Abstract

We present a numerical investigation of fast optical soliton collisions in the presence of delayed Raman response. By employing a high-resolution numerical grid and by averaging over radiation-induced oscillations we are able to accurately measure the Raman-induced cross talk and cross frequency shift. The results of our numerical simulations confirm the analytic predictions based on the adiabatic perturbation theory.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  2. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986).
    [CrossRef] [PubMed]
  3. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt. Lett. 11, 662–664 (1986).
    [CrossRef] [PubMed]
  4. Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
    [CrossRef]
  5. F. Luan, D. V. Skryabin, A. V. Yulin, and J. C. Knight, “Energy exchange between colliding solitons in photonic crystal fibers,” Opt. Express 14, 9844–9853 (2006).
    [CrossRef] [PubMed]
  6. M. H. Frosz, O. Bang, and A. Bjarklev, “Soliton collision and Raman gain regimes in continuous-wave pumped supercontinuum generation,” Opt. Express 14, 9391–9407 (2006).
    [CrossRef] [PubMed]
  7. N. Korneev, E. A. Kuzin, B. Ibarra-Escamilla, M. Bello-Jiménez, and A. Flores-Rosas, “Initial development of supercontinuum in fibers with anomalous dispersion pumped by nanosecond-long pulses,” Opt. Express 16, 2636–2645 (2008).
    [CrossRef] [PubMed]
  8. G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009).
    [CrossRef]
  9. A. Efimov, A. J. Taylor, F. G. Omenetto, and E. Vanin, “Adaptive control of femtosecond soliton self-frequency shift in fibers,” Opt. Lett. 29, 271–273 (2004).
    [CrossRef] [PubMed]
  10. A. Hause and F. Mitschke, “Reduced soliton interaction by Raman self-frequency-shift,” Phys. Rev. A 80, 063824 (2009).
    [CrossRef]
  11. M.N.Islam, ed., Raman Amplifiers for Telecommunications 1: Physical Principles (Springer, 2004).
  12. C.Headley and G.P.Agrawal, eds., Raman Amplification in Fiber Optical Communication Systems (Elsevier, 2005).
  13. A. R. Chraplyvy, “Optical power limits in multichannel wavelength-division- multiplexed systems due to stimulated Raman scattering,” Electron. Lett. 20, 58–59 (1984).
    [CrossRef]
  14. F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “Effect of modulation statistics on Raman crosstalk in WDM systems,” IEEE Photon. Technol. Lett. 7, 101–103 (1995).
    [CrossRef]
  15. K.-P. Ho, “Statistical properties of stimulated Raman crosstalk in WDM systems,” J. Lightwave Technol. 18, 915–921 (2000).
    [CrossRef]
  16. M. Muktoyuk and S. Kumar, “Noise variance due to stimulated Raman scattering among channels of a wavelength-division-multiplexed system,” IEEE Photon. Technol. Lett. 15, 1222–1224 (2003).
    [CrossRef]
  17. A. Peleg, “Intermittent dynamics, strong correlations, and bit-error-rate in multichannel optical fiber communication systems,” Phys. Lett. A 360, 533–538 (2007).
    [CrossRef]
  18. Y. Chung and A. Peleg, “Monte Carlo simulations of pulse propagation in massive multichannel optical fiber communication systems,” Phys. Rev. A 77, 063835 (2008).
    [CrossRef]
  19. T. Yamamoto and S. Norimatsu, “Statistical analysis on stimulated Raman crosstalk in dispersion-managed fiber links,” J. Lightwave Technol. 21, 2229–2239 (2003).
    [CrossRef]
