Abstract

We present a numerical study of the wave breakup and soliton formation in a standard single-mode fiber pumped by variable pulse lengths in the range from 20to400ps in the presence of noise. The average power and the standard deviation of the trailing soliton were calculated. We calculated also the average distance at which the soliton time delay reaches 1.5 times the pulse width. We found that for pulses longer than 100ps the breakup starts from the amplification of the noisy modulation of the amplitude by the modulation instability mechanism even for very low noise power, while for pulses shorter than 20ps the breakup starts from the pulse collapse. For intermediate durations, wave breakup starts from the pulse collapse at low noise power, while for higher noise power, modulation instability prevails.

© 2006 Optical Society of America

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  1. J. R. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air/silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000).
    [CrossRef]
  2. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, "Supercontinuum generation in tapered fibers," Opt. Lett. 25, 1415-1417 (2000).
    [CrossRef]
  3. S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber," Opt. Lett. 26, 1356-1358 (2001).
    [CrossRef]
  4. A. K. Abeeluck and C. Headley, "Continuus-wave pumping in the anomalous- and normal-dispersion regime of nonlinear fibers for supercontinuum generation," Opt. Lett. 30, 61-63 (2005).
    [CrossRef] [PubMed]
  5. A. Mussot, E. Lantz, H. Mailotte, and T. Sylvestre, "Spectral broadening of a partially coherent CW laser beam in single-mode optical fibers," Opt. Express 12, 2838-2848 (2004).
    [CrossRef] [PubMed]
  6. A. Demircan and U. Bandelow, "Supercontinuum generation by the modulation instability," Opt. Commun. 244, 181-185 (2005).
    [CrossRef]
  7. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  8. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, "Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers," Opt. Lett. 8, 289-291 (1983).
    [CrossRef] [PubMed]
  9. E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, and A. A. Fomichev, "Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985).
    [CrossRef]
  10. F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986).
    [CrossRef] [PubMed]
  11. J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1988).
    [CrossRef]
  12. E. A. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, "Numerical analysis of the Raman spectrum evolution and soliton pulse generation in single-mode fibers," J. Opt. Soc. Am. B 8, 1626-1632 (1991).
    [CrossRef]
  13. A. S. Gouveia-Neto, M. E. Faldon, and J. R. Taylor, "Raman amplification of modulation instability and solitary-wave formation," Opt. Lett. 13, 1029-1031 (1988).
    [CrossRef] [PubMed]
  14. W. Hodel and H. P. Weber, "Decay of femtosecond higher-order soliton in an optical fiber induced by Raman self-pumping," Opt. Lett. 12, 924-926 (1987).
    [CrossRef] [PubMed]
  15. P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, "Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron. QE-23, 1938-1946 (1987).
    [CrossRef]
  16. N. Nishizawa and T. Goto, "Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers," IEEE Photon. Technol. Lett. 11, 325-327 (1999).
    [CrossRef]
  17. E. Brainis and D. Amans, "Scalar and vector modulation instability induced by vacuum fluctuations in fibers: numerical study," Phys. Rev. A 71, 023808 (2005).
    [CrossRef]
  18. A. Betlej, P. Schmitt, P. Sidereas, R. Tracy, Ch. G. Goeddle, and J. R. Thompson, "Increased Stokes pulse energy variation from amplified classical noise in a fiber Raman generator," Opt. Express 13, 2948-2960 (2005).
    [CrossRef] [PubMed]

2005 (4)

2004 (1)

2001 (1)

2000 (2)

1999 (1)

N. Nishizawa and T. Goto, "Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers," IEEE Photon. Technol. Lett. 11, 325-327 (1999).
[CrossRef]

1991 (1)

1988 (2)

1987 (2)

W. Hodel and H. P. Weber, "Decay of femtosecond higher-order soliton in an optical fiber induced by Raman self-pumping," Opt. Lett. 12, 924-926 (1987).
[CrossRef] [PubMed]

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, "Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron. QE-23, 1938-1946 (1987).
[CrossRef]

1986 (1)

1985 (1)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, and A. A. Fomichev, "Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985).
[CrossRef]

1983 (1)

Abeeluck, A. K.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Amans, D.

