Meng, H. J. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
[Crossref]

Mafang, S. F.

Marhic, M. E.

M. E. Marhic, V. Curri, and L. G. Kazovsky, “Bessel function solution for the gain of one-pump fiber optical parametric amplifier,” in Proceedings of IEEE Conference on Nonlinear Optics (IEEE, 1998), pp. 221–223.
[Crossref]

Martin-Lopez, S.

Martin-López, S.

D. Alasia, M. González-Herráez, L. Abrardi, S. Martin-López, and L. Thévenaz, “Detrimental effect of modulation instability on distributed optical fiber sensors using stimulated Brillouin scattering,” Proc. SPIE 5855, 587–590 (2005).
[Crossref]

Martins, H. F.

Massar, S.

E. Brainis, D. Amans, and S. Massar, “Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: numerical study,” Phys. Rev. A 71(2), 023808 (2005).
[Crossref]

McKinstrie, C.

Mehendale, M.

Mehrany, K.

Meng, Z.

W. Chen, Z. Meng, H. J. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
[Crossref]

Millot, G.

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
[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(10), 790–795 (2010).
[Crossref]

Mussot, A.

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4(1), 011054 (2014).
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Myslivets, E.

R. Nissim, A. Pejkic, E. Myslivets, B. P. Kuo, N. Alic, and S. Radic, “Ultrafast optics. Ultrafast optical control by few photons in engineered fiber,” Science 345(6195), 417–419 (2014).
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Newson, T. P.

Nissim, R.

R. Nissim, A. Pejkic, E. Myslivets, B. P. Kuo, N. Alic, and S. Radic, “Ultrafast optics. Ultrafast optical control by few photons in engineered fiber,” Science 345(6195), 417–419 (2014).
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Pejkic, A.

R. Nissim, A. Pejkic, E. Myslivets, B. P. Kuo, N. Alic, and S. Radic, “Ultrafast optics. Ultrafast optical control by few photons in engineered fiber,” Science 345(6195), 417–419 (2014).
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Podivilov, E. V.

S. A. Babin, A. E. Ismagulov, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability at propagation of narrowband 100-ns pulses in optical fibers of various types,” Laser Phys. 20(2), 334–340 (2010).
[Crossref]

A. E. Ismagulov, S. A. Babin, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability of narrow-band nanosecond pulses propagating in anomalous-dispersion fibre,” Quantum Electron. 39(8), 765–769 (2009).
[Crossref]

Poggiolini, P.

A. Carena, V. Curri, R. Guadino, P. Poggiolini, and S. Benedetto, “New analytical results on fiber parametric gain and its effects on ASE noise,” IEEE Photon. Technol. Lett. 9(4), 535–537 (1997).
[Crossref]

Radic, S.

R. Nissim, A. Pejkic, E. Myslivets, B. P. Kuo, N. Alic, and S. Radic, “Ultrafast optics. Ultrafast optical control by few photons in engineered fiber,” Science 345(6195), 417–419 (2014).
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C. McKinstrie, M. Yu, M. G. Raymer, and S. Radic, “Quantum noise properties of parametric processes,” Opt. Express 13(13), 4986–5012 (2005).
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Salgado, P.

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Shelemba, I. S.

S. A. Babin, A. E. Ismagulov, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability at propagation of narrowband 100-ns pulses in optical fibers of various types,” Laser Phys. 20(2), 334–340 (2010).
[Crossref]

A. E. Ismagulov, S. A. Babin, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability of narrow-band nanosecond pulses propagating in anomalous-dispersion fibre,” Quantum Electron. 39(8), 765–769 (2009).
[Crossref]

Shimizu, K.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering: optical fiber sensors,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[Crossref]

Shoaie, M. A.

Shtyrina, O. V.

S. A. Babin, A. E. Ismagulov, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability at propagation of narrowband 100-ns pulses in optical fibers of various types,” Laser Phys. 20(2), 334–340 (2010).
[Crossref]

A. E. Ismagulov, S. A. Babin, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability of narrow-band nanosecond pulses propagating in anomalous-dispersion fibre,” Quantum Electron. 39(8), 765–769 (2009).
[Crossref]

Smirnov, S. V.

Smith, R. G.