  20. Y. Chung and A. Peleg, “Strongly non-Gaussian statistics of optical soliton parameters due to collisions in the presence of delayed Raman response,” Nonlinearity 18, 1555–1574 (2005).
    [CrossRef]
  21. 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]
  22. A. Peleg, “Energy exchange in fast optical soliton collisions as a random cascade model,” Phys. Lett. A 373, 2734–2738 (2009).
    [CrossRef]
  23. M. Olivier, V. Roy, and M. Pichè, “Influence of the Raman effect on bound states of dissipative solitons,” Opt. Express 14, 9728–9742 (2006).
    [CrossRef] [PubMed]
  24. S. Chi and S. Wen, “Raman cross talk of soliton collision in a lossless fiber,” Opt. Lett. 14, 1216–1218 (1989).
    [CrossRef] [PubMed]
  25. S. Kumar, “Influence of Raman effects in wavelength-division multiplexed soliton systems,” Opt. Lett. 23, 1450–1452 (1998).
    [CrossRef]
  26. T. I. Lakoba and D. J. Kaup, “Influence of the Raman effect on dispersion-managed solitons and their interchannel collisions,” Opt. Lett. 24, 808–810 (1999).
    [CrossRef]
  27. C. Headley III and G. P. Agrawal, “Unified description of ultrafast stimulated Raman scattering in optical fibers,” J. Opt. Soc. Am. B 13, 2170–2177 (1996).
    [CrossRef]
  28. The dimensionless z in Eq. is z=(|β2|X)/(2τ02), where X is the actual position, τ0 is the soliton width, and β2 is the second order dispersion coefficient. The dimensionless retarded time is t=τ/τ0, where τ is the retarded time. The spectral width is ν0=1/(π2τ0) and the frequency difference is Δν=(πΔβν0)/2. ψ=E/P0, where E is proportional to the electric field and P0 is the peak power. The dimensionless second order dispersion coefficient is d=−1=β2/(γP0τ02), where γ is the Kerr nonlinearity coefficient. The coefficient ϵR is given by ϵR=0.006/τ0, where τ0 is in picoseconds.
  29. B. A. Malomed, “Radiative losses in soliton-soliton collisions in an optical fiber with the third-order dispersion,” Phys. Rev. A 43, 3114–3116 (1991).
    [CrossRef] [PubMed]
  30. A. Peleg, M. Chertkov, and I. Gabitov, “Interchannel interaction of optical solitons,” Phys. Rev. E 68, 026605 (2003).
    [CrossRef]
  31. A. Peleg, M. Chertkov, and I. Gabitov, “Inelastic interchannel collisions of pulses in optical fibers in the presence of third-order dispersion,” J. Opt. Soc. Am. B 21, 18–23 (2004).
    [CrossRef]
  32. 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]
  33. D. J. Kaup, “Second-order perturbations for solitons in optical fibers,” Phys. Rev. A 44, 4582–4590 (1991).
    [CrossRef] [PubMed]
  34. M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, “Shedding and interaction of solitons in weakly disordered optical fibers,” Phys. Rev. E 67, 036615 (2003).
    [CrossRef]
  35. H. Yoshida, “Construction of higher order symplectic integrators,” Phys. Lett. A 150, 262–268 (1990).
    [CrossRef]
  36. E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87, 201–215 (1995).
    [CrossRef]
  37. A. Peleg and Y. Chung, “Stationary solutions to the nonlinear Schrödinger equation in the presence of third order dispersion,” J. Phys. A 36, 10039–10051 (2003).
    [CrossRef]
  38. J. Soneson and A. Peleg, “Effect of quintic nonlinearity on soliton collisions in optical fibers,” Physica D 195, 123–140 (2004).
    [CrossRef]
  39. D. E. Pelinovsky, Y. S. Kivshar, and V. V. Afanasjev, “Internal modes of envelope solitons,” Physica D 116, 121–142 (1998).
    [CrossRef]