E. Brainis and D. Amans, "Scalar and vector modulation instability induced by vacuum fluctuations in fibers: numerical study," Phys. Rev. A 71, 023808 (2005).
[CrossRef]

Bandelow, U.

A. Demircan and U. Bandelow, "Supercontinuum generation by the modulation instability," Opt. Commun. 244, 181-185 (2005).
[CrossRef]

Beaud, P.

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, "Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron. QE-23, 1938-1946 (1987).
[CrossRef]

Betlej, A.

Birks, T. A.

Brainis, E.

E. Brainis and D. Amans, "Scalar and vector modulation instability induced by vacuum fluctuations in fibers: numerical study," Phys. Rev. A 71, 023808 (2005).
[CrossRef]

Chau, A. H. L.

Coen, S.

Demircan, A.

A. Demircan and U. Bandelow, "Supercontinuum generation by the modulation instability," Opt. Commun. 244, 181-185 (2005).
[CrossRef]

Dianov, E. M.

E. A. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, "Numerical analysis of the Raman spectrum evolution and soliton pulse generation in single-mode fibers," J. Opt. Soc. Am. B 8, 1626-1632 (1991).
[CrossRef]

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, and A. A. Fomichev, "Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985).
[CrossRef]

Faldon, M. E.

Fomichev, A. A.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, and A. A. Fomichev, "Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985).
[CrossRef]

Goeddle, Ch. G.

Golovchenko, E. A.

Gordon, J. P.

Goto, T.

N. Nishizawa and T. Goto, "Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers," IEEE Photon. Technol. Lett. 11, 325-327 (1999).
[CrossRef]

Gouveia-Neto, A. S.

Harvey, J. D.

Headley, C.

Hodel, W.

W. Hodel and H. P. Weber, "Decay of femtosecond higher-order soliton in an optical fiber induced by Raman self-pumping," Opt. Lett. 12, 924-926 (1987).
[CrossRef] [PubMed]

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, "Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron. QE-23, 1938-1946 (1987).
[CrossRef]

Karasik, A. Ya.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, and A. A. Fomichev, "Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985).
[CrossRef]

Knight, J. C.

Lantz, E.

Leonhardt, R.

Mailotte, H.

Mamyshev, P. V.

E. A. Golovchenko, P. V. Mamyshev, A. N. Pilipetskii, and E. M. Dianov, "Numerical analysis of the Raman spectrum evolution and soliton pulse generation in single-mode fibers," J. Opt. Soc. Am. B 8, 1626-1632 (1991).
[CrossRef]

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, and A. A. Fomichev, "Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985).
[CrossRef]

Mitschke, F. M.

Mollenauer, L. F.

Mussot, A.

Nishizawa, N.

N. Nishizawa and T. Goto, "Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers," IEEE Photon. Technol. Lett. 11, 325-327 (1999).
[CrossRef]

Pilipetskii, A. N.

Prokhorov, A. M.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, and A. A. Fomichev, "Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985).
[CrossRef]

Ranka, J. R.

Russell, P. St. J.

Schmitt, P.

Serkin, V. N.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, and A. A. Fomichev, "Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985).
[CrossRef]

Sidereas, P.

Stelmakh, M. F.

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, and A. A. Fomichev, "Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985).
[CrossRef]

Stentz, A. J.

Stolen, R. H.

Sylvestre, T.

Taylor, J. R.

Thompson, J. R.

Tomlinson, W. J.

Tracy, R.

Wadsworth, W. J.

Weber, H. P.

W. Hodel and H. P. Weber, "Decay of femtosecond higher-order soliton in an optical fiber induced by Raman self-pumping," Opt. Lett. 12, 924-926 (1987).
[CrossRef] [PubMed]

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, "Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron. QE-23, 1938-1946 (1987).
[CrossRef]

Windeler, R. S.

Zysset, B.

