Abstract

The coherence characteristics of the interactions between colored solitons are explored employing a novel perturbation model. The model broadens the existing particlelike models for colored solitons and identifies a phase-sensitive force (similar to same-color soliton interaction) and a novel damping coefficient; both are important for describing the soliton capture phenomenon. A soliton–soliton parametric energy exchange is identified and analyzed as the source for capture, escape, and intermediate processes. As the solitons assimilate colorwise, the coupling is enhanced. For low carrier-frequency difference, capture occurs and a complete (periodical) energy exchange between the solitons takes place. The capture process of equal-amplitude solitons with a similar initial phase exhibits an instability that tends to break the captured pair.

© 2005 Optical Society of America

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References

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  1. A. F. Benner, J. R. Sauer, and M. J. Ablowitz, "Interaction effects on wavelength-multiplexed soliton data packets," J. Opt. Soc. Am. B 10, 2331-2340 (1993).
    [CrossRef]
  2. E. Feigenbaum and M. Orenstein, "Enhanced mutual capture of colored solitons by matched modulator," Opt. Express 12, 3759-3764 (2004).
    [CrossRef] [PubMed]
  3. M. Karlsson, D. Anderson, A. Höök, and M. Lisak, "A variational approach to optical soliton collisions," Phys. Scr. 50, 265-270 (1994).
    [CrossRef]
  4. D. Anderson and M. Lisak, "Variational approach to incoherent two-soliton interaction," Phys. Scr. 33, 193-196 (1986).
    [CrossRef]
  5. E. Feigenbaum and M. Orenstein, "Colored solitons interactions: particle-like and beyond," Opt. Express 12, 2193-2206 (2004).
    [CrossRef] [PubMed]
  6. A. Mecozzi and H. A. Haus, "Effect of filter on soliton interactions in wavelength-division-multiplexing systems," Opt. Lett. 17, 988-990 (1992).
    [CrossRef]
  7. D. J. Kaup and B. A. Malomed, "Soliton trapping and daughter waves in the Manakov model," Phys. Rev. A 48, 599-604 (1993).
    [CrossRef] [PubMed]
  8. B. A. Malomed and R. S. Tasgal, "Internal vibrations of a vector soliton in the coupled nonlinear Schrodinger equations," Phys. Rev. E 58, 2564-2575 (1998).
    [CrossRef]
  9. T. Ueda and W. L. Kath, "Dynamics of coupled solitons in nonlinear optical fibers," Phys. Rev. A 42, 563-571 (1990).
    [CrossRef] [PubMed]
  10. Y. S. Kivshar, "Soliton stability in birefringent optical fibers: analytical approach," J. Opt. Soc. Am. B 7, 2204-2209 (1990).
    [CrossRef]
  11. M. F. Mahmood, W. W. Zachary, and T. L. Gill, "Polarization dynamics of vector solitons in an elliptically low-birefringent Kerr medium," Opt. Eng. 35, 1844-1846 (1996).
    [CrossRef]
  12. J. Yang, "Multisoliton perturbation theory for Manakov equations and its applications to nonlinear optics," Phys. Rev. E 59, 2393-2405 (1999).
    [CrossRef]
  13. R. Radhakrishnan, M. Lakshmanan, and J. Heitarinta, "Inelastic collision and switching of coupled bright solitons in optical fibers," Phys. Rev. E 56, 2213-2216 (1997).
    [CrossRef]
  14. J. P. Gordon, "Interaction forces among solitons in optical fibers," Opt. Lett. 8, 596-598 (1983).
    [CrossRef] [PubMed]
  15. D. Arbel and M. Orenstein, "Self stabilization of dense soliton trains in passively modelocked ring laser," IEEE J. Quantum Electron. 35, 977-982 (1999).
    [CrossRef]
  16. B. A. Malomed, "Polarization dynamics and interactions of solitons in a birefringent optical fiber," Phys. Rev. A 43, 410-423 (1991).
    [CrossRef] [PubMed]
  17. V. I. Karpman and E. M. Maslov, "Inverse method for perturbed nonlinear Schrödinger equation," Phys. Lett. 61A, 355-357 (1977).
    [CrossRef]
  18. N. C. Panoiu, I. V. Mel'nikov, D. Mihalache, C. Etrich, and F. Lederer, "Soliton generation in optical fibers for dual-frequency input," Phys. Rev. E 60, 4868-4876 (1999).
    [CrossRef]
  19. V. V. Afanasjev and V. A. Vysloukh, "Interaction of initially overlapping solitons with different frequencies," J. Opt. Soc. Am. B 11, 2385-2393 (1994).
    [CrossRef]
  20. N. C. Panoiu, D. Mihalache, D. Mazilu, L. C. Crasovan, and I. V. Mel'nikov, "Soliton dynamics of symmetry-endowed two-soliton solutions of the nonlinear Schrödinger equation," Chaos 10, 625-640 (2000).
    [CrossRef]
  21. C. Etrich, N. C. Panoiu, D. Mihalache, and F. Lederer, "Limits for interchanel frequency separation in a soliton wavelength-division multiplexing system," Phys. Rev. E 63, 016609 (2001).
    [CrossRef]
  22. H. A. Haus and W. S. Wong, "Solitons in optical communication," Rev. Mod. Phys. 68, 423-444 (1996).
    [CrossRef]
  23. C. R. Menyuk, "Application of multiple-length-scale methods to the study of optical fiber tansmission," J. Eng. Math. 36, 113-136 (1999).
    [CrossRef]
  24. G. P. Agrawal, Nonlinear Fiber Optics, 2nd. ed. (Academic, 1995).
  25. S. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method (Plenum, 1984), pp. 68-79.
  26. A. Meccozi, J. D. Moors, H. A. Haus, and Y. Lai, "Modulation and filtering control of soliton transmission," J. Opt. Soc. Am. B 9, 1350-1357 (1992).
  27. R. A. Fisher and W. K. Bischel, "Numerical studies of the interplay between self-phase modulation and dispersion for intense plane wave laser pulses," J. Appl. Phys. 46, 4921-4934 (1975).
    [CrossRef]
  28. C. R. Menyuk, "Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes," J. Opt. Soc. Am. B 5, 392-402 (1988).
    [CrossRef]
  29. M. Shih, Z. Chen, M. Mitchell, M. Segev, H. Lee, R. S. Feigelson, and J. P. Widle, "Waveguides induced by photorefractive screening solitons," J. Opt. Soc. Am. B 14, 3091-3101 (1997).
    [CrossRef]

