Abstract

We propose and compare with experimental data a two-stage model of supercontinuum formation in a fiber for nanosecond-long pulse with intensities in 10W range. As a result of the first stage, the sea of solitons is formed. The second stage is spectrum modification because of Raman interaction.

© 2008 Optical Society of America

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  1. J. K. 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. A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, D. Chorvat Jr., V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).
  3. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, "Supercontinuum generation in tapered fibers," Opt. Lett. 25, 1415-1417 (2000).
    [CrossRef]
  4. A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, Jr., D. Chorvat, V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).
  5. J. M. Dudley, L. Provino, N. Grossard, H. Mailotte, R. S. Windeler, B. J. Eggleton, and S. Coen, "Supercontinuum generation in air-silica microstructure fibers with nanosecond and femtosecond pulse pumping," J. Opt. Soc. Am. B 19,765-771 (2002).
    [CrossRef]
  6. B. R. Washburn, S. E. Ralph, and R. S. Windeler, "Ultrashort pulse propagation in air-silica microstructure fiber," Opt. Express 10, 575-580 (2002).
    [PubMed]
  7. F. Lu, Y. Deng, and W. H. Knox, "Generation of broadband femtosecond visible pulses in dispersion-micromanaged holey fibers," Opt. Lett. 30, 1566-1568 (2005).
    [CrossRef] [PubMed]
  8. A. Ortigosa-Blanch, J. C. Knight, and P. St. J. Russell, "Pulse breaking and supercontinuum generation with 200-fs pump pulses in photonic crystal fibers," J. Opt. Soc. Am. B 19, 2567-2572 (2002).
    [CrossRef]
  9. K. M. Hilligsøe, H. N. Paulsen, J. Thøgersen, S. R. Keiding, and J. J. Larsen, "Initial steps of supercontinuum generation in photonic crystal fibers," J. Opt. Soc. Am. B 20, 1887-1893 (2003).
    [CrossRef]
  10. K. Mori, H. Takara, and S. Kawanichi, "Analysis and design of supercontinuum pulse generation in a single-mode optical fiber," J. Opt. Soc. Am. B 18, 1780-1792 (2001).
    [CrossRef]
  11. S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russel, "White light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber," Opt. Lett. 26, 1356-1358 (2001).
    [CrossRef]
  12. L. Provino, J. M. Dudley, H. Maillotte, N. Grossard, R. S. Windeler, and B. J. Eggleton, "Compact broadband continuum source based on a microchip laser pumped microstructure fiber," Electron. Lett. 37, 558-560 (2001).
    [CrossRef]
  13. A. A. Fotiadi and P. Mégret, "Self-Q-switched Er-Brillouin fiber source with extra-cavity generation of a Raman supercontinuum in a dispersion-shifted fiber," Opt. Lett. 31, 1621-1623 (2006).
    [CrossRef] [PubMed]
  14. V. Avdokhin, S. V. Popov, and J. R. Taylor, "Continuous-wave, high-power, Raman continuum generation in holey fibers," Opt. Lett. 28, 1353-1355 (2003).
    [CrossRef] [PubMed]
  15. C. Travers, R. E. Kennedy, S. V. Popov, J. R. Taylor, H. Sabert, and B. Mangan, "Extended continuous-wave supercontinuum generation in a low-water-loss holey fiber," Opt. Lett. 30, 1938-1940 (2005).
    [CrossRef] [PubMed]
  16. A. K. Abeeluck, C. Headley, and C. G. Jørgensten, "High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser," Opt. Lett. 29, 2163-2165 (2004).
    [CrossRef] [PubMed]
  17. W. Zhang, Y. Wang, J. Peng, and X. Liu, "Broadband high power continuous wave fiber Raman source and its applications," Opt. Commun. 231, 371 - 374 (2004).
    [CrossRef]
  18. A. Mussot, E. Lantz, H. Mailotte, T. Sylvestre, C. Finot, and S. Pitois, "Spectral broadening of a partially coherent CW laser beam in single mode optical fibers," Opt. Express 12, 2838-2843 (2004).
    [CrossRef] [PubMed]
  19. S. Martin-Lopez, A. Carrasco-Sans, P. Corderera, L. Abrardi, M. L. Hernanz, and M. Gonzalez-Herraez, "Experimental investigation of the effect of pump incoherence on nonlinear pump spectral broadening and continuous-wave supercontinuum generation," Opt. Lett. 31, 3477-3479 (2006).
    [CrossRef] [PubMed]
  20. A. Podlipensky, P. Szarniak, N. Y. Joly, C. G. Poulton, and P. St. J. Russel, "Bound soliton pairs in photonic cristal fiber," Opt. Express 15, 1653-1662 (2007).
    [CrossRef] [PubMed]
  21. M. Dudley and S. Coen, "Numerical simulation and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers," IEEE J. Sel. Top. Quantum Electron. 8, 651-659 (2002).
    [CrossRef]
  22. V. E. Zakharov and A. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 61, 62-69 (1972).
  23. A. Peleg, "Log-normal distribution of pulse amplitudes due to Raman cross talk in wavelength division multiplexing soliton transmission," Opt. Lett. 29, 1980-1982 (2004).
    [CrossRef] [PubMed]
  24. B. A. Malomed, "Soliton-collision problem in the nonlinear Schrödinger equation with a nonlinear damping term," Phys. Rev. A 44, 1412-1414 (1991).
    [CrossRef] [PubMed]
  25. G. P. Agrawal, Nonlinear Fiber Optics, (Optics and Photonics, 3rd ed., Academic Press, San Diego, 2001).
  26. S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, "Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrodinger equation," Physica D 57, 96-160 (1992).
    [CrossRef]
  27. E. A. Kuzin, S. Mendoza-Vasquez, J. Gutierrez-Gutierrez, B. Ibarra-Escamilla, J. W. Haus, and R. Rojas-Laguna, " Intra-pulse Raman frequency shift versus conventional Stokes generation of diode laser pulses in optical fibers," Opt. Express 13, 3388-3396 (2005).
    [CrossRef] [PubMed]