2009 (3)

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009).
[CrossRef]

A. Hause and F. Mitschke, “Reduced soliton interaction by Raman self-frequency-shift,” Phys. Rev. A 80, 063824 (2009).
[CrossRef]

A. Peleg, “Energy exchange in fast optical soliton collisions as a random cascade model,” Phys. Lett. A 373, 2734–2738 (2009).
[CrossRef]

2008 (2)

2007 (1)

A. Peleg, “Intermittent dynamics, strong correlations, and bit-error-rate in multichannel optical fiber communication systems,” Phys. Lett. A 360, 533–538 (2007).
[CrossRef]

2006 (3)

2005 (1)

Y. Chung and A. Peleg, “Strongly non-Gaussian statistics of optical soliton parameters due to collisions in the presence of delayed Raman response,” Nonlinearity 18, 1555–1574 (2005).
[CrossRef]

2004 (4)

2003 (5)

T. Yamamoto and S. Norimatsu, “Statistical analysis on stimulated Raman crosstalk in dispersion-managed fiber links,” J. Lightwave Technol. 21, 2229–2239 (2003).
[CrossRef]

M. Muktoyuk and S. Kumar, “Noise variance due to stimulated Raman scattering among channels of a wavelength-division-multiplexed system,” IEEE Photon. Technol. Lett. 15, 1222–1224 (2003).
[CrossRef]

A. Peleg, M. Chertkov, and I. Gabitov, “Interchannel interaction of optical solitons,” Phys. Rev. E 68, 026605 (2003).
[CrossRef]

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, “Shedding and interaction of solitons in weakly disordered optical fibers,” Phys. Rev. E 67, 036615 (2003).
[CrossRef]

A. Peleg and Y. Chung, “Stationary solutions to the nonlinear Schrödinger equation in the presence of third order dispersion,” J. Phys. A 36, 10039–10051 (2003).
[CrossRef]

2000 (1)

1999 (1)

1998 (2)

S. Kumar, “Influence of Raman effects in wavelength-division multiplexed soliton systems,” Opt. Lett. 23, 1450–1452 (1998).
[CrossRef]

D. E. Pelinovsky, Y. S. Kivshar, and V. V. Afanasjev, “Internal modes of envelope solitons,” Physica D 116, 121–142 (1998).
[CrossRef]

1996 (1)

1995 (2)

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87, 201–215 (1995).
[CrossRef]

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “Effect of modulation statistics on Raman crosstalk in WDM systems,” IEEE Photon. Technol. Lett. 7, 101–103 (1995).
[CrossRef]

1991 (3)

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]

D. J. Kaup, “Second-order perturbations for solitons in optical fibers,” Phys. Rev. A 44, 4582–4590 (1991).
[CrossRef] [PubMed]

B. A. Malomed, “Radiative losses in soliton-soliton collisions in an optical fiber with the third-order dispersion,” Phys. Rev. A 43, 3114–3116 (1991).
[CrossRef] [PubMed]

1990 (1)

H. Yoshida, “Construction of higher order symplectic integrators,” Phys. Lett. A 150, 262–268 (1990).
[CrossRef]

1989 (1)

1987 (1)

Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
[CrossRef]

1986 (2)

1984 (1)

A. R. Chraplyvy, “Optical power limits in multichannel wavelength-division- multiplexed systems due to stimulated Raman scattering,” Electron. Lett. 20, 58–59 (1984).
[CrossRef]

Afanasjev, V. V.

D. E. Pelinovsky, Y. S. Kivshar, and V. V. Afanasjev, “Internal modes of envelope solitons,” Physica D 116, 121–142 (1998).
[CrossRef]

Agrawal, G. P.

Bang, O.

Bello-Jiménez, M.

Bjarklev, A.

Chertkov, M.

A. Peleg, M. Chertkov, and I. Gabitov, “Inelastic interchannel collisions of pulses in optical fibers in the presence of third-order dispersion,” J. Opt. Soc. Am. B 21, 18–23 (2004).
[CrossRef]

A. Peleg, M. Chertkov, and I. Gabitov, “Interchannel interaction of optical solitons,” Phys. Rev. E 68, 026605 (2003).
[CrossRef]

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, “Shedding and interaction of solitons in weakly disordered optical fibers,” Phys. Rev. E 67, 036615 (2003).
[CrossRef]

Chi, S.

Chraplyvy, A. R.