2004 (2)

2001 (1)

C. Etrich, N. C. Panoiu, D. Mihalache, and F. Lederer, "Limits for interchanel frequency separation in a soliton wavelength-division multiplexing system," Phys. Rev. E 63, 016609 (2001).
[CrossRef]

2000 (1)

N. C. Panoiu, D. Mihalache, D. Mazilu, L. C. Crasovan, and I. V. Mel'nikov, "Soliton dynamics of symmetry-endowed two-soliton solutions of the nonlinear Schrödinger equation," Chaos 10, 625-640 (2000).
[CrossRef]

1999 (4)

N. C. Panoiu, I. V. Mel'nikov, D. Mihalache, C. Etrich, and F. Lederer, "Soliton generation in optical fibers for dual-frequency input," Phys. Rev. E 60, 4868-4876 (1999).
[CrossRef]

D. Arbel and M. Orenstein, "Self stabilization of dense soliton trains in passively modelocked ring laser," IEEE J. Quantum Electron. 35, 977-982 (1999).
[CrossRef]

C. R. Menyuk, "Application of multiple-length-scale methods to the study of optical fiber tansmission," J. Eng. Math. 36, 113-136 (1999).
[CrossRef]

J. Yang, "Multisoliton perturbation theory for Manakov equations and its applications to nonlinear optics," Phys. Rev. E 59, 2393-2405 (1999).
[CrossRef]

1998 (1)

B. A. Malomed and R. S. Tasgal, "Internal vibrations of a vector soliton in the coupled nonlinear Schrodinger equations," Phys. Rev. E 58, 2564-2575 (1998).
[CrossRef]

1997 (2)

R. Radhakrishnan, M. Lakshmanan, and J. Heitarinta, "Inelastic collision and switching of coupled bright solitons in optical fibers," Phys. Rev. E 56, 2213-2216 (1997).
[CrossRef]

M. Shih, Z. Chen, M. Mitchell, M. Segev, H. Lee, R. S. Feigelson, and J. P. Widle, "Waveguides induced by photorefractive screening solitons," J. Opt. Soc. Am. B 14, 3091-3101 (1997).
[CrossRef]

1996 (2)