2007 (1)

2006 (2)

2005 (3)

2004 (4)

2003 (2)

2002 (4)

2001 (3)

2000 (4)

J. K. 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]

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, D. Chorvat Jr., V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

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

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, Jr., D. Chorvat, V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

1992 (1)

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, "Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrodinger equation," Physica D 57, 96-160 (1992).
[CrossRef]

1991 (1)

B. A. Malomed, "Soliton-collision problem in the nonlinear Schrödinger equation with a nonlinear damping term," Phys. Rev. A 44, 1412-1414 (1991).
[CrossRef] [PubMed]

1972 (1)

V. E. Zakharov and A. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 61, 62-69 (1972).

Abeeluck, A. K.

Abrardi, L.

Alfimov, M. V.

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, Jr., D. Chorvat, V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, D. Chorvat Jr., V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

Avdokhin, V.

Birks, T. A.

Carrasco-Sans, A.

Chau, A. H. L.

Chorvat, D.

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, D. Chorvat Jr., V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, Jr., D. Chorvat, V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

Coen, S.

Corderera, P.

Deng, Y.

Dudley, J. M.

J. M. Dudley, L. Provino, N. Grossard, H. Mailotte, R. S. Windeler, B. J. Eggleton, and S. Coen, "Supercontinuum generation in air-silica microstructure fibers with nanosecond and femtosecond pulse pumping," J. Opt. Soc. Am. B 19,765-771 (2002).
[CrossRef]

L. Provino, J. M. Dudley, H. Maillotte, N. Grossard, R. S. Windeler, and B. J. Eggleton, "Compact broadband continuum source based on a microchip laser pumped microstructure fiber," Electron. Lett. 37, 558-560 (2001).
[CrossRef]

Dudley, M.

