Abstract

Strong frequency conversion among light waves propagating in a low-birefringence optical fiber in the normal-dispersion regime is experimentally investigated. Modulational gain spectra are obtained by injection of a signal orthogonally polarized with respect to a pump beam aligned with the slow fiber axis. Measurements reveal that, for signal power levels above a certain threshold value, peak conversion is obtained at pump signal frequency detunings far from the phase-matching condition. The large-signal three-wave mixing regime is well described by integrable nonlinear coupled-wave equations.

© 1998 Optical Society of America

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  1. See, e.g., G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).
  2. A. A. Vedenov and L. I. Rudakov, Dok. Akad. Nauk SSSR 159, 767 (1964) [Sov. Phys. Dokl. 9, 1073 (1965)].
  3. L. A. Ostroskii, Zh. Eksp. Teor. Fiz. 51, 1189 (1966) [Sov. Phys. JETP 24, 797 (1967).]
  4. V. I. Bespalov and V. I. Talanov, Pis’ma Zh. Eksp. Teor. Fiz. 3, 471 (1966) [JETP Lett. 3, 307 (1966)].
  5. V. I. Karpman, JETP Lett. 6, 277 (1967).
  6. T. J. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
    [CrossRef]
  7. A. Hasegawa, Opt. Lett. 9, 288 (1984).
    [CrossRef] [PubMed]
  8. K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
    [CrossRef]
  9. A. L. Berkhoer and V. E. Zakharov, Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970).]
  10. S. Wabnitz, Phys. Rev. A 38, 2018 (1988).
    [CrossRef] [PubMed]
  11. G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987). Note that reducing the coupling of two frequencies to a set of just two incoherently coupled NLS equations involves the approximation of neglecting all four-wave mixing products; see J. E. Rothenberg, Phys. Rev. Lett. 64, 813 (1987); S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A PLRAAN 50, 1732 (1994).
    [CrossRef] [PubMed]
  12. R. H. Stolen, M. A. Bosch, and C. Lin, Opt. Lett. 6, 213 (1981).
    [CrossRef] [PubMed]
  13. P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, Opt. Commun. 78, 137 (1990).
    [CrossRef]
  14. J. E. Rothenberg, Phys. Rev. A 42, 682 (1990).
    [CrossRef] [PubMed]
  15. S. Trillo and S. Wabnitz, J. Opt. Soc. Am. B 9, 1061 (1992).
    [CrossRef]
  16. E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
    [CrossRef] [PubMed]
  17. E. Lantz, D. Gindre, H. Maillotte, and J. Monneret, J. Opt. Soc. Am. B 14, 116 (1997).
    [CrossRef]
  18. S. Trillo and S. Wabnitz, J. Opt. Soc. Am. B 6, 238 (1989).
    [CrossRef]
  19. B. Daino, G. Gregori, and S. Wabnitz, J. Appl. Phys. 58, 4512 (1985); Opt. Lett. 11, 42 (1986).
    [CrossRef]
  20. H. G. Winful, Opt. Lett. 11, 33 (1986).
    [CrossRef]
  21. S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986).
    [CrossRef]
  22. S. F. Feldman, D. A. Weinberger, and H. G. Winful, Opt. Lett. 15, 311 (1990); J. Opt. Soc. Am. B 10, 1191 (1993).
    [CrossRef]
  23. S. G. Murdoch, R. Leonhardt, and J. D. Harvey, Opt. Lett. 20, 866 (1995).
    [CrossRef] [PubMed]
  24. R. Leonhardt, S. G. Murdoch, and J. D. Harvey, Opt. Commun. 130, 25 (1996).
    [CrossRef]
  25. T. A. B. Kennedy and S. Wabnitz, Phys. Rev. A 38, 563 (1988).
    [CrossRef] [PubMed]
  26. G. Millot, E. Seve, and S. Wabnitz, Phys. Rev. Lett. 79, 661 (1997).
    [CrossRef]
  27. G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, J. Opt. Soc. Am. B 15, 1266 (1998).
    [CrossRef]
  28. S. Trillo and S. Wabnitz, Phys. Rev. E 55, R4897 (1997); Phys. Rev. E 56, 1048 (1997).
    [CrossRef]
  29. S. G. Murdoch, M. D. Thomson, R. Leonhardt, and J. D. Harvey, Opt. Lett. 22, 682 (1997).
    [CrossRef] [PubMed]
  30. S. G. Murdoch, M. D. Thomson, R. Leonhardt, J. D. Harvey, and T. B. Kennedy, J. Opt. Soc. Am. B 14, 1816 (1997).
    [CrossRef]
  31. R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. 7, 512 (1982).
  32. G. Cappellini and S. Trillo, Opt. Lett. 16, 895 (1991); Phys. Rev. A 44, 7509 (1991); S. Trillo and S. Wabnitz, Phys. Lett. A PYLAAG 159, 252 (1991).
    [CrossRef] [PubMed]
  33. G. Millot, E. Seve, S. Wabnitz, and S. Trillo, in Quantum Electronics and Laser Science Conference, Vol. 12 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper QPD14; Phys. Rev. Lett. 80, 504 (1998).
    [CrossRef]
  34. S. G. Murdoch, R. Leonhardt, and J. D. Harvey, J. Opt. Soc. Am. B 14, 3403 (1997).
    [CrossRef]
  35. E. Infeld, Phys. Rev. Lett. 47, 717 (1981).
    [CrossRef]
  36. G. Cappellini and S. Trillo, J. Opt. Soc. Am. B 8, 824 (1991).
    [CrossRef]
  37. S. Trillo and S. Wabnitz, Opt. Lett. 16, 986 (1991).
    [CrossRef] [PubMed]
  38. C. De Angelis, M. Santagiustina, and S. Trillo, Opt. Lett. 19, 335 (1994); Phys. Rev. A 51, 774 (1995).
    [CrossRef] [PubMed]
  39. P. S. Pershan, Phys. Rev. 130, 919 (1963).
    [CrossRef]
  40. For a review see S. Trillo and S. Wabnitz, in Guided Wave Nonlinear Optics, R. Reinish and D. Ostrowski, eds., NATO ASI Series E214 (Kluwer Academic, Dordrecht, The Netherlands, 1992), pp. 489–534.
  41. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  42. M. J. Ablowitz and B. M. Herbst, Phys. Rev. Lett. 62, 2065 (1989).
    [CrossRef]

