Abstract

The copropagation of two optical pulses of different frequencies in single-mode birefringent fibers is investigated. Various combinations of solitary-wave solutions are obtained. It is shown that a dark pulse on the slow axis and a bright pulse on the fast axis simultaneously propagate without distortion in the presence of a bright pulse of different frequency on the slow or the fast axis.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Optical wave breaking and pulse compression due to cross-phase modulation in optical fibers,” Opt. Lett. 14, 137 (1989).
    [Crossref] [PubMed]
  2. G. P. Agrawal, “Modulational instability induced by cross phase modulation,” Phys. Rev. Lett. 59, 880 (1987).
    [Crossref] [PubMed]
  3. D. Schadt and B. Jaskorzynska, “Generation of short pulse from cw light by influence of cross phase modulation (CPM) in optical fibers,” Electron. Lett. 23, 1090 (1987).
    [Crossref]
  4. V. L. da Silva and C. H. Brito Cruz, “Walk-off effect on the generation of ultrashort pulses from cw light using cross-phase modulation in optical fibers,” J. Opt. Soc. Am. B 7, 750 (1990).
    [Crossref]
  5. A. R. Chraplyvy, D. Marcuse, and P. S. Henry, “Carrier induced phase noise in angle-modulated optical fiber systems,” J. Lightwave Technol. LT-2, 6 (1984).
    [Crossref]
  6. P. C. Subramaniam, “Wavelength division multiplexing of phase modulated solitons,” Opt. Commun. 93, 294 (1992).
    [Crossref]
  7. D. Schadt and B. Jaskorzynska, “Frequency chirp and spectra due to self-phase modulation and stimulated Raman scattering influenced by pulse walk-off in optical fibers,” J. Opt. Soc. Am. B 4, 856 (1987).
    [Crossref]
  8. A. Höök, D. Anderson, and M. Lisak, “Solitonlike Stokes pulses in stimulated Raman scattering,” Opt. Lett. 13, 1114 (1989).
    [Crossref]
  9. D. Schadt and B. Jaskorzynska, “Suppression of the Raman self-frequency shift by cross-phase modulation,” J. Opt. Soc. Am. B 5, 2374 (1988).
    [Crossref]
  10. V. V. Afanasjev, E. M. Dianov, and V. N. Serkin, “Nonlinear pairing of short bright and dark soliton pulses by phase cross modulation,” IEEE J. Quantum Electron. 25, 2656 (1989).
    [Crossref]
  11. V. V. Afanasjev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14, 805 (1989).
    [Crossref]
  12. V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, “Nonlinear pairing of bright and dark optical solitons,” JETP Lett. 48, 638 (1989).
  13. P. C. Subramaniam, “Propagation of solitonlike pulses under cross phase modulation,” Opt. Lett. 16, 1560 (1991).
    [Crossref] [PubMed]
  14. P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507 (1964).
    [Crossref]
  15. M. N. Islam, L. F. Mollenauer, R. H. Stolen, J. R. Simpson, and H. T. Shang, “Cross-phase modulation in optical fibers,” Opt. Lett. 12, 625 (1987).
    [Crossref] [PubMed]
  16. S. Trill, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871 (1988).
    [Crossref]
  17. V. Ya. Khasilev, “Envelope solitons with different carrier frequencies in a dispersive nonlinear medium,” JETP Lett. 56, 195 (1992).
  18. M. Lisak, A. Höök, and D. Anderson, “Symbiotic solitary-wave pairs sustained by cross-phase modulation in optical fibers,” J. Opt. Soc. Am. B 7, 810 (1990).
    [Crossref]
  19. Y. S. Kivshar, “Stable vector solitons composed of bright and dark pulses,” Opt. Lett. 17, 1322 (1992).
    [Crossref] [PubMed]
  20. J. T. Manassah, “Ultrafast solitary waves sustained through induced phase modulation by a copropagating pump,” Opt. Lett. 15, 670 (1990).
    [Crossref] [PubMed]
  21. C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. QE-23, 174 (1987).
    [Crossref]
  22. K. J. Blow, N. J. Doran, and D. Wood, “Polarization instabilities for solitons in birefringent fibers,” Opt. Lett. 12, 202 (1987).
    [Crossref] [PubMed]
  23. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes,” Opt. Lett. 12, 614 (1987).
    [Crossref] [PubMed]
  24. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes,” J. Opt. Soc. Am. B 5, 392 (1988).
    [Crossref]
  25. D. N. Christodoulides and R. I. Joseph, “Vector solitons in birefringent nonlinear dispersive media,” Opt. Lett. 13, 53 (1988).
    [Crossref] [PubMed]
  26. D. N. Christodoulides, “Black and white vector solitons in weakly birefringent optical fibers,” Phys. Lett. A 132, 451 (1988).
    [Crossref]
  27. C. R. Menyuk, “Pulse propagation in elliptically birefringent medium,” IEEE J. Quantum Electron. QE-25, 2674 (1989).
    [Crossref]
  28. S. Trillo and S. Wabnitz, “Ultrafast pulse train generation through induced modulational polarization instability in a birefringent Kerr-like medium,” J. Opt. Soc. Am. B 6, 238 (1989).
    [Crossref]
  29. C.-J. Chen, P. K. A. Wai, and C. R. Menyuk, “Soliton switch using birefringent optical fibers,” Opt. Lett. 15, 477 (1990).
    [Crossref] [PubMed]
  30. S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarization instabilities of dark and bright coupled solitary waves in birefringent optical fibers,” Phys. Rev. A 41, 6415 (1990).
    [Crossref] [PubMed]
  31. N. A. Kostov and I. M. Uzunov, “New kinds of periodical waves in birefringent optical fibers,” Opt. Commun. 89, 389 (1992).
    [Crossref]
  32. M. V. Tratnik, “Twisted solitons in birefringent optical fibers,” Opt. Lett. 17, 917 (1992).
    [Crossref] [PubMed]
  33. Q. Wang, P. K. A. Wai, C.-J. Chen, and C. R. Menyuk, “Soliton shadows in birefringent optical fibers,” Opt. Lett. 17, 1265 (1992).
    [Crossref] [PubMed]
  34. B. A. Malomed, “Inelastic collisions of polarized solitons in a birefringent optical fiber,” J. Opt. Soc. Am. B 9, 2075 (1992).
    [Crossref]
  35. I. P. Kaminov, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15 (1981).
    [Crossref]
  36. B. Crosignani and P. Di Porto, “Soliton propagation in multimode fibers,” Opt. Lett. 6, 329 (1981).
    [Crossref] [PubMed]
  37. J. Kay and H. E. Moses, “Reflectionless transmission through dielectrics and scattering potentials,” J. Appl. Phys. 27, 1503 (1956).
    [Crossref]
  38. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  39. S. C. Rashleigh, “Wavelength dependence of birefringence in highly birefringent fibers,” Opt. Lett. 7, 294 (1982).
    [Crossref] [PubMed]
  40. Y. S. Kivshar, D. Anderson, A. Höök, M. Lisak, A. A. Afanasjev, and V. N. Serkin, “Symbiotic optical solitons and modulation instability,” Phys. Scr. 44, 195 (1991).
    [Crossref]
  41. M. Nakazawa, K. Suzuki, and H. A. Haus, “The modulation instability laser—Part I. Experiment,” IEEE J. Quantum Electron. 25, 2036 (1989).
    [Crossref]
  42. J. E. Rothenberg, “Observation of the buildup of modulation instability from wave breaking,” Opt. Lett. 16, 18 (1991).
    [Crossref] [PubMed]
  43. D. Yevick and B. Hermansson, “Soliton analysis with the propagating beam method,” Opt. Commun. 47, 101 (1983).
    [Crossref]
  44. N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266 (1981).
    [Crossref]
  45. A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, Berlin, 1989).
    [Crossref]

