Abstract

We present a set of experimental observations that demonstrate the generation of vector trains of dark-soliton pulses in the orthogonal axes of a highly birefringent optical fiber. We generated dark-soliton trains with terahertz repetition rate in the normal group-velocity dispersion regime by inducing a polarization modulational instability by mixing two intense, orthogonal continuous laser beams. Numerical solutions of the propagation equations were used to optimize the emission of vector dark pulses at the fiber output.

© 1999 Optical Society of America

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995), Chaps. 5 and 7.
  2. W. Zhao and E. Bourkoff, “Propagation properties of dark solitons,” Opt. Lett. 14, 703–705 (1989); “Interaction between dark solitons,” Opt. Lett. 14, 1371–1373 (1989); J. P. Hamaide, Ph. Emplit, and M. Haelterman, “Dark-soliton jitter in amplified optical transmission systems,” Opt. Lett. OPLEDP 16, 1578–1580 (1991); Y. S. Kivshar, M. Haelterman, Ph. Emplit, and J. P. Hamaide, “Gordon–Haus effect on dark solitons,” Opt. Lett. OPLEDP 19, 19–21 (1994).
    [CrossRef] [PubMed]
  3. M. Haelterman and A. P. Sheppard, “Polarization domain walls in diffractive or dispersive Kerr media,” Opt. Lett. 19, 96–98 (1994).
    [CrossRef] [PubMed]
  4. A. Hasegawa, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Opt. Lett. 9, 288–290 (1994).
    [CrossRef]
  5. T. Taniuti and H. Washimi, “Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma,” Phys. Rev. Lett. 21, 209–212 (1968).
    [CrossRef]
  6. T. B. Benjamin and J. E. Feir, “The disintegration of wave-trains on deep water. 1. Theory,” J. Fluid Mech. 27, 417–430 (1967).
    [CrossRef]
  7. Y. S. Kivshar and M. Peyrard, “Modulational instabilities in discrete lattices,” Phys. Rev. A 46, 3198–3205 (1992).
    [CrossRef] [PubMed]
  8. J. M. Bilbault, P. Marquie, and B. Michaux, “Modulational instability of two counterpropagating waves in an experimental transmission line,” Phys. Rev. E 51, 817–820 (1995).
    [CrossRef]
  9. V. I. Bespalov and V. I. Talanov, “Filamentary structures of light beams in nonlinear liquids,” JETP Lett. 3, 307–309 (1966).
  10. K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
    [CrossRef] [PubMed]
  11. A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–490 (1970).
  12. G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
    [CrossRef] [PubMed]
  13. G. P. Agrawal, “Modulational instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987); S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A 38, 2018–2021 (1988); S. Trillo and S. Wabnitz, “Ultrashort pulse train generation through induced modulational polarization instability in a birefringent Kerr-like medium,” J. Opt. Soc. Am. B JOBPDE 6, 238–249 (1989); J. E. Rothenberg, “Modulational instability of copropagating frequencies for normal dispersion,” Phys. Rev. Lett. PRLTAO 64, 813–813 (1990); “Modulational instability for normal dispersion,” Phys. Rev. A PLRAAN 42, 682–685 (1990); P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and D. J. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. OPCOB8 78, 137–142 (1990); G. Millot, S. Pitois, P. Tchofo-Dinda, and M. Haelterman, “Observation of modulational instability induced by velocity-matched cross-phase modulation in a normally dispersive bimodal fiber,” Opt. Lett. OPLEDP 22, 1686–1688 (1997).
    [CrossRef] [PubMed]
  14. E. Lantz, D. Gindre, H. Maillotte, and J. Monneret, “Phase matching for parametric amplification in a single-mode birefringent fiber: influence of the non-phase-matched waves,” J. Opt. Soc. Am. B 14, 116–125 (1997).
    [CrossRef]
  15. Y. S. Kivshar and S. K. Turitsyn, “Vector dark solitons,” Opt. Lett. 18, 337–339 (1993); A. P. Sheppard and Y. S. Kivshar, “Polarized dark solitons in isotropic Kerr media,” Phys. Rev. E 55, 4773–4782 (1997).
    [CrossRef] [PubMed]
  16. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. II. Arbitrary amplitudes,” J. Opt. Soc. Am. B 5, 392–402 (1988).
    [CrossRef]
  17. E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, “Modulational instability and critical regime in a highly birefringent fiber,” Phys. Rev. A 54, 3519–3534 (1996).
    [CrossRef] [PubMed]
  18. M. Lisak, A. Hook, and D. Anderson, “Symbiotic solitary-wave pairs sustained by cross-phase modulation in optical fibers,” J. Opt. Soc. Am. B 7, 810–814 (1990); Y. S. Kivshar and W. Krolikowski, “Lagrangian approach for dark solitons,” Opt. Commun. 114, 353–362 (1995).
    [CrossRef]
  19. M. Haelterman, “Modulational instability, periodic waves and black and white vector solitons in birefringent Kerr media,” Opt. Commun. 111, 86–92 (1994).
    [CrossRef]
  20. S. Trillo and S. Wabnitz, “Nonlinear modulation of coupled waves in birefringent optical fibers,” Phys. Lett. A 159, 252–256 (1991); S. Trillo and S. Wabnitz, “Modulational polarization instabilities and disorder in birefringent optical fibers,” in Nonlinearity with Disorder, F. Abdullaev, A. R. Bishop, and S. Pnevmatikos, eds. (Springer-Verlag, Berlin, 1992), p. 269.
    [CrossRef]
  21. G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Dark-solitonlike pulse-train generation from induced modulational polarization instability in a birefringent fiber,” Opt. Lett. 23, 511–513 (1998); “Observation of induced modulational polarization instabilities and pulse-train generation in the normal-dispersion regime of a birefringent optical fiber,” J. Opt. Soc. Am. B 15, 1266–1277 (1998).
    [CrossRef]
  22. N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894–899 (1985).
  23. P. V. Mamyshev, P. G. Wigley, J. Wilson, C. Bosshard, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. 64, 3374–3376 (1994).
    [CrossRef]
  24. C. De Angelis, M. Santagiustina, and S. Trillo, “Four-photon homoclinic instabilities in nonlinear highly birefringent media,” Phys. Rev. A 51, 774–791 (1991).
    [CrossRef]
  25. E. Seve, G. Millot, and S. Wabnitz, “Buildup of terahertz vector dark-soliton trains from induced modulation instability in highly birefringent optical fiber,” Opt. Lett. 23, 1829–1831 (1998).
    [CrossRef]