Snyder, A. W.

Soto, M. A.

M. Alem, M. A. Soto, and L. Thévenaz, “Modelling the depletion length induced by modulation instability in distributed optical fibre sensors,” Proc. SPIE 9157, 91575S (2014).

F. Alishahi, A. Vedadi, M. A. Shoaie, M. A. Soto, A. Denisov, K. Mehrany, L. Thévenaz, and C. S. Brès, “Power evolution along phase-sensitive parametric amplifiers: an experimental survey,” Opt. Lett. 39(21), 6114–6117 (2014).
[Crossref] [PubMed]

M. A. Soto and L. Thévenaz, “Modeling and evaluating the performance of Brillouin distributed optical fiber sensors,” Opt. Express 21(25), 31347–31366 (2013).
[Crossref] [PubMed]

M. A. Soto, M. Alem, W. Chen, and L. Thévenaz, “Mitigating modulation instability in Brillouin distributed fibre sensors,” Proc. SPIE 8794, 87943J (2013).
[Crossref]

Sudo, S.

Szriftgiser, P.

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4(1), 011054 (2014).
[Crossref]

Tai, K.

A. Hasegawa and K. Tai, “Effects of modulational instability on coherent transmission systems,” Opt. Lett. 14(10), 512–513 (1989).
[Crossref] [PubMed]

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236 (1986).
[Crossref]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[Crossref] [PubMed]

Tajima, K.

K. Tajima, “Self-amplitude modulation in PSK coherent optical transmission systems,” J. Lightwave Technol. 4(7), 900–904 (1986).
[Crossref]

Tateda, M.

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering: optical fiber sensors,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[Crossref]

T. Horiguchi and M. Tateda, “BOTDA-Nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989).
[Crossref]

Thévenaz, L.

M. Alem, M. A. Soto, and L. Thévenaz, “Modelling the depletion length induced by modulation instability in distributed optical fibre sensors,” Proc. SPIE 9157, 91575S (2014).

F. Alishahi, A. Vedadi, M. A. Shoaie, M. A. Soto, A. Denisov, K. Mehrany, L. Thévenaz, and C. S. Brès, “Power evolution along phase-sensitive parametric amplifiers: an experimental survey,” Opt. Lett. 39(21), 6114–6117 (2014).
[Crossref] [PubMed]

M. A. Soto and L. Thévenaz, “Modeling and evaluating the performance of Brillouin distributed optical fiber sensors,” Opt. Express 21(25), 31347–31366 (2013).
[Crossref] [PubMed]

L. Thévenaz, S. F. Mafang, and J. Lin, “Effect of pulse depletion in a Brillouin optical time-domain analysis system,” Opt. Express 21(12), 14017–14035 (2013).
[Crossref] [PubMed]

M. A. Soto, M. Alem, W. Chen, and L. Thévenaz, “Mitigating modulation instability in Brillouin distributed fibre sensors,” Proc. SPIE 8794, 87943J (2013).
[Crossref]

S. M. Foaleng and L. Thévenaz, “Impact of Raman scattering and modulation instability on the performances of Brillouin sensors,” Proc. SPIE 7753, 77539V (2011).
[Crossref]

D. Alasia, M. González-Herráez, L. Abrardi, S. Martin-López, and L. Thévenaz, “Detrimental effect of modulation instability on distributed optical fiber sensors using stimulated Brillouin scattering,” Proc. SPIE 5855, 587–590 (2005).
[Crossref]

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[Crossref] [PubMed]

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236 (1986).
[Crossref]

Trillo, S.

Tsuda, S.

Van Simaeys, G.

G. Van Simaeys, P. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B 19(3), 477–486 (2002).
[Crossref]

G. Van Simaeys, P. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[Crossref] [PubMed]

Vasilyev, M.

Vedadi, A.

Vinegoni, C.

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurements of the nonlinear coefficient of standard, SMF, DSF, and DCF fibers using a self-aligned interferometer and a Faraday mirror,” IEEE Photon. Technol. Lett. 13(12), 1337–1339 (2001).
[Crossref]

Wabnitz, S.

Wait, P. C.

Wegmuller, M.