1992 (7)

P. C. Subramaniam, “Wavelength division multiplexing of phase modulated solitons,” Opt. Commun. 93, 294 (1992).
[Crossref]

V. Ya. Khasilev, “Envelope solitons with different carrier frequencies in a dispersive nonlinear medium,” JETP Lett. 56, 195 (1992).

N. A. Kostov and I. M. Uzunov, “New kinds of periodical waves in birefringent optical fibers,” Opt. Commun. 89, 389 (1992).
[Crossref]

B. A. Malomed, “Inelastic collisions of polarized solitons in a birefringent optical fiber,” J. Opt. Soc. Am. B 9, 2075 (1992).
[Crossref]

M. V. Tratnik, “Twisted solitons in birefringent optical fibers,” Opt. Lett. 17, 917 (1992).
[Crossref] [PubMed]

Q. Wang, P. K. A. Wai, C.-J. Chen, and C. R. Menyuk, “Soliton shadows in birefringent optical fibers,” Opt. Lett. 17, 1265 (1992).
[Crossref] [PubMed]

Y. S. Kivshar, “Stable vector solitons composed of bright and dark pulses,” Opt. Lett. 17, 1322 (1992).
[Crossref] [PubMed]

1991 (3)

1990 (5)

1989 (8)

A. Höök, D. Anderson, and M. Lisak, “Solitonlike Stokes pulses in stimulated Raman scattering,” Opt. Lett. 13, 1114 (1989).
[Crossref]

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Optical wave breaking and pulse compression due to cross-phase modulation in optical fibers,” Opt. Lett. 14, 137 (1989).
[Crossref] [PubMed]

V. V. Afanasjev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14, 805 (1989).
[Crossref]

S. Trillo and S. Wabnitz, “Ultrafast pulse train generation through induced modulational polarization instability in a birefringent Kerr-like medium,” J. Opt. Soc. Am. B 6, 238 (1989).
[Crossref]

C. R. Menyuk, “Pulse propagation in elliptically birefringent medium,” IEEE J. Quantum Electron. QE-25, 2674 (1989).
[Crossref]

M. Nakazawa, K. Suzuki, and H. A. Haus, “The modulation instability laser—Part I. Experiment,” IEEE J. Quantum Electron. 25, 2036 (1989).
[Crossref]

V. V. Afanasjev, E. M. Dianov, and V. N. Serkin, “Nonlinear pairing of short bright and dark soliton pulses by phase cross modulation,” IEEE J. Quantum Electron. 25, 2656 (1989).
[Crossref]

V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, “Nonlinear pairing of bright and dark optical solitons,” JETP Lett. 48, 638 (1989).