M. F. Mahmood, W. W. Zachary, and T. L. Gill, "Polarization dynamics of vector solitons in an elliptically low-birefringent Kerr medium," Opt. Eng. 35, 1844-1846 (1996).
[CrossRef]

H. A. Haus and W. S. Wong, "Solitons in optical communication," Rev. Mod. Phys. 68, 423-444 (1996).
[CrossRef]

1994 (2)

M. Karlsson, D. Anderson, A. Höök, and M. Lisak, "A variational approach to optical soliton collisions," Phys. Scr. 50, 265-270 (1994).
[CrossRef]

V. V. Afanasjev and V. A. Vysloukh, "Interaction of initially overlapping solitons with different frequencies," J. Opt. Soc. Am. B 11, 2385-2393 (1994).
[CrossRef]

1993 (2)

1992 (2)

1991 (1)

B. A. Malomed, "Polarization dynamics and interactions of solitons in a birefringent optical fiber," Phys. Rev. A 43, 410-423 (1991).
[CrossRef] [PubMed]

1990 (2)

T. Ueda and W. L. Kath, "Dynamics of coupled solitons in nonlinear optical fibers," Phys. Rev. A 42, 563-571 (1990).
[CrossRef] [PubMed]

Y. S. Kivshar, "Soliton stability in birefringent optical fibers: analytical approach," J. Opt. Soc. Am. B 7, 2204-2209 (1990).
[CrossRef]

1988 (1)

1986 (1)

D. Anderson and M. Lisak, "Variational approach to incoherent two-soliton interaction," Phys. Scr. 33, 193-196 (1986).
[CrossRef]

1983 (1)

1977 (1)

V. I. Karpman and E. M. Maslov, "Inverse method for perturbed nonlinear Schrödinger equation," Phys. Lett. 61A, 355-357 (1977).
[CrossRef]

1975 (1)

R. A. Fisher and W. K. Bischel, "Numerical studies of the interplay between self-phase modulation and dispersion for intense plane wave laser pulses," J. Appl. Phys. 46, 4921-4934 (1975).
[CrossRef]

Ablowitz, M. J.

Afanasjev, V. V.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 2nd. ed. (Academic, 1995).

Anderson, D.

M. Karlsson, D. Anderson, A. Höök, and M. Lisak, "A variational approach to optical soliton collisions," Phys. Scr. 50, 265-270 (1994).
[CrossRef]

D. Anderson and M. Lisak, "Variational approach to incoherent two-soliton interaction," Phys. Scr. 33, 193-196 (1986).
[CrossRef]

Arbel, D.

D. Arbel and M. Orenstein, "Self stabilization of dense soliton trains in passively modelocked ring laser," IEEE J. Quantum Electron. 35, 977-982 (1999).
[CrossRef]

Benner, A. F.

Bischel, W. K.

R. A. Fisher and W. K. Bischel, "Numerical studies of the interplay between self-phase modulation and dispersion for intense plane wave laser pulses," J. Appl. Phys. 46, 4921-4934 (1975).
[CrossRef]

Chen, Z.

Crasovan, L. C.

N. C. Panoiu, D. Mihalache, D. Mazilu, L. C. Crasovan, and I. V. Mel'nikov, "Soliton dynamics of symmetry-endowed two-soliton solutions of the nonlinear Schrödinger equation," Chaos 10, 625-640 (2000).
[CrossRef]

Etrich, C.

C. Etrich, N. C. Panoiu, D. Mihalache, and F. Lederer, "Limits for interchanel frequency separation in a soliton wavelength-division multiplexing system," Phys. Rev. E 63, 016609 (2001).
[CrossRef]

N. C. Panoiu, I. V. Mel'nikov, D. Mihalache, C. Etrich, and F. Lederer, "Soliton generation in optical fibers for dual-frequency input," Phys. Rev. E 60, 4868-4876 (1999).
[CrossRef]

Feigelson, R. S.

Feigenbaum, E.

Fisher, R. A.

R. A. Fisher and W. K. Bischel, "Numerical studies of the interplay between self-phase modulation and dispersion for intense plane wave laser pulses," J. Appl. Phys. 46, 4921-4934 (1975).
[CrossRef]

Gill, T. L.

M. F. Mahmood, W. W. Zachary, and T. L. Gill, "Polarization dynamics of vector solitons in an elliptically low-birefringent Kerr medium," Opt. Eng. 35, 1844-1846 (1996).
[CrossRef]

Gordon, J. P.