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurements of the nonlinear coefficient of standard, SMF, DSF, and DCF fibers using a self-aligned interferometer and a Faraday mirror,” IEEE Photon. Technol. Lett. 13(12), 1337–1339 (2001).
[Crossref]

Wetzel, B.

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, “Akhmediev breather evolution in optical fiber for realistic initial conditions,” Phys. Lett. A 375(19), 2029–2034 (2011).
[Crossref]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
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Willinger, A.

Yevick, D.

B. Hermansson and D. Yevick, “Modulational instability effects in PSK modulated coherent fiber systems and their reduction by optical loss,” Opt. Commun. 52(2), 99–102 (1984).
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Yu, M.

Zhou, H. J.

W. Chen, Z. Meng, H. J. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, “Generation of subpicosecond solitonlike optical pulses at 0.3 THz repetition rate by induced modulational instability,” Appl. Phys. Lett. 49(5), 236 (1986).
[Crossref]

IEEE J. Quantum Electron. (1)

A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. 16(7), 694–697 (1980).
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IEEE Photon. Technol. Lett. (2)

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[Crossref]

C. Vinegoni, M. Wegmuller, and N. Gisin, “Measurements of the nonlinear coefficient of standard, SMF, DSF, and DCF fibers using a self-aligned interferometer and a Faraday mirror,” IEEE Photon. Technol. Lett. 13(12), 1337–1339 (2001).
[Crossref]

J. Lightwave Technol. (5)

A. Kobyakov, M. Mehendale, M. Vasilyev, S. Tsuda, and A. F. Evans, “Stimulated Brillouin scattering in Raman-pumped fibers: a theoretical approach,” J. Lightwave Technol. 20(8), 1635–1643 (2002).
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S. Roy, M. Santagiustina, A. Willinger, G. Eisenstein, S. Combrié, and A. De Rossi, “Parametric gain and conversion efficiency in nanophotonic waveguides with dispersive propagation coefficients and loss,” J. Lightwave Technol. 32(6), 1177–1182 (2014).
[Crossref]

T. Horiguchi and M. Tateda, “BOTDA-Nondestructive measurement of single-mode optical fiber attenuation characteristics using Brillouin interaction: theory,” J. Lightwave Technol. 7(8), 1170–1176 (1989).
[Crossref]

T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, “Development of a distributed sensing technique using Brillouin scattering: optical fiber sensors,” J. Lightwave Technol. 13(7), 1296–1302 (1995).
[Crossref]

K. Tajima, “Self-amplitude modulation in PSK coherent optical transmission systems,” J. Lightwave Technol. 4(7), 900–904 (1986).
[Crossref]

J. Opt. Soc. Am. B (4)

Laser Phys. (2)

W. Chen, Z. Meng, H. J. Zhou, and H. Luo, “Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission,” Laser Phys. 22(8), 1305–1309 (2012).
[Crossref]

S. A. Babin, A. E. Ismagulov, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability at propagation of narrowband 100-ns pulses in optical fibers of various types,” Laser Phys. 20(2), 334–340 (2010).
[Crossref]

Nat. Photonics (1)

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]

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(10), 790–795 (2010).
[Crossref]

Opt. Commun. (3)

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78(2), 137–142 (1990).
[Crossref]

B. Hermansson and D. Yevick, “Modulational instability effects in PSK modulated coherent fiber systems and their reduction by optical loss,” Opt. Commun. 52(2), 99–102 (1984).
[Crossref]

A. Kobyakov, S. A. Darmanyan, and D. Q. Chowdhury, “Exact analytical treatment of noise initiation of SBS in the presence of loss,” Opt. Commun. 260(1), 46–49 (2006).
[Crossref]

Opt. Express (5)

Opt. Lett. (9)

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S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16(13), 986–988 (1991).
[Crossref] [PubMed]

A. Hasegawa, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Opt. Lett. 9(7), 288–290 (1984).
[Crossref] [PubMed]

K. Hammani, B. Wetzel, B. Kibler, J. Fatome, C. Finot, G. Millot, N. Akhmediev, and J. M. Dudley, “Spectral dynamics of modulation instability described using Akhmediev breather theory,” Opt. Lett. 36(11), 2140–2142 (2011).
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D. Anderson and M. Lisak, “Modulational instability of coherent optical-fiber transmission signals,” Opt. Lett. 9(10), 468–470 (1984).
[Crossref] [PubMed]