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “Effect of modulation statistics on Raman crosstalk in WDM systems,” IEEE Photon. Technol. Lett. 7, 101–103 (1995).
[CrossRef]

A. R. Chraplyvy, “Optical power limits in multichannel wavelength-division- multiplexed systems due to stimulated Raman scattering,” Electron. Lett. 20, 58–59 (1984).
[CrossRef]

Chung, Y.

Y. Chung and A. Peleg, “Monte Carlo simulations of pulse propagation in massive multichannel optical fiber communication systems,” Phys. Rev. A 77, 063835 (2008).
[CrossRef]

Y. Chung and A. Peleg, “Strongly non-Gaussian statistics of optical soliton parameters due to collisions in the presence of delayed Raman response,” Nonlinearity 18, 1555–1574 (2005).
[CrossRef]

A. Peleg and Y. Chung, “Stationary solutions to the nonlinear Schrödinger equation in the presence of third order dispersion,” J. Phys. A 36, 10039–10051 (2003).
[CrossRef]

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, “Shedding and interaction of solitons in weakly disordered optical fibers,” Phys. Rev. E 67, 036615 (2003).
[CrossRef]

Dudley, J. M.

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009).
[CrossRef]

Dyachenko, A.

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, “Shedding and interaction of solitons in weakly disordered optical fibers,” Phys. Rev. E 67, 036615 (2003).
[CrossRef]

Efimov, A.

Eggleton, B. J.

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009).
[CrossRef]

Flores-Rosas, A.

Forghieri, F.

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “Effect of modulation statistics on Raman crosstalk in WDM systems,” IEEE Photon. Technol. Lett. 7, 101–103 (1995).
[CrossRef]

Frosz, M. H.

Gabitov, I.

A. Peleg, M. Chertkov, and I. Gabitov, “Inelastic interchannel collisions of pulses in optical fibers in the presence of third-order dispersion,” J. Opt. Soc. Am. B 21, 18–23 (2004).
[CrossRef]

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, “Shedding and interaction of solitons in weakly disordered optical fibers,” Phys. Rev. E 67, 036615 (2003).
[CrossRef]

A. Peleg, M. Chertkov, and I. Gabitov, “Interchannel interaction of optical solitons,” Phys. Rev. E 68, 026605 (2003).
[CrossRef]

Genty, G.

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009).
[CrossRef]

Gordon, J. P.

Hasegawa, A.

Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
[CrossRef]

Hause, A.

A. Hause and F. Mitschke, “Reduced soliton interaction by Raman self-frequency-shift,” Phys. Rev. A 80, 063824 (2009).
[CrossRef]

Headley, C.

Ho, K. -P.

Ibarra-Escamilla, B.

Kaup, D. J.

Kivshar, Y. S.

D. E. Pelinovsky, Y. S. Kivshar, and V. V. Afanasjev, “Internal modes of envelope solitons,” Physica D 116, 121–142 (1998).
[CrossRef]

Knight, J. C.

Kodama, Y.

Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
[CrossRef]

Kolokolov, I.

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, “Shedding and interaction of solitons in weakly disordered optical fibers,” Phys. Rev. E 67, 036615 (2003).
[CrossRef]

Korneev, N.

Kumar, S.

M. Muktoyuk and S. Kumar, “Noise variance due to stimulated Raman scattering among channels of a wavelength-division-multiplexed system,” IEEE Photon. Technol. Lett. 15, 1222–1224 (2003).
[CrossRef]

S. Kumar, “Influence of Raman effects in wavelength-division multiplexed soliton systems,” Opt. Lett. 23, 1450–1452 (1998).
[CrossRef]

Kuzin, E. A.

Kuznetsov, E. A.

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87, 201–215 (1995).
[CrossRef]

Lakoba, T. I.

Lebedev, V.

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, “Shedding and interaction of solitons in weakly disordered optical fibers,” Phys. Rev. E 67, 036615 (2003).
[CrossRef]

Luan, F.