1998 (1)

1997 (1)

1996 (1)

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, “Modulational instability and critical regime in a highly birefringent fiber,” Phys. Rev. A 54, 3519–3534 (1996).
[CrossRef] [PubMed]

1995 (1)

J. M. Bilbault, P. Marquie, and B. Michaux, “Modulational instability of two counterpropagating waves in an experimental transmission line,” Phys. Rev. E 51, 817–820 (1995).
[CrossRef]

1994 (4)

M. Haelterman and A. P. Sheppard, “Polarization domain walls in diffractive or dispersive Kerr media,” Opt. Lett. 19, 96–98 (1994).
[CrossRef] [PubMed]

A. Hasegawa, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Opt. Lett. 9, 288–290 (1994).
[CrossRef]

M. Haelterman, “Modulational instability, periodic waves and black and white vector solitons in birefringent Kerr media,” Opt. Commun. 111, 86–92 (1994).
[CrossRef]

P. V. Mamyshev, P. G. Wigley, J. Wilson, C. Bosshard, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. 64, 3374–3376 (1994).
[CrossRef]

1992 (1)

Y. S. Kivshar and M. Peyrard, “Modulational instabilities in discrete lattices,” Phys. Rev. A 46, 3198–3205 (1992).
[CrossRef] [PubMed]

1991 (1)

C. De Angelis, M. Santagiustina, and S. Trillo, “Four-photon homoclinic instabilities in nonlinear highly birefringent media,” Phys. Rev. A 51, 774–791 (1991).
[CrossRef]

1988 (1)

1987 (1)

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[CrossRef] [PubMed]

1986 (1)

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef] [PubMed]

1985 (1)

N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894–899 (1985).

1970 (1)

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–490 (1970).