Y. Chen and A. W. Snyder, “Four-photon parametric mixing in optical fibers: effect of pump depletion,” Opt. Lett. 14(1), 87–89 (1989).
[Crossref] [PubMed]

H. F. Martins, S. Martin-Lopez, P. Corredera, P. Salgado, O. Frazão, and M. González-Herráez, “Modulation instability-induced fading in phase-sensitive optical time-domain reflectometry,” Opt. Lett. 38(6), 872–874 (2013).
[Crossref] [PubMed]

A. Hasegawa and K. Tai, “Effects of modulational instability on coherent transmission systems,” Opt. Lett. 14(10), 512–513 (1989).
[Crossref] [PubMed]

F. Alishahi, A. Vedadi, M. A. Shoaie, M. A. Soto, A. Denisov, K. Mehrany, L. Thévenaz, and C. S. Brès, “Power evolution along phase-sensitive parametric amplifiers: an experimental survey,” Opt. Lett. 39(21), 6114–6117 (2014).
[Crossref] [PubMed]

Phys. Lett. A (1)

M. Erkintalo, G. Genty, B. Wetzel, and J. M. Dudley, “Akhmediev breather evolution in optical fiber for realistic initial conditions,” Phys. Lett. A 375(19), 2029–2034 (2011).
[Crossref]

Phys. Rev. A (3)

J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A 42(1), 682–685 (1990).
[Crossref] [PubMed]

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Modulation instability induced by cross-phase modulation in optical fibers,” Phys. Rev. A 39(7), 3406–3413 (1989).
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[Crossref]

Phys. Rev. Lett. (4)

G. Van Simaeys, P. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87(3), 033902 (2001).
[Crossref] [PubMed]

M. Erkintalo, K. Hammani, B. Kibler, C. Finot, N. Akhmediev, J. M. Dudley, and G. Genty, “Higher-order modulation instability in nonlinear fiber optics,” Phys. Rev. Lett. 107(25), 253901 (2011).
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[Crossref] [PubMed]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56(2), 135–138 (1986).
[Crossref] [PubMed]

Phys. Rev. X (1)

A. Mussot, A. Kudlinski, M. Droques, P. Szriftgiser, and N. Akhmediev, “Fermi-Pasta-Ulam recurrence in nonlinear fiber optics: the role of reversible and irreversible losses,” Phys. Rev. X 4(1), 011054 (2014).
[Crossref]

Proc. SPIE (5)

M. A. Soto, M. Alem, W. Chen, and L. Thévenaz, “Mitigating modulation instability in Brillouin distributed fibre sensors,” Proc. SPIE 8794, 87943J (2013).
[Crossref]

M. Alem, M. A. Soto, and L. Thévenaz, “Modelling the depletion length induced by modulation instability in distributed optical fibre sensors,” Proc. SPIE 9157, 91575S (2014).

Y. Dong and X. Bao, “High spatial resolution and long-distance BOTDA using differential Brillouin gain in a dispersion shifted fiber,” Proc. SPIE 7503, 750384 (2009).
[Crossref]

D. Alasia, M. González-Herráez, L. Abrardi, S. Martin-López, and L. Thévenaz, “Detrimental effect of modulation instability on distributed optical fiber sensors using stimulated Brillouin scattering,” Proc. SPIE 5855, 587–590 (2005).
[Crossref]

S. M. Foaleng and L. Thévenaz, “Impact of Raman scattering and modulation instability on the performances of Brillouin sensors,” Proc. SPIE 7753, 77539V (2011).
[Crossref]

Quantum Electron. (1)

A. E. Ismagulov, S. A. Babin, E. V. Podivilov, M. P. Fedoruk, I. S. Shelemba, and O. V. Shtyrina, “Modulation instability of narrow-band nanosecond pulses propagating in anomalous-dispersion fibre,” Quantum Electron. 39(8), 765–769 (2009).
[Crossref]

Science (1)

R. Nissim, A. Pejkic, E. Myslivets, B. P. Kuo, N. Alic, and S. Radic, “Ultrafast optics. Ultrafast optical control by few photons in engineered fiber,” Science 345(6195), 417–419 (2014).
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M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge University, 2008).