1988 (5)

1987 (7)

1984 (1)

A. R. Chraplyvy, D. Marcuse, and P. S. Henry, “Carrier induced phase noise in angle-modulated optical fiber systems,” J. Lightwave Technol. LT-2, 6 (1984).
[Crossref]

1983 (1)

D. Yevick and B. Hermansson, “Soliton analysis with the propagating beam method,” Opt. Commun. 47, 101 (1983).
[Crossref]

1982 (1)

1981 (3)

B. Crosignani and P. Di Porto, “Soliton propagation in multimode fibers,” Opt. Lett. 6, 329 (1981).
[Crossref] [PubMed]

N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266 (1981).
[Crossref]

I. P. Kaminov, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15 (1981).
[Crossref]

1964 (1)

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507 (1964).
[Crossref]

1956 (1)

J. Kay and H. E. Moses, “Reflectionless transmission through dielectrics and scattering potentials,” J. Appl. Phys. 27, 1503 (1956).
[Crossref]

Afanasjev, A. A.

Y. S. Kivshar, D. Anderson, A. Höök, M. Lisak, A. A. Afanasjev, and V. N. Serkin, “Symbiotic optical solitons and modulation instability,” Phys. Scr. 44, 195 (1991).
[Crossref]

Afanasjev, V. V.

V. V. Afanasjev, E. M. Dianov, and V. N. Serkin, “Nonlinear pairing of short bright and dark soliton pulses by phase cross modulation,” IEEE J. Quantum Electron. 25, 2656 (1989).
[Crossref]

V. V. Afanasjev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14, 805 (1989).
[Crossref]

Afanasyev, V. V.

V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, “Nonlinear pairing of bright and dark optical solitons,” JETP Lett. 48, 638 (1989).

Agrawal, G. P.

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Optical wave breaking and pulse compression due to cross-phase modulation in optical fibers,” Opt. Lett. 14, 137 (1989).
[Crossref] [PubMed]

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

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

Alfano, R. R.

Anderson, D.

Baldeck, P. L.

Blow, K. J.

Brito Cruz, C. H.

Chen, C.-J.

Chraplyvy, A. R.

A. R. Chraplyvy, D. Marcuse, and P. S. Henry, “Carrier induced phase noise in angle-modulated optical fiber systems,” J. Lightwave Technol. LT-2, 6 (1984).
[Crossref]

Christodoulides, D. N.

D. N. Christodoulides, “Black and white vector solitons in weakly birefringent optical fibers,” Phys. Lett. A 132, 451 (1988).
[Crossref]

D. N. Christodoulides and R. I. Joseph, “Vector solitons in birefringent nonlinear dispersive media,” Opt. Lett. 13, 53 (1988).
[Crossref] [PubMed]

Crosignani, B.

da Silva, V. L.

Di Porto, P.

Dianov, E. M.

V. V. Afanasjev, E. M. Dianov, and V. N. Serkin, “Nonlinear pairing of short bright and dark soliton pulses by phase cross modulation,” IEEE J. Quantum Electron. 25, 2656 (1989).
[Crossref]

V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, “Nonlinear pairing of bright and dark optical solitons,” JETP Lett. 48, 638 (1989).

Doran, N. J.

Hasegawa, A.

A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, Berlin, 1989).
[Crossref]

Haus, H. A.

M. Nakazawa, K. Suzuki, and H. A. Haus, “The modulation instability laser—Part I. Experiment,” IEEE J. Quantum Electron. 25, 2036 (1989).
[Crossref]

Henry, P. S.

A. R. Chraplyvy, D. Marcuse, and P. S. Henry, “Carrier induced phase noise in angle-modulated optical fiber systems,” J. Lightwave Technol. LT-2, 6 (1984).
[Crossref]

Hermansson, B.

D. Yevick and B. Hermansson, “Soliton analysis with the propagating beam method,” Opt. Commun. 47, 101 (1983).
[Crossref]

Höök, A.

Islam, M. N.

Jain, M.

N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266 (1981).
[Crossref]

Jaskorzynska, B.

Joseph, R. I.

Kaminov, I. P.

I. P. Kaminov, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15 (1981).
[Crossref]

Kay, J.

J. Kay and H. E. Moses, “Reflectionless transmission through dielectrics and scattering potentials,” J. Appl. Phys. 27, 1503 (1956).
[Crossref]

Khasilev, V. Ya.

V. Ya. Khasilev, “Envelope solitons with different carrier frequencies in a dispersive nonlinear medium,” JETP Lett. 56, 195 (1992).