1998 (1)

1997 (5)

1996 (2)

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

R. Leonhardt, S. G. Murdoch, and J. D. Harvey, Opt. Commun. 130, 25 (1996).
[CrossRef]

1995 (1)

1992 (2)

For a review see S. Trillo and S. Wabnitz, in Guided Wave Nonlinear Optics, R. Reinish and D. Ostrowski, eds., NATO ASI Series E214 (Kluwer Academic, Dordrecht, The Netherlands, 1992), pp. 489–534.

S. Trillo and S. Wabnitz, J. Opt. Soc. Am. B 9, 1061 (1992).
[CrossRef]

1991 (2)

1990 (2)

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, Opt. Commun. 78, 137 (1990).
[CrossRef]

J. E. Rothenberg, Phys. Rev. A 42, 682 (1990).
[CrossRef] [PubMed]

1989 (2)

M. J. Ablowitz and B. M. Herbst, Phys. Rev. Lett. 62, 2065 (1989).
[CrossRef]

S. Trillo and S. Wabnitz, J. Opt. Soc. Am. B 6, 238 (1989).
[CrossRef]

1988 (2)

T. A. B. Kennedy and S. Wabnitz, Phys. Rev. A 38, 563 (1988).
[CrossRef] [PubMed]

S. Wabnitz, Phys. Rev. A 38, 2018 (1988).
[CrossRef] [PubMed]

1986 (3)

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986).
[CrossRef]

H. G. Winful, Opt. Lett. 11, 33 (1986).
[CrossRef]

1984 (1)

1982 (1)

R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. 7, 512 (1982).

1981 (2)

1970 (1)

A. L. Berkhoer and V. E. Zakharov, Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970).]

1967 (3)

L. A. Ostroskii, Zh. Eksp. Teor. Fiz. 51, 1189 (1966) [Sov. Phys. JETP 24, 797 (1967).]

V. I. Karpman, JETP Lett. 6, 277 (1967).

T. J. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

1966 (1)

V. I. Bespalov and V. I. Talanov, Pis’ma Zh. Eksp. Teor. Fiz. 3, 471 (1966) [JETP Lett. 3, 307 (1966)].

1965 (1)

A. A. Vedenov and L. I. Rudakov, Dok. Akad. Nauk SSSR 159, 767 (1964) [Sov. Phys. Dokl. 9, 1073 (1965)].

1963 (1)

P. S. Pershan, Phys. Rev. 130, 919 (1963).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz and B. M. Herbst, Phys. Rev. Lett. 62, 2065 (1989).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Assanto, G.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986).
[CrossRef]

Benjamin, T. J.

T. J. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Berkhoer, A. L.

A. L. Berkhoer and V. E. Zakharov, Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970).]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, Pis’ma Zh. Eksp. Teor. Fiz. 3, 471 (1966) [JETP Lett. 3, 307 (1966)].

Bilbault, J. M.