1968 (1)

T. Taniuti and H. Washimi, “Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma,” Phys. Rev. Lett. 21, 209–212 (1968).
[CrossRef]

1967 (1)

T. B. Benjamin and J. E. Feir, “The disintegration of wave-trains on deep water. 1. Theory,” J. Fluid Mech. 27, 417–430 (1967).
[CrossRef]

1966 (1)

V. I. Bespalov and V. I. Talanov, “Filamentary structures of light beams in nonlinear liquids,” JETP Lett. 3, 307–309 (1966).

Agrawal, G. P.

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[CrossRef] [PubMed]

Akhmediev, N. N.

N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894–899 (1985).

Benjamin, T. B.

T. B. Benjamin and J. E. Feir, “The disintegration of wave-trains on deep water. 1. Theory,” J. Fluid Mech. 27, 417–430 (1967).
[CrossRef]

Berkhoer, A. L.

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–490 (1970).

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structures of light beams in nonlinear liquids,” JETP Lett. 3, 307–309 (1966).

Bilbault, J. M.

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, “Modulational instability and critical regime in a highly birefringent fiber,” Phys. Rev. A 54, 3519–3534 (1996).
[CrossRef] [PubMed]

J. M. Bilbault, P. Marquie, and B. Michaux, “Modulational instability of two counterpropagating waves in an experimental transmission line,” Phys. Rev. E 51, 817–820 (1995).
[CrossRef]

Bosshard, C.

P. V. Mamyshev, P. G. Wigley, J. Wilson, C. Bosshard, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. 64, 3374–3376 (1994).
[CrossRef]

De Angelis, C.

C. De Angelis, M. Santagiustina, and S. Trillo, “Four-photon homoclinic instabilities in nonlinear highly birefringent media,” Phys. Rev. A 51, 774–791 (1991).
[CrossRef]

Eleonskii, V. M.

N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894–899 (1985).

Feir, J. E.

T. B. Benjamin and J. E. Feir, “The disintegration of wave-trains on deep water. 1. Theory,” J. Fluid Mech. 27, 417–430 (1967).
[CrossRef]

Gindre, D.

Haelterman, M.

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, “Modulational instability and critical regime in a highly birefringent fiber,” Phys. Rev. A 54, 3519–3534 (1996).
[CrossRef] [PubMed]

M. Haelterman, “Modulational instability, periodic waves and black and white vector solitons in birefringent Kerr media,” Opt. Commun. 111, 86–92 (1994).
[CrossRef]

M. Haelterman and A. P. Sheppard, “Polarization domain walls in diffractive or dispersive Kerr media,” Opt. Lett. 19, 96–98 (1994).
[CrossRef] [PubMed]

Hasegawa, A.

A. Hasegawa, “Generation of a train of soliton pulses by induced modulational instability in optical fibers,” Opt. Lett. 9, 288–290 (1994).
[CrossRef]

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef] [PubMed]

Kivshar, Y. S.

Y. S. Kivshar and M. Peyrard, “Modulational instabilities in discrete lattices,” Phys. Rev. A 46, 3198–3205 (1992).
[CrossRef] [PubMed]

Kulagin, N. E.

N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894–899 (1985).

Lantz, E.

Maillotte, H.

Mamyshev, P. V.

P. V. Mamyshev, P. G. Wigley, J. Wilson, C. Bosshard, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. 64, 3374–3376 (1994).
[CrossRef]

Marquie, P.

J. M. Bilbault, P. Marquie, and B. Michaux, “Modulational instability of two counterpropagating waves in an experimental transmission line,” Phys. Rev. E 51, 817–820 (1995).
[CrossRef]

Menyuk, C. R.

Michaux, B.

J. M. Bilbault, P. Marquie, and B. Michaux, “Modulational instability of two counterpropagating waves in an experimental transmission line,” Phys. Rev. E 51, 817–820 (1995).
[CrossRef]

Millot, G.

E. Seve, G. Millot, and S. Wabnitz, “Buildup of terahertz vector dark-soliton trains from induced modulation instability in highly birefringent optical fiber,” Opt. Lett. 23, 1829–1831 (1998).
[CrossRef]

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, “Modulational instability and critical regime in a highly birefringent fiber,” Phys. Rev. A 54, 3519–3534 (1996).
[CrossRef] [PubMed]

Monneret, J.