Kivshar, Y. S.

Konotop, V. V.

Kostov, N. A.

N. A. Kostov and I. M. Uzunov, “New kinds of periodical waves in birefringent optical fibers,” Opt. Commun. 89, 389 (1992).
[Crossref]

Lisak, M.

Maker, P. D.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507 (1964).
[Crossref]

Malomed, B. A.

Manassah, J. T.

Marcuse, D.

A. R. Chraplyvy, D. Marcuse, and P. S. Henry, “Carrier induced phase noise in angle-modulated optical fiber systems,” J. Lightwave Technol. LT-2, 6 (1984).
[Crossref]

Menyuk, C. R.

Mollenauer, L. F.

Moses, H. E.

J. Kay and H. E. Moses, “Reflectionless transmission through dielectrics and scattering potentials,” J. Appl. Phys. 27, 1503 (1956).
[Crossref]

Nakazawa, M.

M. Nakazawa, K. Suzuki, and H. A. Haus, “The modulation instability laser—Part I. Experiment,” IEEE J. Quantum Electron. 25, 2036 (1989).
[Crossref]

Prokhorov, A. M.

V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, “Nonlinear pairing of bright and dark optical solitons,” JETP Lett. 48, 638 (1989).

Rashleigh, S. C.

Rothenberg, J. E.

Savage, C. M.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507 (1964).
[Crossref]

Schadt, D.

Serkin, V. N.

Y. S. Kivshar, D. Anderson, A. Höök, M. Lisak, A. A. Afanasjev, and V. N. Serkin, “Symbiotic optical solitons and modulation instability,” Phys. Scr. 44, 195 (1991).
[Crossref]

V. V. Afanasjev, E. M. Dianov, and V. N. Serkin, “Nonlinear pairing of short bright and dark soliton pulses by phase cross modulation,” IEEE J. Quantum Electron. 25, 2656 (1989).
[Crossref]

V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, “Nonlinear pairing of bright and dark optical solitons,” JETP Lett. 48, 638 (1989).

V. V. Afanasjev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14, 805 (1989).
[Crossref]

Shang, H. T.

Simpson, J. R.

Stegeman, G. I.

S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarization instabilities of dark and bright coupled solitary waves in birefringent optical fibers,” Phys. Rev. A 41, 6415 (1990).
[Crossref] [PubMed]

S. Trill, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871 (1988).
[Crossref]

Stolen, R. H.

Subramaniam, P. C.

P. C. Subramaniam, “Wavelength division multiplexing of phase modulated solitons,” Opt. Commun. 93, 294 (1992).
[Crossref]

P. C. Subramaniam, “Propagation of solitonlike pulses under cross phase modulation,” Opt. Lett. 16, 1560 (1991).
[Crossref] [PubMed]

Suzuki, K.

M. Nakazawa, K. Suzuki, and H. A. Haus, “The modulation instability laser—Part I. Experiment,” IEEE J. Quantum Electron. 25, 2036 (1989).
[Crossref]

Terhune, R. W.

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507 (1964).
[Crossref]

Tratnik, M. V.

Trill, S.

Trillo, S.

Tzoar, N.

N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266 (1981).
[Crossref]

Uzunov, I. M.

N. A. Kostov and I. M. Uzunov, “New kinds of periodical waves in birefringent optical fibers,” Opt. Commun. 89, 389 (1992).
[Crossref]

Wabnitz, S.

Wai, P. K. A.

Wang, Q.

Wood, D.

Wright, E. M.

S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarization instabilities of dark and bright coupled solitary waves in birefringent optical fibers,” Phys. Rev. A 41, 6415 (1990).
[Crossref] [PubMed]

S. Trill, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871 (1988).
[Crossref]

Yevick, D.

D. Yevick and B. Hermansson, “Soliton analysis with the propagating beam method,” Opt. Commun. 47, 101 (1983).
[Crossref]

Electron. Lett. (1)

D. Schadt and B. Jaskorzynska, “Generation of short pulse from cw light by influence of cross phase modulation (CPM) in optical fibers,” Electron. Lett. 23, 1090 (1987).
[Crossref]

IEEE J. Quantum Electron. (5)

V. V. Afanasjev, E. M. Dianov, and V. N. Serkin, “Nonlinear pairing of short bright and dark soliton pulses by phase cross modulation,” IEEE J. Quantum Electron. 25, 2656 (1989).
[Crossref]

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron. QE-23, 174 (1987).
[Crossref]

C. R. Menyuk, “Pulse propagation in elliptically birefringent medium,” IEEE J. Quantum Electron. QE-25, 2674 (1989).
[Crossref]

I. P. Kaminov, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15 (1981).
[Crossref]

M. Nakazawa, K. Suzuki, and H. A. Haus, “The modulation instability laser—Part I. Experiment,” IEEE J. Quantum Electron. 25, 2036 (1989).
[Crossref]

J. Appl. Phys. (1)

J. Kay and H. E. Moses, “Reflectionless transmission through dielectrics and scattering potentials,” J. Appl. Phys. 27, 1503 (1956).
[Crossref]

J. Lightwave Technol. (1)

A. R. Chraplyvy, D. Marcuse, and P. S. Henry, “Carrier induced phase noise in angle-modulated optical fiber systems,” J. Lightwave Technol. LT-2, 6 (1984).
[Crossref]

J. Opt. Soc. Am. B (7)

JETP Lett. (2)

V. Ya. Khasilev, “Envelope solitons with different carrier frequencies in a dispersive nonlinear medium,” JETP Lett. 56, 195 (1992).