Haus, H. A.

Heitarinta, J.

R. Radhakrishnan, M. Lakshmanan, and J. Heitarinta, "Inelastic collision and switching of coupled bright solitons in optical fibers," Phys. Rev. E 56, 2213-2216 (1997).
[CrossRef]

Höök, A.

M. Karlsson, D. Anderson, A. Höök, and M. Lisak, "A variational approach to optical soliton collisions," Phys. Scr. 50, 265-270 (1994).
[CrossRef]

Karlsson, M.

M. Karlsson, D. Anderson, A. Höök, and M. Lisak, "A variational approach to optical soliton collisions," Phys. Scr. 50, 265-270 (1994).
[CrossRef]

Karpman, V. I.

V. I. Karpman and E. M. Maslov, "Inverse method for perturbed nonlinear Schrödinger equation," Phys. Lett. 61A, 355-357 (1977).
[CrossRef]

Kath, W. L.

T. Ueda and W. L. Kath, "Dynamics of coupled solitons in nonlinear optical fibers," Phys. Rev. A 42, 563-571 (1990).
[CrossRef] [PubMed]

Kaup, D. J.

D. J. Kaup and B. A. Malomed, "Soliton trapping and daughter waves in the Manakov model," Phys. Rev. A 48, 599-604 (1993).
[CrossRef] [PubMed]

Kivshar, Y. S.

Lai, Y.

Lakshmanan, M.

R. Radhakrishnan, M. Lakshmanan, and J. Heitarinta, "Inelastic collision and switching of coupled bright solitons in optical fibers," Phys. Rev. E 56, 2213-2216 (1997).
[CrossRef]

Lederer, F.

C. Etrich, N. C. Panoiu, D. Mihalache, and F. Lederer, "Limits for interchanel frequency separation in a soliton wavelength-division multiplexing system," Phys. Rev. E 63, 016609 (2001).
[CrossRef]

N. C. Panoiu, I. V. Mel'nikov, D. Mihalache, C. Etrich, and F. Lederer, "Soliton generation in optical fibers for dual-frequency input," Phys. Rev. E 60, 4868-4876 (1999).
[CrossRef]

Lee, H.

Lisak, M.

M. Karlsson, D. Anderson, A. Höök, and M. Lisak, "A variational approach to optical soliton collisions," Phys. Scr. 50, 265-270 (1994).
[CrossRef]

D. Anderson and M. Lisak, "Variational approach to incoherent two-soliton interaction," Phys. Scr. 33, 193-196 (1986).
[CrossRef]

Mahmood, M. F.

M. F. Mahmood, W. W. Zachary, and T. L. Gill, "Polarization dynamics of vector solitons in an elliptically low-birefringent Kerr medium," Opt. Eng. 35, 1844-1846 (1996).
[CrossRef]

Malomed, B. A.

B. A. Malomed and R. S. Tasgal, "Internal vibrations of a vector soliton in the coupled nonlinear Schrodinger equations," Phys. Rev. E 58, 2564-2575 (1998).
[CrossRef]

D. J. Kaup and B. A. Malomed, "Soliton trapping and daughter waves in the Manakov model," Phys. Rev. A 48, 599-604 (1993).
[CrossRef] [PubMed]

B. A. Malomed, "Polarization dynamics and interactions of solitons in a birefringent optical fiber," Phys. Rev. A 43, 410-423 (1991).
[CrossRef] [PubMed]

Manakov, S. V.

S. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method (Plenum, 1984), pp. 68-79.

Maslov, E. M.

V. I. Karpman and E. M. Maslov, "Inverse method for perturbed nonlinear Schrödinger equation," Phys. Lett. 61A, 355-357 (1977).
[CrossRef]

Mazilu, D.

N. C. Panoiu, D. Mihalache, D. Mazilu, L. C. Crasovan, and I. V. Mel'nikov, "Soliton dynamics of symmetry-endowed two-soliton solutions of the nonlinear Schrödinger equation," Chaos 10, 625-640 (2000).
[CrossRef]

Meccozi, A.

Mecozzi, A.

Mel'nikov, I. V.