M. Dudley and S. Coen, "Numerical simulation and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers," IEEE J. Sel. Top. Quantum Electron. 8, 651-659 (2002).
[CrossRef]

Dyachenko, S.

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, "Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrodinger equation," Physica D 57, 96-160 (1992).
[CrossRef]

Eggleton, B. J.

J. M. Dudley, L. Provino, N. Grossard, H. Mailotte, R. S. Windeler, B. J. Eggleton, and S. Coen, "Supercontinuum generation in air-silica microstructure fibers with nanosecond and femtosecond pulse pumping," J. Opt. Soc. Am. B 19,765-771 (2002).
[CrossRef]

L. Provino, J. M. Dudley, H. Maillotte, N. Grossard, R. S. Windeler, and B. J. Eggleton, "Compact broadband continuum source based on a microchip laser pumped microstructure fiber," Electron. Lett. 37, 558-560 (2001).
[CrossRef]

Fedotov, A. B.

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, D. Chorvat Jr., V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, Jr., D. Chorvat, V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

Finot, C.

Fotiadi, A. A.

Gonzalez-Herraez, M.

Grossard, N.

J. M. Dudley, L. Provino, N. Grossard, H. Mailotte, R. S. Windeler, B. J. Eggleton, and S. Coen, "Supercontinuum generation in air-silica microstructure fibers with nanosecond and femtosecond pulse pumping," J. Opt. Soc. Am. B 19,765-771 (2002).
[CrossRef]

L. Provino, J. M. Dudley, H. Maillotte, N. Grossard, R. S. Windeler, and B. J. Eggleton, "Compact broadband continuum source based on a microchip laser pumped microstructure fiber," Electron. Lett. 37, 558-560 (2001).
[CrossRef]

Gutierrez-Gutierrez, J.

Harvey, J. D.

Haus, J. W.

Headley, C.

Hernanz, M. L.

Hilligsøe, K. M.

Ibarra-Escamilla, B.

Ivanov, A. A.

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, Jr., D. Chorvat, V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, D. Chorvat Jr., V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

Joly, N. Y.

Jørgensten, C. G.

Kawanichi, S.

Keiding, S. R.

Kennedy, R. E.

Knight, J. C.

Knox, W. H.

Kuzin, E. A.

Lantz, E.

Larsen, J. J.

Leonhardt, R.

Liu, X.

W. Zhang, Y. Wang, J. Peng, and X. Liu, "Broadband high power continuous wave fiber Raman source and its applications," Opt. Commun. 231, 371 - 374 (2004).
[CrossRef]

Lu, F.

Maillotte, H.

L. Provino, J. M. Dudley, H. Maillotte, N. Grossard, R. S. Windeler, and B. J. Eggleton, "Compact broadband continuum source based on a microchip laser pumped microstructure fiber," Electron. Lett. 37, 558-560 (2001).
[CrossRef]

Mailotte, H.

Malomed, B. A.

B. A. Malomed, "Soliton-collision problem in the nonlinear Schrödinger equation with a nonlinear damping term," Phys. Rev. A 44, 1412-1414 (1991).
[CrossRef] [PubMed]

Mangan, B.

Martin-Lopez, S.

Mégret, P.

Mendoza-Vasquez, S.

Mori, K.

Mussot, A.

Newell, A. C.

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, "Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrodinger equation," Physica D 57, 96-160 (1992).
[CrossRef]

Ortigosa-Blanch, A.

Paulsen, H. N.

Peleg, A.

Peng, J.

W. Zhang, Y. Wang, J. Peng, and X. Liu, "Broadband high power continuous wave fiber Raman source and its applications," Opt. Commun. 231, 371 - 374 (2004).
[CrossRef]

Pitois, S.

Podlipensky, A.

Popov, S. V.

Poulton, C. G.

Provino, L.