V. V. Afanasyev, E. M. Dianov, A. M. Prokhorov, and V. N. Serkin, “Nonlinear pairing of bright and dark optical solitons,” JETP Lett. 48, 638 (1989).

Opt. Commun. (3)

P. C. Subramaniam, “Wavelength division multiplexing of phase modulated solitons,” Opt. Commun. 93, 294 (1992).
[Crossref]

N. A. Kostov and I. M. Uzunov, “New kinds of periodical waves in birefringent optical fibers,” Opt. Commun. 89, 389 (1992).
[Crossref]

D. Yevick and B. Hermansson, “Soliton analysis with the propagating beam method,” Opt. Commun. 47, 101 (1983).
[Crossref]

Opt. Lett. (17)

J. E. Rothenberg, “Observation of the buildup of modulation instability from wave breaking,” Opt. Lett. 16, 18 (1991).
[Crossref] [PubMed]

S. C. Rashleigh, “Wavelength dependence of birefringence in highly birefringent fibers,” Opt. Lett. 7, 294 (1982).
[Crossref] [PubMed]

M. V. Tratnik, “Twisted solitons in birefringent optical fibers,” Opt. Lett. 17, 917 (1992).
[Crossref] [PubMed]

Q. Wang, P. K. A. Wai, C.-J. Chen, and C. R. Menyuk, “Soliton shadows in birefringent optical fibers,” Opt. Lett. 17, 1265 (1992).
[Crossref] [PubMed]

D. N. Christodoulides and R. I. Joseph, “Vector solitons in birefringent nonlinear dispersive media,” Opt. Lett. 13, 53 (1988).
[Crossref] [PubMed]

B. Crosignani and P. Di Porto, “Soliton propagation in multimode fibers,” Opt. Lett. 6, 329 (1981).
[Crossref] [PubMed]

Y. S. Kivshar, “Stable vector solitons composed of bright and dark pulses,” Opt. Lett. 17, 1322 (1992).
[Crossref] [PubMed]

J. T. Manassah, “Ultrafast solitary waves sustained through induced phase modulation by a copropagating pump,” Opt. Lett. 15, 670 (1990).
[Crossref] [PubMed]

K. J. Blow, N. J. Doran, and D. Wood, “Polarization instabilities for solitons in birefringent fibers,” Opt. Lett. 12, 202 (1987).
[Crossref] [PubMed]

C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes,” Opt. Lett. 12, 614 (1987).
[Crossref] [PubMed]

C.-J. Chen, P. K. A. Wai, and C. R. Menyuk, “Soliton switch using birefringent optical fibers,” Opt. Lett. 15, 477 (1990).
[Crossref] [PubMed]

A. Höök, D. Anderson, and M. Lisak, “Solitonlike Stokes pulses in stimulated Raman scattering,” Opt. Lett. 13, 1114 (1989).
[Crossref]

G. P. Agrawal, P. L. Baldeck, and R. R. Alfano, “Optical wave breaking and pulse compression due to cross-phase modulation in optical fibers,” Opt. Lett. 14, 137 (1989).
[Crossref] [PubMed]

P. C. Subramaniam, “Propagation of solitonlike pulses under cross phase modulation,” Opt. Lett. 16, 1560 (1991).
[Crossref] [PubMed]

V. V. Afanasjev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14, 805 (1989).
[Crossref]

M. N. Islam, L. F. Mollenauer, R. H. Stolen, J. R. Simpson, and H. T. Shang, “Cross-phase modulation in optical fibers,” Opt. Lett. 12, 625 (1987).
[Crossref] [PubMed]

S. Trill, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871 (1988).
[Crossref]

Phys. Lett. A (1)

D. N. Christodoulides, “Black and white vector solitons in weakly birefringent optical fibers,” Phys. Lett. A 132, 451 (1988).
[Crossref]

Phys. Rev. A (2)

S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Polarization instabilities of dark and bright coupled solitary waves in birefringent optical fibers,” Phys. Rev. A 41, 6415 (1990).
[Crossref] [PubMed]

N. Tzoar and M. Jain, “Self-phase modulation in long-geometry optical waveguides,” Phys. Rev. A 23, 1266 (1981).
[Crossref]

Phys. Rev. Lett. (2)

P. D. Maker, R. W. Terhune, and C. M. Savage, “Intensity dependent changes in the refractive index of liquids,” Phys. Rev. Lett. 12, 507 (1964).
[Crossref]

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

Phys. Scr. (1)

Y. S. Kivshar, D. Anderson, A. Höök, M. Lisak, A. A. Afanasjev, and V. N. Serkin, “Symbiotic optical solitons and modulation instability,” Phys. Scr. 44, 195 (1991).
[Crossref]

Other (2)

A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, Berlin, 1989).
[Crossref]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

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 (3)

Fig. 1
Fig. 1

Gain spectrum of the modulation instability for different angles of polarization of the first wave. β1″ ≈ β2″ = 0.06 ps2/m, P3 = 1.5.