N. C. Panoiu, D. Mihalache, D. Mazilu, L. C. Crasovan, and I. V. Mel'nikov, "Soliton dynamics of symmetry-endowed two-soliton solutions of the nonlinear Schrödinger equation," Chaos 10, 625-640 (2000).
[CrossRef]

N. C. Panoiu, I. V. Mel'nikov, D. Mihalache, C. Etrich, and F. Lederer, "Soliton generation in optical fibers for dual-frequency input," Phys. Rev. E 60, 4868-4876 (1999).
[CrossRef]

Menyuk, C. R.

C. R. Menyuk, "Application of multiple-length-scale methods to the study of optical fiber tansmission," J. Eng. Math. 36, 113-136 (1999).
[CrossRef]

C. R. Menyuk, "Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes," J. Opt. Soc. Am. B 5, 392-402 (1988).
[CrossRef]

Mihalache, D.

C. Etrich, N. C. Panoiu, D. Mihalache, and F. Lederer, "Limits for interchanel frequency separation in a soliton wavelength-division multiplexing system," Phys. Rev. E 63, 016609 (2001).
[CrossRef]

N. C. Panoiu, D. Mihalache, D. Mazilu, L. C. Crasovan, and I. V. Mel'nikov, "Soliton dynamics of symmetry-endowed two-soliton solutions of the nonlinear Schrödinger equation," Chaos 10, 625-640 (2000).
[CrossRef]

N. C. Panoiu, I. V. Mel'nikov, D. Mihalache, C. Etrich, and F. Lederer, "Soliton generation in optical fibers for dual-frequency input," Phys. Rev. E 60, 4868-4876 (1999).
[CrossRef]

Mitchell, M.

Moors, J. D.

Novikov, S.

S. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method (Plenum, 1984), pp. 68-79.

Orenstein, M.

Panoiu, N. C.

C. Etrich, N. C. Panoiu, D. Mihalache, and F. Lederer, "Limits for interchanel frequency separation in a soliton wavelength-division multiplexing system," Phys. Rev. E 63, 016609 (2001).
[CrossRef]

N. C. Panoiu, D. Mihalache, D. Mazilu, L. C. Crasovan, and I. V. Mel'nikov, "Soliton dynamics of symmetry-endowed two-soliton solutions of the nonlinear Schrödinger equation," Chaos 10, 625-640 (2000).
[CrossRef]

N. C. Panoiu, I. V. Mel'nikov, D. Mihalache, C. Etrich, and F. Lederer, "Soliton generation in optical fibers for dual-frequency input," Phys. Rev. E 60, 4868-4876 (1999).
[CrossRef]

Pitaevskii, L. P.

S. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method (Plenum, 1984), pp. 68-79.

Radhakrishnan, R.

R. Radhakrishnan, M. Lakshmanan, and J. Heitarinta, "Inelastic collision and switching of coupled bright solitons in optical fibers," Phys. Rev. E 56, 2213-2216 (1997).
[CrossRef]

Sauer, J. R.

Segev, M.

Shih, M.

Tasgal, R. S.

B. A. Malomed and R. S. Tasgal, "Internal vibrations of a vector soliton in the coupled nonlinear Schrodinger equations," Phys. Rev. E 58, 2564-2575 (1998).
[CrossRef]

Ueda, T.

T. Ueda and W. L. Kath, "Dynamics of coupled solitons in nonlinear optical fibers," Phys. Rev. A 42, 563-571 (1990).
[CrossRef] [PubMed]

Vysloukh, V. A.

Widle, J. P.

Wong, W. S.

H. A. Haus and W. S. Wong, "Solitons in optical communication," Rev. Mod. Phys. 68, 423-444 (1996).
[CrossRef]

Yang, J.

J. Yang, "Multisoliton perturbation theory for Manakov equations and its applications to nonlinear optics," Phys. Rev. E 59, 2393-2405 (1999).
[CrossRef]

Zachary, W. W.

M. F. Mahmood, W. W. Zachary, and T. L. Gill, "Polarization dynamics of vector solitons in an elliptically low-birefringent Kerr medium," Opt. Eng. 35, 1844-1846 (1996).
[CrossRef]

Zakharov, V. E.

S. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method (Plenum, 1984), pp. 68-79.