J. M. Dudley, L. Provino, N. Grossard, H. Mailotte, R. S. Windeler, B. J. Eggleton, and S. Coen, "Supercontinuum generation in air-silica microstructure fibers with nanosecond and femtosecond pulse pumping," J. Opt. Soc. Am. B 19,765-771 (2002).
[CrossRef]

L. Provino, J. M. Dudley, H. Maillotte, N. Grossard, R. S. Windeler, and B. J. Eggleton, "Compact broadband continuum source based on a microchip laser pumped microstructure fiber," Electron. Lett. 37, 558-560 (2001).
[CrossRef]

Pushkarev, A.

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, "Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrodinger equation," Physica D 57, 96-160 (1992).
[CrossRef]

Ralph, S. E.

Ranka, J. K.

Rojas-Laguna, R.

Russel, P. St. J.

Russell, P. St. J.

Sabert, H.

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 61, 62-69 (1972).

Stentz, A. J.

Sylvestre, T.

Szarniak, P.

Takara, H.

Taylor, J. R.

Thøgersen, J.

Travers, C.

Wadsworth, W. J.

Wang, Y.

W. Zhang, Y. Wang, J. Peng, and X. Liu, "Broadband high power continuous wave fiber Raman source and its applications," Opt. Commun. 231, 371 - 374 (2004).
[CrossRef]

Washburn, B. R.

Windeler, R. S.

Zakharov, V. E.

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, "Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrodinger equation," Physica D 57, 96-160 (1992).
[CrossRef]

V. E. Zakharov and A. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 61, 62-69 (1972).

Zhang, W.

W. Zhang, Y. Wang, J. Peng, and X. Liu, "Broadband high power continuous wave fiber Raman source and its applications," Opt. Commun. 231, 371 - 374 (2004).
[CrossRef]

Zheltikov, A. M.

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, Jr., D. Chorvat, V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, D. Chorvat Jr., V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

Electron. Lett. (1)

L. Provino, J. M. Dudley, H. Maillotte, N. Grossard, R. S. Windeler, and B. J. Eggleton, "Compact broadband continuum source based on a microchip laser pumped microstructure fiber," Electron. Lett. 37, 558-560 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Dudley and S. Coen, "Numerical simulation and coherence properties of supercontinuum generation in photonic crystal and tapered optical fibers," IEEE J. Sel. Top. Quantum Electron. 8, 651-659 (2002).
[CrossRef]

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

Laser Phys. (2)

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, D. Chorvat Jr., V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

A. B. Fedotov, A. M. Zheltikov, A. A. Ivanov, M. V. Alfimov, D. Chorvat, Jr., D. Chorvat, V. I. Beloglazov, and D. Von Der Linde, "Supercontinuum-generating holey fibers as new broadband sources for spectroscopic applications," Laser Phys. 10, 723-726 (2000).

Opt. Commun. (1)

W. Zhang, Y. Wang, J. Peng, and X. Liu, "Broadband high power continuous wave fiber Raman source and its applications," Opt. Commun. 231, 371 - 374 (2004).
[CrossRef]

Opt. Express (4)

Opt. Lett. (10)

A. Peleg, "Log-normal distribution of pulse amplitudes due to Raman cross talk in wavelength division multiplexing soliton transmission," Opt. Lett. 29, 1980-1982 (2004).
[CrossRef] [PubMed]

F. Lu, Y. Deng, and W. H. Knox, "Generation of broadband femtosecond visible pulses in dispersion-micromanaged holey fibers," Opt. Lett. 30, 1566-1568 (2005).
[CrossRef] [PubMed]

S. Martin-Lopez, A. Carrasco-Sans, P. Corderera, L. Abrardi, M. L. Hernanz, and M. Gonzalez-Herraez, "Experimental investigation of the effect of pump incoherence on nonlinear pump spectral broadening and continuous-wave supercontinuum generation," Opt. Lett. 31, 3477-3479 (2006).
[CrossRef] [PubMed]