Fig. 2
Fig. 2

Evolution of the pulse (α = 1.0, δ11 = −δ12 = 0.1, δ21 = 1.5, δ22 = 1.3, γ/R = 1.1) at (a) χ = 0; (b) and (c) χ = π.

Fig. 3
Fig. 3

Variation of the maximum location (δ11 = −δ12 = 0.1, δ21 = 1.5, δ22 = 1.3, γ/R = 1.1) for (a) α = 0.7, (b) α = 1.0, (c) α = 1.3.

Equations (74)

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

E ( x , y , z , t ) = e ^ 1 { E 11 ( z , t ) ϕ 11 ( x , y ) exp [ i ( β 11 z - ω 1 t ) ] + E 21 ( z , t ) ϕ 21 ( x , y ) exp [ i ( β 21 z - ω 2 t ) ] } + e ^ 2 { E 12 ( z , t ) ϕ 12 ( x , y ) exp [ i ( β 12 z - ω 1 t ) ] , + E 22 ( z , t ) ϕ 22 ( x , y ) exp [ i ( β 22 z - ω 2 t ) ] } ,
i ( E l m z + β l m E l m t ) - 1 2 β l m 2 E l m t 2 + χ l m ( E l m 2 + 2 E p m 2 + P E l q 2 + P E p q 2 ) E l m = - ( 1 - P ) χ l m ( E l q 2 E l m * exp [ 2 i ( β l q - β l m ) z ] + 2 E l q E p q E p m * exp { i [ ( β l q - β l m ) + ( β p q - β p m ) ] z } ) - P χ l m E l q E p m E p q * exp { i [ ( β l q - β l m ) - ( β p q - β p m ) ] z } ,
l , m = 1 , 2 ,             p = 3 - l ,             q = 3 - m ,
U l m = E l m P 0 ,             ξ = π z 2 z 0 ,             s = t - z β ¯ 1 t 0 , t 0 = 0.568 τ ,             β 1 = - π t 0 2 2 z 0 ,             π 2 P 0 z 0 = χ 11 , β l 1 - β l 2 = ( β l 1 - β l 2 ) ω l ,             l = 1 , 2 , β ¯ 1 = β 11 + β 12 2 ,             δ l m = 2 z 0 ( β l m - β ¯ 1 ) π t 0 , g m = z 0 ( β 2 m - β 2 q ) π t 0 ,             q = 3 - m ,             m = 1 , 2 , γ = β 21 β 11 ,             W = 2 t 0 ω 1 ,             R = χ 21 χ 11 ,
β l 1 = β l 2 ,             χ l 1 χ l 2 ,             l = 1 , 2 ,
i ( U 1 m ξ + δ 1 m U 1 m s ) + 1 2 2 U l m s 2 + ( U 1 m 2 + 2 U 2 m 2 + P U 1 q 2 + P U 2 q 2 ) U 1 m = - ( 1 - P ) { U 1 q 2 U 1 m * exp ( - i 2 W δ 1 m ξ ) + 2 U 1 q U 2 m * U 2 q exp [ - i W ( δ 1 m + g m ) ξ ] } - P U 1 q U 2 q * U 2 m exp [ - i W ( δ 1 m - g m ) ξ ] ,
i ( U 2 m ξ + δ 2 m U 2 m s ) + γ 2 2 U 2 m s 2 + R ( U 2 m 2 + 2 U 1 m 2 + P U 2 q 2 + P U 1 q 2 ) U 2 m = - ( 1 - P ) R { U 2 q 2 U 2 m * exp ( - i 2 W g m ξ ) + 2 U 2 q U 1 m * U 1 q exp [ - i W ( g m + δ 1 m ) ξ ] } - P U 2 q U 1 q * U 1 m exp [ - i W ( g m - δ 1 m ) ξ ] ,
m = 1 , 2 ;             q = 3 - m .
U 1 m = X m ( s ) exp [ - i ( μ + W δ 1 m / 2 ) ξ ] ,
U 2 m = α X m ( s ) exp [ - i ( μ γ + W g m / 2 ) ξ ] ,             m = 1 , 2 ,
( μ + δ 11 W 2 ) X 1 + 1 2 d 2 X 1 d s 2 + ( 1 + 2 α 2 ) ( X 1 2 + X 2 2 ) X 1 = 0 ,