Peyrard, M.

Y. S. Kivshar and M. Peyrard, “Modulational instabilities in discrete lattices,” Phys. Rev. A 46, 3198–3205 (1992).
[CrossRef] [PubMed]

Remoissenet, M.

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, “Modulational instability and critical regime in a highly birefringent fiber,” Phys. Rev. A 54, 3519–3534 (1996).
[CrossRef] [PubMed]

Santagiustina, M.

C. De Angelis, M. Santagiustina, and S. Trillo, “Four-photon homoclinic instabilities in nonlinear highly birefringent media,” Phys. Rev. A 51, 774–791 (1991).
[CrossRef]

Seve, E.

E. Seve, G. Millot, and S. Wabnitz, “Buildup of terahertz vector dark-soliton trains from induced modulation instability in highly birefringent optical fiber,” Opt. Lett. 23, 1829–1831 (1998).
[CrossRef]

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, “Modulational instability and critical regime in a highly birefringent fiber,” Phys. Rev. A 54, 3519–3534 (1996).
[CrossRef] [PubMed]

Sheppard, A. P.

Stegeman, G. I.

P. V. Mamyshev, P. G. Wigley, J. Wilson, C. Bosshard, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. 64, 3374–3376 (1994).
[CrossRef]

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef] [PubMed]

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structures of light beams in nonlinear liquids,” JETP Lett. 3, 307–309 (1966).

Taniuti, T.

T. Taniuti and H. Washimi, “Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma,” Phys. Rev. Lett. 21, 209–212 (1968).
[CrossRef]

Tchofo-Dinda, P.

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, “Modulational instability and critical regime in a highly birefringent fiber,” Phys. Rev. A 54, 3519–3534 (1996).
[CrossRef] [PubMed]

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef] [PubMed]

Trillo, S.

C. De Angelis, M. Santagiustina, and S. Trillo, “Four-photon homoclinic instabilities in nonlinear highly birefringent media,” Phys. Rev. A 51, 774–791 (1991).
[CrossRef]

Wabnitz, S.

Washimi, H.

T. Taniuti and H. Washimi, “Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma,” Phys. Rev. Lett. 21, 209–212 (1968).
[CrossRef]

Wigley, P. G.

P. V. Mamyshev, P. G. Wigley, J. Wilson, C. Bosshard, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. 64, 3374–3376 (1994).
[CrossRef]

Wilson, J.

P. V. Mamyshev, P. G. Wigley, J. Wilson, C. Bosshard, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. 64, 3374–3376 (1994).
[CrossRef]

Zakharov, V. E.

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–490 (1970).

Appl. Phys. Lett. (1)

P. V. Mamyshev, P. G. Wigley, J. Wilson, C. Bosshard, and G. I. Stegeman, “Restoration of dual-frequency signals with nonlinear propagation in fibers with positive group velocity dispersion,” Appl. Phys. Lett. 64, 3374–3376 (1994).
[CrossRef]

J. Fluid Mech. (1)

T. B. Benjamin and J. E. Feir, “The disintegration of wave-trains on deep water. 1. Theory,” J. Fluid Mech. 27, 417–430 (1967).
[CrossRef]

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

JETP Lett. (1)

V. I. Bespalov and V. I. Talanov, “Filamentary structures of light beams in nonlinear liquids,” JETP Lett. 3, 307–309 (1966).

Opt. Commun. (1)

M. Haelterman, “Modulational instability, periodic waves and black and white vector solitons in birefringent Kerr media,” Opt. Commun. 111, 86–92 (1994).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (3)

C. De Angelis, M. Santagiustina, and S. Trillo, “Four-photon homoclinic instabilities in nonlinear highly birefringent media,” Phys. Rev. A 51, 774–791 (1991).
[CrossRef]

Y. S. Kivshar and M. Peyrard, “Modulational instabilities in discrete lattices,” Phys. Rev. A 46, 3198–3205 (1992).
[CrossRef] [PubMed]

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, “Modulational instability and critical regime in a highly birefringent fiber,” Phys. Rev. A 54, 3519–3534 (1996).
[CrossRef] [PubMed]

Phys. Rev. E (1)

J. M. Bilbault, P. Marquie, and B. Michaux, “Modulational instability of two counterpropagating waves in an experimental transmission line,” Phys. Rev. E 51, 817–820 (1995).
[CrossRef]

Phys. Rev. Lett. (3)

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
[CrossRef] [PubMed]

T. Taniuti and H. Washimi, “Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma,” Phys. Rev. Lett. 21, 209–212 (1968).
[CrossRef]

G. P. Agrawal, “Modulation instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987).
[CrossRef] [PubMed]

Sov. Phys. JETP (2)

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP 31, 486–490 (1970).