Malomed, B. A.

B. A. Malomed, “Radiative losses in soliton-soliton collisions in an optical fiber with the third-order dispersion,” Phys. Rev. A 43, 3114–3116 (1991).
[CrossRef] [PubMed]

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]

Mikhailov, A. V.

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87, 201–215 (1995).
[CrossRef]

Mitschke, F.

A. Hause and F. Mitschke, “Reduced soliton interaction by Raman self-frequency-shift,” Phys. Rev. A 80, 063824 (2009).
[CrossRef]

Mitschke, F. M.

Mollenauer, L. F.

Muktoyuk, M.

M. Muktoyuk and S. Kumar, “Noise variance due to stimulated Raman scattering among channels of a wavelength-division-multiplexed system,” IEEE Photon. Technol. Lett. 15, 1222–1224 (2003).
[CrossRef]

Norimatsu, S.

Olivier, M.

Omenetto, F. G.

Peleg, A.

A. Peleg, “Energy exchange in fast optical soliton collisions as a random cascade model,” Phys. Lett. A 373, 2734–2738 (2009).
[CrossRef]

Y. Chung and A. Peleg, “Monte Carlo simulations of pulse propagation in massive multichannel optical fiber communication systems,” Phys. Rev. A 77, 063835 (2008).
[CrossRef]

A. Peleg, “Intermittent dynamics, strong correlations, and bit-error-rate in multichannel optical fiber communication systems,” Phys. Lett. A 360, 533–538 (2007).
[CrossRef]

Y. Chung and A. Peleg, “Strongly non-Gaussian statistics of optical soliton parameters due to collisions in the presence of delayed Raman response,” Nonlinearity 18, 1555–1574 (2005).
[CrossRef]

A. Peleg, M. Chertkov, and I. Gabitov, “Inelastic interchannel collisions of pulses in optical fibers in the presence of third-order dispersion,” J. Opt. Soc. Am. B 21, 18–23 (2004).
[CrossRef]

J. Soneson and A. Peleg, “Effect of quintic nonlinearity on soliton collisions in optical fibers,” Physica D 195, 123–140 (2004).
[CrossRef]

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]

A. Peleg, M. Chertkov, and I. Gabitov, “Interchannel interaction of optical solitons,” Phys. Rev. E 68, 026605 (2003).
[CrossRef]

A. Peleg and Y. Chung, “Stationary solutions to the nonlinear Schrödinger equation in the presence of third order dispersion,” J. Phys. A 36, 10039–10051 (2003).
[CrossRef]

Pelinovsky, D. E.

D. E. Pelinovsky, Y. S. Kivshar, and V. V. Afanasjev, “Internal modes of envelope solitons,” Physica D 116, 121–142 (1998).
[CrossRef]

Pichè, M.

Roy, V.

Shimokhin, I. A.

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87, 201–215 (1995).
[CrossRef]

Skryabin, D. V.

Soneson, J.

J. Soneson and A. Peleg, “Effect of quintic nonlinearity on soliton collisions in optical fibers,” Physica D 195, 123–140 (2004).
[CrossRef]

Taylor, A. J.

Tkach, R. W.

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “Effect of modulation statistics on Raman crosstalk in WDM systems,” IEEE Photon. Technol. Lett. 7, 101–103 (1995).
[CrossRef]

Vanin, E.

Wen, S.

Yamamoto, T.

Yoshida, H.

H. Yoshida, “Construction of higher order symplectic integrators,” Phys. Lett. A 150, 262–268 (1990).
[CrossRef]

Yulin, A. V.