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, "Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron. QE-23, 1938-1946 (1987).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Beaud, W. Hodel, B. Zysset, and H. P. Weber, "Ultrashort pulse propagation, pulse breakup, and fundamental soliton formation in a single-mode optical fiber," IEEE J. Quantum Electron. QE-23, 1938-1946 (1987).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

N. Nishizawa and T. Goto, "Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers," IEEE Photon. Technol. Lett. 11, 325-327 (1999).
[CrossRef]

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

JETP Lett. (1)

E. M. Dianov, A. Ya. Karasik, P. V. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stelmakh, and A. A. Fomichev, "Stimulated-Raman conversion of multisoliton pulses in quartz optical fibers," JETP Lett. 41, 294-297 (1985).
[CrossRef]

Opt. Commun. (1)

A. Demircan and U. Bandelow, "Supercontinuum generation by the modulation instability," Opt. Commun. 244, 181-185 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (9)

F. M. Mitschke and L. F. Mollenauer, "Discovery of the soliton self-frequency shift," Opt. Lett. 11, 659-661 (1986).
[CrossRef] [PubMed]

J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662-664 (1988).
[CrossRef]

A. S. Gouveia-Neto, M. E. Faldon, and J. R. Taylor, "Raman amplification of modulation instability and solitary-wave formation," Opt. Lett. 13, 1029-1031 (1988).
[CrossRef] [PubMed]

W. Hodel and H. P. Weber, "Decay of femtosecond higher-order soliton in an optical fiber induced by Raman self-pumping," Opt. Lett. 12, 924-926 (1987).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, and W. J. Tomlinson, "Extreme picosecond pulse narrowing by means of soliton effect in single-mode optical fibers," Opt. Lett. 8, 289-291 (1983).
[CrossRef] [PubMed]

J. R. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air/silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000).
[CrossRef]

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, "Supercontinuum generation in tapered fibers," Opt. Lett. 25, 1415-1417 (2000).
[CrossRef]

S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber," Opt. Lett. 26, 1356-1358 (2001).
[CrossRef]

A. K. Abeeluck and C. Headley, "Continuus-wave pumping in the anomalous- and normal-dispersion regime of nonlinear fibers for supercontinuum generation," Opt. Lett. 30, 61-63 (2005).
[CrossRef] [PubMed]

Phys. Rev. A (1)

E. Brainis and D. Amans, "Scalar and vector modulation instability induced by vacuum fluctuations in fibers: numerical study," Phys. Rev. A 71, 023808 (2005).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (8)

Fig. 1
Fig. 1

Wave breakup for the 100 ps pulse without noise at the input: (a) the temporal waveform, (b) the scaled power spectrum.

Fig. 2
Fig. 2

Start of the wave breakup for the 400 ps pulse without noise at the input: (a) waveform, (b) power spectrum.

Fig. 3
Fig. 3

(a) Distance and (b) pulse power necessary for the initiation of wave breakup.

Fig. 4
Fig. 4

Start of the wave breakup for the 100 ps pulse at the presence of noise: (a) waveform and (b) power spectrum after propagating 400 m .

Fig. 5
Fig. 5

Collapse of the 20 ps pulse in the presence of noise: (a) waveform and (b) power spectrum after 300 m propagation distance.

Fig. 6
Fig. 6

(a) Soliton sequence and (b) the first extracted soliton.

Fig. 7
Fig. 7

(a) Soliton peak power and (b) the relative standard deviation of the soliton peak power versus the noise power.

Fig. 8
Fig. 8

(a) Distance providing the 3 T 0 delay and (b) the relative standard deviation of the distance versus the noise power.

Equations (4)

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i A z + i β 2 2 2 A T 2 = i γ ( A 2 A T R A A 2 T ) ,
A ( 0 ) = P 0 exp [ ( T T 0 ) 2 ] ,
A noise ( t n ) = A 0 [ a ( t n ) + i b ( t n ) ] ,
s = ( 1 m 1 i m ( x i x ¯ ) 2 ) 1 2 ,

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