N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Generation of periodic trains of picosecond pulses in an optical fiber: exact solutions,” Sov. Phys. JETP 62, 894–899 (1985).

Other (7)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995), Chaps. 5 and 7.

W. Zhao and E. Bourkoff, “Propagation properties of dark solitons,” Opt. Lett. 14, 703–705 (1989); “Interaction between dark solitons,” Opt. Lett. 14, 1371–1373 (1989); J. P. Hamaide, Ph. Emplit, and M. Haelterman, “Dark-soliton jitter in amplified optical transmission systems,” Opt. Lett. OPLEDP 16, 1578–1580 (1991); Y. S. Kivshar, M. Haelterman, Ph. Emplit, and J. P. Hamaide, “Gordon–Haus effect on dark solitons,” Opt. Lett. OPLEDP 19, 19–21 (1994).
[CrossRef] [PubMed]

G. P. Agrawal, “Modulational instability induced by cross-phase modulation,” Phys. Rev. Lett. 59, 880–883 (1987); S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A 38, 2018–2021 (1988); S. Trillo and S. Wabnitz, “Ultrashort pulse train generation through induced modulational polarization instability in a birefringent Kerr-like medium,” J. Opt. Soc. Am. B JOBPDE 6, 238–249 (1989); J. E. Rothenberg, “Modulational instability of copropagating frequencies for normal dispersion,” Phys. Rev. Lett. PRLTAO 64, 813–813 (1990); “Modulational instability for normal dispersion,” Phys. Rev. A PLRAAN 42, 682–685 (1990); P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and D. J. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. OPCOB8 78, 137–142 (1990); G. Millot, S. Pitois, P. Tchofo-Dinda, and M. Haelterman, “Observation of modulational instability induced by velocity-matched cross-phase modulation in a normally dispersive bimodal fiber,” Opt. Lett. OPLEDP 22, 1686–1688 (1997).
[CrossRef] [PubMed]

Y. S. Kivshar and S. K. Turitsyn, “Vector dark solitons,” Opt. Lett. 18, 337–339 (1993); A. P. Sheppard and Y. S. Kivshar, “Polarized dark solitons in isotropic Kerr media,” Phys. Rev. E 55, 4773–4782 (1997).
[CrossRef] [PubMed]

M. Lisak, A. Hook, and D. Anderson, “Symbiotic solitary-wave pairs sustained by cross-phase modulation in optical fibers,” J. Opt. Soc. Am. B 7, 810–814 (1990); Y. S. Kivshar and W. Krolikowski, “Lagrangian approach for dark solitons,” Opt. Commun. 114, 353–362 (1995).
[CrossRef]

S. Trillo and S. Wabnitz, “Nonlinear modulation of coupled waves in birefringent optical fibers,” Phys. Lett. A 159, 252–256 (1991); S. Trillo and S. Wabnitz, “Modulational polarization instabilities and disorder in birefringent optical fibers,” in Nonlinearity with Disorder, F. Abdullaev, A. R. Bishop, and S. Pnevmatikos, eds. (Springer-Verlag, Berlin, 1992), p. 269.
[CrossRef]

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Dark-solitonlike pulse-train generation from induced modulational polarization instability in a birefringent fiber,” Opt. Lett. 23, 511–513 (1998); “Observation of induced modulational polarization instabilities and pulse-train generation in the normal-dispersion regime of a birefringent optical fiber,” J. Opt. Soc. Am. B 15, 1266–1277 (1998).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Theoretical evolution with distance z of the powers in the slow- and fast-polarization components of the field versus time t. The total pump (signal) power is 112 W (2 W), the frequency detuning is 2.5 THz, and the fiber length is 1.8 m.