Appl. Phys. B (1)

G. Genty, J. M. Dudley, and B. J. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94, 187–194 (2009).
[CrossRef]

Electron. Lett. (1)

A. R. Chraplyvy, “Optical power limits in multichannel wavelength-division- multiplexed systems due to stimulated Raman scattering,” Electron. Lett. 20, 58–59 (1984).
[CrossRef]

IEEE J. Quantum Electron. (1)

Y. Kodama and A. Hasegawa, “Nonlinear pulse propagation in a monomode dielectric guide,” IEEE J. Quantum Electron. 23, 510–524 (1987).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, “Effect of modulation statistics on Raman crosstalk in WDM systems,” IEEE Photon. Technol. Lett. 7, 101–103 (1995).
[CrossRef]

M. Muktoyuk and S. Kumar, “Noise variance due to stimulated Raman scattering among channels of a wavelength-division-multiplexed system,” IEEE Photon. Technol. Lett. 15, 1222–1224 (2003).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (2)

J. Phys. A (1)

A. Peleg and Y. Chung, “Stationary solutions to the nonlinear Schrödinger equation in the presence of third order dispersion,” J. Phys. A 36, 10039–10051 (2003).
[CrossRef]

Nonlinearity (1)

Y. Chung and A. Peleg, “Strongly non-Gaussian statistics of optical soliton parameters due to collisions in the presence of delayed Raman response,” Nonlinearity 18, 1555–1574 (2005).
[CrossRef]

Opt. Express (4)

Opt. Lett. (7)

Phys. Lett. A (3)

H. Yoshida, “Construction of higher order symplectic integrators,” Phys. Lett. A 150, 262–268 (1990).
[CrossRef]

A. Peleg, “Energy exchange in fast optical soliton collisions as a random cascade model,” Phys. Lett. A 373, 2734–2738 (2009).
[CrossRef]

A. Peleg, “Intermittent dynamics, strong correlations, and bit-error-rate in multichannel optical fiber communication systems,” Phys. Lett. A 360, 533–538 (2007).
[CrossRef]

Phys. Rev. A (5)

Y. Chung and A. Peleg, “Monte Carlo simulations of pulse propagation in massive multichannel optical fiber communication systems,” Phys. Rev. A 77, 063835 (2008).
[CrossRef]

A. Hause and F. Mitschke, “Reduced soliton interaction by Raman self-frequency-shift,” Phys. Rev. A 80, 063824 (2009).
[CrossRef]

B. A. Malomed, “Radiative losses in soliton-soliton collisions in an optical fiber with the third-order dispersion,” Phys. Rev. A 43, 3114–3116 (1991).
[CrossRef] [PubMed]

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]

D. J. Kaup, “Second-order perturbations for solitons in optical fibers,” Phys. Rev. A 44, 4582–4590 (1991).
[CrossRef] [PubMed]

Phys. Rev. E (2)

M. Chertkov, Y. Chung, A. Dyachenko, I. Gabitov, I. Kolokolov, and V. Lebedev, “Shedding and interaction of solitons in weakly disordered optical fibers,” Phys. Rev. E 67, 036615 (2003).
[CrossRef]

A. Peleg, M. Chertkov, and I. Gabitov, “Interchannel interaction of optical solitons,” Phys. Rev. E 68, 026605 (2003).
[CrossRef]

Physica D (3)

E. A. Kuznetsov, A. V. Mikhailov, and I. A. Shimokhin, “Nonlinear interaction of solitons and radiation,” Physica D 87, 201–215 (1995).
[CrossRef]

J. Soneson and A. Peleg, “Effect of quintic nonlinearity on soliton collisions in optical fibers,” Physica D 195, 123–140 (2004).
[CrossRef]

D. E. Pelinovsky, Y. S. Kivshar, and V. V. Afanasjev, “Internal modes of envelope solitons,” Physica D 116, 121–142 (1998).
[CrossRef]

Other (4)

The dimensionless z in Eq. is z=(|β2|X)/(2τ02), where X is the actual position, τ0 is the soliton width, and β2 is the second order dispersion coefficient. The dimensionless retarded time is t=τ/τ0, where τ is the retarded time. The spectral width is ν0=1/(π2τ0) and the frequency difference is Δν=(πΔβν0)/2. ψ=E/P0, where E is proportional to the electric field and P0 is the peak power. The dimensionless second order dispersion coefficient is d=−1=β2/(γP0τ02), where γ is the Kerr nonlinearity coefficient. The coefficient ϵR is given by ϵR=0.006/τ0, where τ0 is in picoseconds.