Chaos (1)

N. C. Panoiu, D. Mihalache, D. Mazilu, L. C. Crasovan, and I. V. Mel'nikov, "Soliton dynamics of symmetry-endowed two-soliton solutions of the nonlinear Schrödinger equation," Chaos 10, 625-640 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Arbel and M. Orenstein, "Self stabilization of dense soliton trains in passively modelocked ring laser," IEEE J. Quantum Electron. 35, 977-982 (1999).
[CrossRef]

J. Appl. Phys. (1)

R. A. Fisher and W. K. Bischel, "Numerical studies of the interplay between self-phase modulation and dispersion for intense plane wave laser pulses," J. Appl. Phys. 46, 4921-4934 (1975).
[CrossRef]

J. Eng. Math. (1)

C. R. Menyuk, "Application of multiple-length-scale methods to the study of optical fiber tansmission," J. Eng. Math. 36, 113-136 (1999).
[CrossRef]

J. Opt. Soc. Am. B (6)

Opt. Eng. (1)

M. F. Mahmood, W. W. Zachary, and T. L. Gill, "Polarization dynamics of vector solitons in an elliptically low-birefringent Kerr medium," Opt. Eng. 35, 1844-1846 (1996).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Lett. (1)

V. I. Karpman and E. M. Maslov, "Inverse method for perturbed nonlinear Schrödinger equation," Phys. Lett. 61A, 355-357 (1977).
[CrossRef]

Phys. Rev. A (3)

B. A. Malomed, "Polarization dynamics and interactions of solitons in a birefringent optical fiber," Phys. Rev. A 43, 410-423 (1991).
[CrossRef] [PubMed]

D. J. Kaup and B. A. Malomed, "Soliton trapping and daughter waves in the Manakov model," Phys. Rev. A 48, 599-604 (1993).
[CrossRef] [PubMed]

T. Ueda and W. L. Kath, "Dynamics of coupled solitons in nonlinear optical fibers," Phys. Rev. A 42, 563-571 (1990).
[CrossRef] [PubMed]

Phys. Rev. E (5)

B. A. Malomed and R. S. Tasgal, "Internal vibrations of a vector soliton in the coupled nonlinear Schrodinger equations," Phys. Rev. E 58, 2564-2575 (1998).
[CrossRef]

J. Yang, "Multisoliton perturbation theory for Manakov equations and its applications to nonlinear optics," Phys. Rev. E 59, 2393-2405 (1999).
[CrossRef]

R. Radhakrishnan, M. Lakshmanan, and J. Heitarinta, "Inelastic collision and switching of coupled bright solitons in optical fibers," Phys. Rev. E 56, 2213-2216 (1997).
[CrossRef]

N. C. Panoiu, I. V. Mel'nikov, D. Mihalache, C. Etrich, and F. Lederer, "Soliton generation in optical fibers for dual-frequency input," Phys. Rev. E 60, 4868-4876 (1999).
[CrossRef]

C. Etrich, N. C. Panoiu, D. Mihalache, and F. Lederer, "Limits for interchanel frequency separation in a soliton wavelength-division multiplexing system," Phys. Rev. E 63, 016609 (2001).
[CrossRef]

Phys. Scr. (2)

M. Karlsson, D. Anderson, A. Höök, and M. Lisak, "A variational approach to optical soliton collisions," Phys. Scr. 50, 265-270 (1994).
[CrossRef]

D. Anderson and M. Lisak, "Variational approach to incoherent two-soliton interaction," Phys. Scr. 33, 193-196 (1986).
[CrossRef]

Rev. Mod. Phys. (1)

H. A. Haus and W. S. Wong, "Solitons in optical communication," Rev. Mod. Phys. 68, 423-444 (1996).
[CrossRef]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd. ed. (Academic, 1995).

S. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method (Plenum, 1984), pp. 68-79.

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Figures (14)

Fig. 1
Fig. 1

Parameter source difference; W 1 = W 2 = 1 , D θ = 0 ; soliton bandwidth 10 THz .

Fig. 2
Fig. 2

Parameter source difference; W 1 = W 2 = 1 , D θ = π 2 .

Fig. 3
Fig. 3

Parameter source difference; W 1 = 1 , W 2 = 5 , D θ = 0 .

Fig. 4
Fig. 4

(a) NLSE BPM results. (b) Coherent perturbation predictions; W 1 = W 2 = 1 , D τ = 6 , D p = 0.02 × 2 π , D θ = π .

Fig. 5
Fig. 5

(a) NLSE–BPM results. (b) Coherent perturbation predictions; W 1 = 1 , W 2 = 2 , D τ = 6 , D p = 0.1 × 2 π , D θ = π .