Fig. 2
Fig. 2

Theoretical time dependence of output powers (solid curves) and phases (dashed curves) of cw dark-soliton trains in the slow (left) and fast (right) fiber axes, and the corresponding output spectra.

Fig. 3
Fig. 3

Schematic diagram of the phase-matching condition of the associated four-wave mixing process. The two components of the pump and each sideband are represented by filled circles and filled triangles, respectively; filled squares give the central frequency of the dark-soliton pulses train on each axis. Below, MI gain versus frequency detuning for three different total pump powers: 112 W (dotted–dashed curves), 56 W (dashed curves), and 10 W (small solid curves).

Fig. 4
Fig. 4

Left, theoretical power spectrum evolution along the fiber slow axis. The fiber length is 3.5 m, and all other parameters are identical to those in Fig. 1. Right, contour plot for a 7-m fiber. The darkness of the gray levels is proportional to the intensity.

Fig. 5
Fig. 5

Experimental setup for observation of induced MI at the University of Dijon: MPC, multiple-pass cell; ODL, optical delay line; DVP, direct vision prism; P’s, Glan polarizers; F’s, neutral-density filters; BS, beam splitters; MO’s, microscope objectives; PM, photomultiplier; L, lens; λ/2’s, half-wave plates.

Fig. 6
Fig. 6

(a), (b) Theoretical pulse averaged and (c), (d) experimental spectra from (top) slow and (bottom) fast axes, with a pump power of 56 W on each axis. The signal pump power is 2 W and the frequency detuning is 2.5 THz.

Fig. 7
Fig. 7

(a), (b) Theoretical and (c), (d) experimental autocorrelation traces from the slow (top) and fast (bottom) fiber axes, with the same input conditions as in Fig. 6.

Fig. 8
Fig. 8

Theoretical time dependence of output powers in the fast and slow fiber axes.

Fig. 9
Fig. 9

Left, theoretical pulse averaged and right, experimental spectra from (top) slow and (bottom) fast axes, with pump and signal powers of 56 and 2 W, respectively, on each axis. The frequency detuning is 2.6 THz.

Fig. 10
Fig. 10

Left, theoretical and right, experimental autocorrelation traces from the slow (top) and fast (bottom) fiber axes, with input conditions as in Fig. 9.

Fig. 11
Fig. 11

Picosecond experimental setup for observation of induced MI at the University of Besancon: OPG, optical parametric generator–amplifier; ODL, optical delay line; P’s, Glan polarizers; λ/2’s, half-wave plates; BS, beam splitter; O1, O2, microscope objectives.

Fig. 12
Fig. 12

(a) Theoretical temporal power profile at the fiber output on the slow (dotted–dashed curve) and fast (solid curve) axes. (b) Theoretical recombined power profile. (c) Corresponding theoretical global spectrum. (d) Experimental global spectrum.

Equations (13)

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Exz+δExτ+12iβ22Exτ2=iγ|Ex|2+23|Ey|2Ex,
Eyz-δEyτ+12iβ22Eyτ2=iγ|Ey|2+23|Ex|2Ey,
M=-δΩ+β2(Ω2/2)+γPxγPxγPxPyγPxPy-γPx-δΩ-β2(Ω2/2)-γPx-γPxPy-γPxPyγPxPyγPxPyδΩ+β2(Ω2/2)+γPyγPy-γPxPy-γPxPy-γPyδΩ-β2(Ω2/2)-γPy,
G(Ω)=2 |Im{ρ+ξ2±[(ρ+ξ2)2+C2-(ρ-ξ2)]1/2}1/2|,
ρ=½β2Ω2(½β2Ω2+γP),
C=Ω2Pγβ2,ξ=Ωδ.
U=Ex expi-δβ2τ+δ22β2z,
V=Ey expiδβ2τ+δ22β2z,
Uz+12iβ22Uτ2=iγ|U|2+23|V|2U,
Vz+12iβ22Vτ2=iγ|V|2+23|U|2V.
U=V=U0 tanh[(5γ/3β2)1/2U0τ]exp(5/3iγU02z).
Ex(z=0, τ)=P/2+Ps exp(2iπfmodτ),
Ey(z=0, τ)=P/2,

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