( μ - δ 11 W 2 ) X 2 + 1 2 d 2 X 2 d s 2 + ( 1 + 2 α 2 ) ( X 1 2 + X 2 2 ) X 2 = 0 ,
μ γ + W g 1 / 2 μ + W δ 11 / 2 = ( 2 + α 2 ) R 1 + 2 α 2 = γ ,
α = ± ( 2 R - γ 2 γ - R ) 1 / 2 .
γ δ 11 = g 1 ,
X 1 = 1 ( 1 + 2 α 2 ) 1 / 2 η 1 [ cosh ( η 2 s ) - η 2 ( η 1 + η 2 ) - 1 exp ( η 2 s ) ] cosh ( η 1 s ) cosh ( η 2 s ) - η 1 η 2 ( η 1 + η 2 ) - 2 exp [ ( η 1 + η 2 ) s ] ,
X 2 = 1 ( 1 + 2 α 2 ) 1 / 2 η 2 [ cosh ( η 2 s ) - η 1 ( η 1 + η 2 ) - 1 exp ( η 1 s ) ] cosh ( η 1 s ) cosh ( η 2 s ) - η 1 η 2 ( η 1 + η 2 ) - 2 exp [ ( η 1 + η 2 ) s ] ,
η 1 2 = - 2 ( μ + W δ 11 / 2 ) ,
η 2 2 = - 2 ( μ - W δ 11 / 2 ) .
μ < - W δ 11 / 2 ,
R / 2 < γ < 2 R .
U 1 m = m sech ( s ) exp [ - i ξ ( μ + W δ 1 m / 2 ) ] ,             m = 1 , 2 ,
U 22 = A exp ( i R A 2 ξ ) ,
U 21 = 0.
A 2 = ( W δ 11 2 - P ) 1 / 2 ,
μ = - 1 2 [ 1 + W δ 11 ( 2 + P ) 2 - P ] ,
1 2 + 2 2 = 1.
i ( U 1 m ξ + δ 1 m U 1 m s ) + 1 2 2 U 1 m s 2 + ( U 1 m 2 + 2 U 2 m 2 + P U 1 q 2 + P U 2 q 2 ) U 1 m = 0 ,
i ( U 2 m ξ + δ 2 m U 2 m s ) + γ 2 2 U 2 m s 2 + R ( U 2 m 2 + 2 U 1 m 2 + P U 2 q 2 + P U 1 q 2 ) U 2 m = 0.
U 1 m = A 1 sech ( s ) exp { - i [ δ 1 m s - ( 1 + δ 1 m 2 ) ξ / 2 ] } ,
U 2 m = A 2 sech ( s ) exp { - i [ 2 δ 2 m s - ( γ 2 + δ 2 m 2 ) ξ ] / ( 2 γ ) } ,
A 1 = [ ( 2 + P ) γ - ( 1 + P ) R ( 3 + 2 P ) R ] 1 / 2 ,
A 2 = [ ( 2 + P ) R - ( 1 + P ) γ ( 3 + 2 P ) R ] 1 / 2 .
1 + P 2 + P < γ R < 2 + P 1 + P .
A 1 = ( 2 R - γ 3 R ) 1 / 2 ,             A 2 = ( 2 γ - R 3 R ) 1 / 2 .
U 1 m = B 1 tanh ( s ) exp ( - i { δ 1 m s - [ B 1 2 ( 1 + P ) + δ 1 m 2 ] ξ / 2 } ) ,
U 2 m = B 2 sech ( s ) exp ( - i { 2 δ 2 m s - [ 2 B 1 2 ( 2 + P ) R γ + γ 2 + δ 2 m 2 ] ξ } / ( 2 γ ) ) ,
B 1 = [ ( 1 + P ) R - ( 2 + P ) γ ( 3 + 2 P ) R ] 1 / 2 ,
B 2 = [ ( 2 + P ) R - ( 1 + P ) γ ( 3 + 2 P ) R ] 1 / 2 .
U 1 m = ψ 1 ( ξ , s ) exp [ - i ( δ 1 m s - δ 1 m 2 ξ / 2 ) ] ,
U 2 m = ψ 2 ( ξ , s ) exp [ - i ( 2 δ 2 m s - δ 2 m 2 ξ ) / ( 2 γ ) ] ,
i ψ 1 ξ + 1 2 2 ψ 1 s 2 + [ ( 1 + P ) ψ 1 2 + ( 2 + P ) ψ 2 2 ] ψ 1 = 0 ,
i ψ 2 ξ + γ 2 2 ψ 2 s 2 + R [ ( 1 + P ) ψ 2 2 + ( 2 + P ) ψ 1 2 ] ψ 2 = 0.
ψ 1 = A 1 Ψ ,             ψ 2 = A 2 Ψ ,
i Ψ ξ + 1 2 2 Ψ s 2 + Ψ 2 Ψ = 0.
U 11 = C 1 sech ( s ) exp { - i [ δ 11 s - ( 1 + δ 11 2 ) ξ / 2 ] } ,
U 12 = C 2 sech ( s ) exp { i [ δ 11 s + ( 1 + δ 11 2 ) ξ / 2 ] } ,
U 21 = C 3 sech ( s ) exp { - i [ 2 δ 21 s - ( γ 2 + δ 21 2 ) ξ ] / ( 2 γ ) } ,