Fig. 6
Fig. 6

(a) NLSE–BPM results. (b) Coherent perturbation predictions; W 1 = 1 , W 2 = 2 , D τ = 4 , D p = 0.04 × 2 π , D θ = π .

Fig. 7
Fig. 7

Parametric amplification. For W 1 = W 2 = 1 , D τ = 6 , D p = 0.02 × 2 π , θ 1 = θ 2 = 0.1 × π ; (a) NLSE–BPM results, (b) coherent model predictions. For θ 1 = θ 2 = + 0.1 × π ; (c) NLSE–BPM results.

Fig. 8
Fig. 8

NLSE BPM results for W 1 = 1 , W 2 = 2 , θ 1 = θ 2 = 0.25 × π , D τ = 0 .

Fig. 9
Fig. 9

Coherent model calculations for W 1 = W 2 = 2 , θ 1 = θ 2 = 0.25 × π , D τ = 0 .

Fig. 10
Fig. 10

NLSE BPM results. For D θ = 0 , W 1 = W 2 = 1 , τ 1 = τ 2 = 1 ; p 1 = ( a ) 0.15 × 2 π , (b) 0.134 × 2 π , (c) 0.133 × 2 π , (d) 0.13 × 2 π , (e) 0.12 × 2 π .

Fig. 11
Fig. 11

Coherent model calcualtions. For D θ = 0 , W 1 = W 2 = 1 , τ 1 = τ 2 = 1 ; p 1 = ( a ) 0.150 × 2 π , (b) 0.123 × 2 π , (c) 0.122 × 2 π , (d) 0.120 × 2 π .

Fig. 12
Fig. 12

Capture threshold frequency ( p 0 TH ) versus initial center difference ( D τ 0 ) . BPM simulation (asterisks), coherent model (solid curve), particlelike model (dotted curve).

Fig. 13
Fig. 13

Soliton parameter dynamics where amplitude diversity appears. W 1 = W 2 = 1 , D θ = 0 , p 1 = 0.1 × 2 π , D τ = 0

Fig. 14
Fig. 14

Diversity creation as a result of added noise; NLSE–BPM results; W 1 = W 2 = 1 , D θ = 0 , D p = 0.1 × 2 π , D τ = 0 . (a) No noise added. WGN added with STD of (b) 0.01, (c) 0.1. (d) D θ = π 2 , STD = 0.1 .

Equations (19)

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z U = j { 1 2 β T 2 + δ U 2 } U ,
U = W sech [ η W ( T τ ) ] exp ( j p T + j θ ) ,
z τ = β p ,
z θ = 1 2 ( δ W 2 + β p 2 ) .
z W = S W ,
z τ = S τ + β p ,
z p = S p ,
z θ = S θ + δ W ( S W d z ) + 1 2 ( δ W 2 + β p 2 ) .
S m Im d T [ f ̱ m * s ( z , T ) exp ( 0.5 j W 2 z ) ] ,
s ( z , T ) = δ { U N + U S 2 ( U N + U S ) U S 2 U S } .
s = 2 δ { U N 2 U S + U S 2 U N } + δ { ( U S ) 2 U N * + ( U N ) 2 U S * } + δ { U N 2 U N } .
U S = W S sech ( η W S T ) exp ( j φ S ) ,
U N = W N sech [ η W N ( T τ N ) ] exp ( j φ N ) ,
φ S = 1 2 δ W S 2 d z + θ S ,
φ N = ( p N p S ) T + 1 2 [ δ W N 2 + β ( p N p S ) 2 ] d z + θ N ,
Δ φ = φ N φ S d z 0 Δ φ ( θ N θ S ) ( p N p S ) T .
S m = δ Im d T [ ( f ̱ m * U 0 * ) ( { W S 3 W N sech 3 ( η W S T ) sech [ η W N ( T τ N ) ] [ 2 exp ( j Δ φ ) + exp ( j Δ φ ) ] } + { W S 2 W N 2 sech 2 ( η W S T ) sech 2 [ η W N ( T τ N ) ] [ exp ( 2 j Δ φ ) + 2 ] } + { W S W N 3 sech ( η W S T ) sech 3 [ η W N ( T τ N ) ] [ exp ( j Δ φ ) ] } ) ] .
V = τ S τ .
S ̃ W = δ η d T { W S 2 W N 2 sech 2 ( η W S T ) sech 2 [ η W N ( T τ N ) ] sin ( 2 j Δ φ ) } .

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