A. A. Fotiadi and P. Mégret, "Self-Q-switched Er-Brillouin fiber source with extra-cavity generation of a Raman supercontinuum in a dispersion-shifted fiber," Opt. Lett. 31, 1621-1623 (2006).
[CrossRef] [PubMed]

V. Avdokhin, S. V. Popov, and J. R. Taylor, "Continuous-wave, high-power, Raman continuum generation in holey fibers," Opt. Lett. 28, 1353-1355 (2003).
[CrossRef] [PubMed]

C. Travers, R. E. Kennedy, S. V. Popov, J. R. Taylor, H. Sabert, and B. Mangan, "Extended continuous-wave supercontinuum generation in a low-water-loss holey fiber," Opt. Lett. 30, 1938-1940 (2005).
[CrossRef] [PubMed]

A. K. Abeeluck, C. Headley, and C. G. Jørgensten, "High-power supercontinuum generation in highly nonlinear, dispersion-shifted fibers by use of a continuous-wave Raman fiber laser," Opt. Lett. 29, 2163-2165 (2004).
[CrossRef] [PubMed]

J. K. 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. Russel, "White light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber," Opt. Lett. 26, 1356-1358 (2001).
[CrossRef]

Phys. Rev. A (1)

B. A. Malomed, "Soliton-collision problem in the nonlinear Schrödinger equation with a nonlinear damping term," Phys. Rev. A 44, 1412-1414 (1991).
[CrossRef] [PubMed]

Physica D (1)

S. Dyachenko, A. C. Newell, A. Pushkarev, and V. E. Zakharov, "Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrodinger equation," Physica D 57, 96-160 (1992).
[CrossRef]

Sov. Phys. JETP (1)

V. E. Zakharov and A. B. Shabat, "Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media," Sov. Phys. JETP 61, 62-69 (1972).

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, (Optics and Photonics, 3rd ed., Academic Press, San Diego, 2001).

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Figures (5)

Fig. 1.
Fig. 1.

The spectrum of a sum of solitons according to Zakharov-Shabat statistics of soliton sea (red line), and the result of numerical simulation for breakup of a long pulse with initially small white noise (blue circles). Approximately 18 solitons are formed. It is seen, that the high-frequency tail is well described by a spectrum resulting from the superposition of independent solitons.

Fig. 2.
Fig. 2.

The developing of the spectra with fiber length calculated from Eq. (7); (a) for 3 ns pulses and (b) for 12 ns pulses. Fiber parameters are close to those used in experiment.

Fig. 3.
Fig. 3.

Comparative spectra at two fixed powers for series of length between 100 m and 8.0 km; (a) the pulse power is 6 W, (b) the pulse power is 10 W.

Fig. 4.
Fig. 4.

Comparison between experimental and Zakharov and Shabat spectra; (a) 6-W pump and 4.5-km fiber; (b) 10-W pump and 1.6-km fiber.

Fig. 5.
Fig. 5.

The growth of the red tail with fiber length for 10-W pump pulses; (a) for the 4.5 km fiber and (b) for the 8-km fiber.

Equations (8)

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z A = i β 2 2 t 2 A + i γ A 2 A i γ T R ( t A 2 ) A
A n = ρ n k 2 cosh ( k ρ n ( t t n ) 2 ) .
ρ n = 4 A 0 2 k n 2 π 2 k 2 T 2
A ( t , z ) = ω A ω z exp ( i ω t ) .
z ( A ( ω ) A * ( ω ) ) =
i γ ω 1 + ω 2 = ω 3 + ω A ( ω 1 ) A ( ω 2 ) A * ( ω 3 ) A * ( ω ) ( 1 iT R ( ω 1 ω 3 ) ) c . c .
z A ω z 2 A ω z 2 = 2 γ T R d ω ( ω ω ) A ω z 2 .
A ω z 2 = A 0 ( ω ) 2 E exp ( 2 γ T R E ω z ) d ω A 0 ( ω ) 2 exp ( 2 γ T R E ω z )

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