M. E. Marhic, V. Curri, and L. G. Kazovsky, “Bessel function solution for the gain of one-pump fiber optical parametric amplifier,” in Proceedings of IEEE Conference on Nonlinear Optics (IEEE, 1998), pp. 221–223.
[Crossref]

E. Fermi, J. Pasta, and H. C. Ulam, “Studies of nonlinear problems,” in Collected Papers of Enrico Fermi, E. Segrè, ed. (University of Chicago, 1965), Vol. 2, pp. 977–988.

J. C. Travers, “Continuous wave supercontinuum generation,” in Supercontinuum Generation in Optical Fibers, J. M. Dudley and J. R. Taylor, eds. (Cambridge University, 2010), Chap. 8.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2006).

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Figures (12)

Fig. 1
Fig. 1 MI gain spectrum for a 10 km lossless SMF with different values of input power and typical values of γ = 1.8 W−1/km and β2 = −22 ps2/km. Comparison between simulations of the NLSE (continuous blue line) and the analytical solution according to Eq. (4) (red dashed line).
Fig. 2
Fig. 2 MI gain spectrum for a 10 km SMF with different values of input power and typical values α = 0.2 dB/km, γ = 1.8 W−1/km and β2 = −22 ps2/km. Note that the negative baseline level (−2 dB) is simply a consequence of the fiber loss here considered in the calculation.
Fig. 3
Fig. 3 Pump power evolution along an SMF of 25 km with α = 0.2 dB/km, γ = 1.8 W−1/km and β2 = −22 ps2/km, in presence of noise with a power spectral density of −121 dBm/Hz. Note that the pump power is normalized to P0eαz to discard the effect of the fiber loss on the curves.
Fig. 4
Fig. 4 Output pump power versus input power for an SMF with length L = 10 km, α = 0.2 dB/km, γ = 1.8 W−1/km and β2 = −22 ps2/km. Note that the pump power is normalized to eαL to discard the effect of the fiber attenuation on the curves.
Fig. 5
Fig. 5 Critical linear gain σcrit versus fiber length obtained from the NLSE, Eq. (16) and Eq. (17) for (a) RD = 10% and (b) RD = 20%, using two values of noise PSD: −121 and −141 dBm/Hz. Note that the critical gain is here obtained considering that the depletion ratio of RD occurs at the end of a given fiber, whose length ranges from 2 km up to 50 km.
Fig. 6
Fig. 6 Experimental setup based on a standard BOTDA scheme; LD: laser diode; SOA: semiconductor optical amplifier; EDFA: erbium-doped fiber amplifier; VOA: variable optical attenuator; FBG: fiber Bragg grating; At.: 10 dB attenuator; PD: photodetector; Osc: Oscilloscope; EOM: electric-optic modulator; SMF: single-mode fiber.
Fig. 7
Fig. 7 Two modifications to the standard BOTDA system; used to analyze the impact of noise on the behavior of modulation instability: (a) Scheme used to couple ASE noise co-propagating with the pump pulses; (b) Scheme used to filter out ASE noise from the pump pulses.
Fig. 8
Fig. 8 Brillouin traces along with their fitted curves, for three different values of input pump power: 130 mW, 290 mW, and 570 mW.
Fig. 9
Fig. 9 Longitudinal BOTDA traces for different noise PSD values, ranging from −135 dBm/Hz up to −115 dBm/Hz, and for an input peak power of (a) 60 mW and (b) 500 mW.
Fig. 10
Fig. 10 (a) BOTDA traces for different peak power levels for filtered and non-filtered cases. (b) SBS gain measured in the last meters of the 25 km SMF versus input pump power, with (red squares) and without (blue circles) narrowband optical filtering.
Fig. 11
Fig. 11 Critical power Pcrit versus fiber length obtained by numerical simulations, experimental measurements and analytical model for two depletion ratios: (a) RD = 10% and (b) RD = 20%.
Fig. 12
Fig. 12 Critical linear gain σcrit versus fiber length for two depletion ratios: (a) RD = 10% and (b) RD = 20%; the plots compare measurements, simulations and results of the proposed analytical model.