U 22 = 0 ,
C 1 2 = ( γ / R ) ( 2 - P 2 ) - P + P 2 - 1 3 - 2 P 2 ,
C 2 2 = 3 - P ( 1 + γ / R ) 3 - 2 P 2 ,
C 3 2 = γ / R ( P 2 - 1 ) + 2 - P - P 2 3 - 2 P 2 .
1 + P - P 2 2 - P 2 < γ R < 2 - P - P 2 1 - P 2 .
U 11 = D 1 tanh ( s ) exp { - i [ δ 11 s - ( 2 D 1 2 + δ 11 2 ) ξ / 2 ] } ,
U 12 = D 2 sech ( s ) exp { i [ δ 11 s + ( 1 + P D 1 2 + δ 11 2 ) ξ / 2 ] } ,
U 21 = D 3 sech ( s ) exp { - i [ 2 δ 21 s - ( γ 2 + δ 21 2 + 4 γ R D 1 2 ) ξ ] / ( 2 γ ) } ,
U 22 = 0 ,
D 1 2 = ( γ / R ) ( P 2 - 2 ) + 1 + P - P 2 3 - 2 P 2 ,
D 2 2 = 3 - P ( 1 + γ / R ) 3 - 2 P 2 ,
D 3 2 = γ / R ( P 2 - 1 ) + 2 - P - P 2 3 - 2 P 2 .
γ R < 1 - P 2 + P 2 - P 2 .
U 11 = ( P 1 + a 1 ) exp ( i Φ 1 ) , U 12 = ( P 2 + a 2 ) exp ( i Φ 2 ) , U 21 = ( P 3 + a 3 ) exp ( i Φ 3 ) , U 22 = 0 ,
Φ 1 = ( P 1 + 2 P 2 + P P 3 ) ξ , Φ 2 = ( P 2 + P P 1 + P P 3 ) ξ , Φ 3 = ( P 3 + 2 P 1 + P P 2 ) R ξ ,
i a 1 ξ + 1 2 2 a 1 s 2 + P 1 ( a 1 + a 1 * ) + 2 P 1 P 3 ( a 3 + a 3 * ) + P P 1 P 2 ( a 2 + a 2 * ) = 0 , i a 2 ξ + 1 2 2 a 2 s 2 + P 2 ( a 2 + a 2 * ) + 2 P 1 P 2 ( a 1 + a 1 * ) + 2 P 2 P 3 ( a 3 + a 3 * ) = 0 , i a 3 ξ + γ 2 2 a 3 s 2 + R [ P 3 ( a 3 + a 3 * ) + 2 P 1 P 3 ( a 1 + a 1 * ) + P P 3 P 2 ( a 2 + a 2 * ) ] = 0.
a j = u j cos ( K ξ - Ω s ) + i v j sin ( K ξ - Ω s ) ,             j = 1 , 2 , 3 ,
( K 2 - f 1 ) ( K 2 - f 2 ) ( K 2 - f 3 ) + 4 Ω 6 R γ P 2 P 1 P 2 P 3 = Ω 2 [ P 2 R γ P 3 P 2 ( K 2 - f 1 ) + P 2 P 1 P 2 ( K 2 - f 3 ) + 4 R γ P 2 P 1 P 3 ( K 2 - f 2 ) ] ,
f j = ± Ω 2 2 ( 2 P j ± Ω 2 2 ) ,             j = 1 , 2 , f 3 = ± Ω 2 γ 2 ( 2 P j R ± Ω 2 γ 2 ) .
U 1 m ( ξ = 0 , s ) = α A 1 sech ( s ) ,
U 2 m ( ξ = 0 , s ) = α A 2 sech ( s ) ,             m = 1 , 2 ,
2 E - 1 c 2 2 D L t 2 = 1 c 2 2 P NL t 2 ,
l , m = 1 , 2 e ^ m { [ ( 2 ϕ l m x 2 ) + ( 2 ϕ l m y 2 ) ] E l m + 2 β l m [ i ( E l m z + β l m E l m t ) - 1 2 β l m 2 E l m t 2 ] ϕ l m } × exp [ i ( β l m z - ω l t ) ] ,
P NL = χ ( 3 ) [ P E ( E · E * ) + ( 1 - P ) E * ( E · E ) ] ,
P NL = ρ χ ( 3 ) l , m = 1 , 2 e ^ m [ ( E l m 2 + 2 E p m 2 + P E l q 2 + P E p q 2 ) E l m + ( 1 - P ) ( E l q 2 E l m * × exp [ 2 i ( β l q - β l m ) z ] + 2 E l q E p q E p m * × exp { i [ ( β l q - β l m ) + ( β p q - β p m ) ] z } ) + P E l q E p m E p q * exp { i [ ( β l q - β l m ) - ( β p q - β p m ) ] z } ] × exp [ i ( β l m z - ω l t ) ] ,
χ l m = β l m χ ( 3 ) ρ 2 .

Metrics