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

M.N.Islam, ed., Raman Amplifiers for Telecommunications 1: Physical Principles (Springer, 2004).

C.Headley and G.P.Agrawal, eds., Raman Amplification in Fiber Optical Communication Systems (Elsevier, 2005).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Dynamics of A 0 ( z ) = max t | ψ 0 ( t , z ) | for a collision between a reference-channel soliton ( β = 0 ) and a soliton with β = 10 . Squares represent the result obtained by numerical simulations with Eq. (1), and the solid line corresponds to A 0 = 1.0408 , the value obtained by averaging of A 0 ( z ) over one period of the oscillations. (b) Change in the amplitude of the reference-channel soliton Δ η 0 as a function of the frequency difference β for ϵ R = 0.02 . Squares represent the result of numerical simulations with Eq. (1) and with averaging over one period of amplitude oscillations, circles correspond to the result of numerical simulations with Eq. (1) while using the formal definition of η 0 , and the solid line stands for the analytic prediction of Eq. (4).

Fig. 2
Fig. 2

Dynamics of B 0 ( c ) ( z ) , the contribution of the Raman-induced XFS to B 0 , for a collision between a reference-channel soliton ( β = 0 ) and a soliton with β = 10 . Squares represent the result obtained by numerical simulations with Eq. (1), and the solid line corresponds to B 0 ( c ) = 0.0062 , the value obtained by averaging of B 0 ( c ) ( z ) over one period of the oscillations.

Fig. 3
Fig. 3

(a) Raman-induced XFS for the reference-channel soliton Δ β 0 ( c ) as a function of the frequency difference β for ϵ R = 0.02 . Squares represent the result of numerical simulations with Eq. (1) and with averaging over one period of frequency oscillations, circles correspond to the result of numerical simulations with Eq. (1) while using the formal definition of β 0 , and the solid line stands for the analytic prediction of Eq. (5). (b) The same data on a ln-ln plot. The squares represent the result of numerical simulations with Eq. (1) (with averaging over one period of frequency oscillations) while the dashed-dotted line corresponds to a linear fit of the form | Δ β 0 ( c ) | = 0.057 / | β | 1.004 for the numerical data. The solid line corresponds to | Δ β 0 ( c ) | = 0.053 / | β | , the result obtained by employing Eq. (5).

Fig. 4
Fig. 4

Collision-induced amplitude and frequency shifts of the reference-channel soliton Δ η 0 and Δ β 0 ( c ) as functions of the initial amplitudes η 0 ( 0 ) and η β ( 0 ) for β = 10 and ϵ R = 0.02 . Squares represent the results of numerical simulations with Eq. (1) with averaging over one period of amplitude or frequency oscillations. Solid lines correspond to the analytic predictions of Eq. (4) in (a) and Eq. (5) in (b) and (c). (a) Amplitude shift versus η 0 ( 0 ) . (b) Raman XFS versus η 0 ( 0 ) . (c) Raman XFS versus η β ( 0 ) .

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

i z ψ + t 2 ψ + 2 | ψ | 2 ψ = ϵ R ψ t | ψ | 2 ,
ψ β ( t , z ) = η β exp ( i χ β ) cosh ( x β ) ,
d β ( s ) ( z ) d z = 8 15 ϵ R η 4 ( z ) ,
Δ η 0 = 2 ϵ R   sgn ( β ) η 0 η β .
Δ β 0 ( c ) = ( 8 ϵ R η 0 2 η β ) / ( 3 | β | ) .
B 0 ( s ) ( z ) = 8 15 ϵ R η 0 4 ( 0 ) z c 8 15 ϵ R [ 1 + 2   sgn ( β ) ϵ R η β ( 0 ) ] 4 η 0 4 ( 0 ) ( z z c ) ,

Metrics