Equations (32)

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i A z β 2 2 2 A τ 2 +i α 2 A+γ P 0 | A | 2 A=0,
G MI =1+2 ( γ P 0 g ) 2 sin h 2 ( gL ),
g 2 = ( γ P 0 ) 2 ( γ P 0 + Δβ 2 ) 2 =Δβ( γ P 0 + Δβ 4 ),
G MI (Ω)=1+ sin h 2 ( 2γ P 0 L ( Ω Ω c ) 2 ( 1 ( Ω Ω c ) 2 ) ) 2 ( Ω Ω c ) 2 ( 1 ( Ω Ω c ) 2 ) ,
Ω c = 4γ P 0 | β 2 | .
L eff = 1 e αL α .
G MI = e αL ( 1+ G P )= e αL ( 1+2 ( γ P 0 g ) 2 sin h 2 ( g L eff ) ),
R D ( z ) P MI ( z ) P 0 e αz = P 0 e αz P( z ) P 0 e αz =1 P( z ) P 0 e αz .
P MI = e αL 2π 0 S n (ω) G P ( ω )dω e αL 2π ω 0 m Ω c ω 0 +m Ω c S n (ω) G P ( ω )dω ,
P MI = e αL S n Ω c 2π lim m m m G P ( x )dx = e αL S n Ω c 2π G P ( x )dx = e αL S n Ω c π 0 G P ( x )dx ,
G P (x)= sin h 2 ( 2γ P 0 L eff x 2 ( 1 x 2 ) ) 2 x 2 ( 1 x 2 ) .
I= 0 G P ( x )dx e 2γ P 0 L eff π 4 2γ P 0 L eff .
P MI = S n e 2γ P 0 L eff αL 2 2π L eff | β 2 | .
e 2γ P 0 L eff = 2 R D 2π L eff | β 2 | S n P 0 .
2γ P crit L eff =ln( 2 R D 2π L eff | β 2 | S n P crit ).
σ crit =ln( R D 2π| β 2 | S n γ L eff σ crit ).
σ crit ln( σ crit )=ln( R D )( S n 10 +9 )ln( 10 )+ ln(2) 2 .
P crit = σ crit 2γ L eff .
A(L)=cosh(gL)+i γ P 0 + Δβ /2 g sinh(gL), B(L)=i γ P 0 g sinh(gL),
G S = | f(L) | 2 = | A(L) | 2 =1+ ( γ P 0 g ) 2 sin h 2 (gL).
G I = | f(L) | 2 = | B(L) | 2 = ( γ P 0 g ) 2 sin h 2 (gL).
| f(L) | 2 = | A(L) | 2 + | B(L) | 2 + e i(φ+ψ) A(L) B * (L)+ e i(φ+ψ) A * (L)B(L).
G MI =E[ | f(L) | 2 ]= | A(L) | 2 + | B(L) | 2 = G S + G I ,
I(s)= + g(x) e sf(x) dx g( x 0 ) e sf( x 0 ) 2π s| f ( x 0 ) | .
I(s)g( x 0 ) + e sf(x) dx .
f(x)f( x 0 )+ f ( x 0 )(x x 0 )+ f ( x 0 ) 2 (x x 0 ) 2 =f( x 0 )+ f ( x 0 ) 2 (x x 0 ) 2 .
+ e sf(x) dx e sf( x 0 ) + e s f ( x 0 ) 2 (x- x 0 ) 2 dx .
+ e s f ( x 0 ) 2 (x- x 0 ) 2 dx = 2π s| f ( x 0 ) | .
sin h 2 ( u ) e 2u 4 ,foru1.
G P (x)= sin h 2 ( 2γ P 0 L eff x 2 ( 1 x 2 ) ) 2 x 2 ( 1 x 2 ) exp( 4γ P 0 L eff x 2 ( 1 x 2 ) ) 8 x 2 ( 1 x 2 ) .
I= 0 G P ( x )dx exp( 4γ P 0 L eff x 2 ( 1 x 2 ) ) 8 x 2 ( 1 x 2 ) dx .
{ s=4γ P 0 L eff f(x)= x 2 ( 1 x 2 ) g(x)= ( 8 x 2 ( 1 x 2 ) ) 1 ,

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