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. 7, 512 (1982).

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Bosch, M. A.

Cappellini, G.

Drummond, P. D.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, Opt. Commun. 78, 137 (1990).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Dudley, J. M.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, Opt. Commun. 78, 137 (1990).
[CrossRef]

Feir, J. E.

T. J. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Gindre, D.

Haelterman, M.

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, J. Opt. Soc. Am. B 15, 1266 (1998).
[CrossRef]

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

Harvey, J. D.

Hasegawa, A.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

A. Hasegawa, Opt. Lett. 9, 288 (1984).
[CrossRef] [PubMed]

Herbst, B. M.

M. J. Ablowitz and B. M. Herbst, Phys. Rev. Lett. 62, 2065 (1989).
[CrossRef]

Infeld, E.

E. Infeld, Phys. Rev. Lett. 47, 717 (1981).
[CrossRef]

Jewell, J. L.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Karpman, V. I.

V. I. Karpman, JETP Lett. 6, 277 (1967).

Kennedy, T. A. B.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, Opt. Commun. 78, 137 (1990).
[CrossRef]

T. A. B. Kennedy and S. Wabnitz, Phys. Rev. A 38, 563 (1988).
[CrossRef] [PubMed]

Kennedy, T. B.

Lantz, E.

Leonhardt, R.

Lin, C.

Maillotte, H.

Millot, G.

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, J. Opt. Soc. Am. B 15, 1266 (1998).
[CrossRef]

G. Millot, E. Seve, and S. Wabnitz, Phys. Rev. Lett. 79, 661 (1997).
[CrossRef]

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

Monneret, J.

Murdoch, S. G.

Ostroskii, L. A.

L. A. Ostroskii, Zh. Eksp. Teor. Fiz. 51, 1189 (1966) [Sov. Phys. JETP 24, 797 (1967).]

Pershan, P. S.

P. S. Pershan, Phys. Rev. 130, 919 (1963).
[CrossRef]

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Remoissenet, M.

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

Rothenberg, J. E.

J. E. Rothenberg, Phys. Rev. A 42, 682 (1990).
[CrossRef] [PubMed]

Rudakov, L. I.

A. A. Vedenov and L. I. Rudakov, Dok. Akad. Nauk SSSR 159, 767 (1964) [Sov. Phys. Dokl. 9, 1073 (1965)].

Seaton, C. T.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986).
[CrossRef]

Seve, E.

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, J. Opt. Soc. Am. B 15, 1266 (1998).
[CrossRef]

G. Millot, E. Seve, and S. Wabnitz, Phys. Rev. Lett. 79, 661 (1997).
[CrossRef]

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

Stegeman, G. I.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986).
[CrossRef]

Stolen, R. H.

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986).
[CrossRef]

R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. 7, 512 (1982).

R. H. Stolen, M. A. Bosch, and C. Lin, Opt. Lett. 6, 213 (1981).
[CrossRef] [PubMed]

Tai, K.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, Pis’ma Zh. Eksp. Teor. Fiz. 3, 471 (1966) [JETP Lett. 3, 307 (1966)].

Tchofo-Dinda, P.

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

Thomson, M. D.

Tomita, A.

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

Trillo, S.

For a review see S. Trillo and S. Wabnitz, in Guided Wave Nonlinear Optics, R. Reinish and D. Ostrowski, eds., NATO ASI Series E214 (Kluwer Academic, Dordrecht, The Netherlands, 1992), pp. 489–534.

S. Trillo and S. Wabnitz, J. Opt. Soc. Am. B 9, 1061 (1992).
[CrossRef]

G. Cappellini and S. Trillo, J. Opt. Soc. Am. B 8, 824 (1991).
[CrossRef]

S. Trillo and S. Wabnitz, Opt. Lett. 16, 986 (1991).
[CrossRef] [PubMed]

S. Trillo and S. Wabnitz, J. Opt. Soc. Am. B 6, 238 (1989).
[CrossRef]

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986).
[CrossRef]

Vedenov, A. A.

A. A. Vedenov and L. I. Rudakov, Dok. Akad. Nauk SSSR 159, 767 (1964) [Sov. Phys. Dokl. 9, 1073 (1965)].

Wabnitz, S.

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, J. Opt. Soc. Am. B 15, 1266 (1998).
[CrossRef]

G. Millot, E. Seve, and S. Wabnitz, Phys. Rev. Lett. 79, 661 (1997).
[CrossRef]

For a review see S. Trillo and S. Wabnitz, in Guided Wave Nonlinear Optics, R. Reinish and D. Ostrowski, eds., NATO ASI Series E214 (Kluwer Academic, Dordrecht, The Netherlands, 1992), pp. 489–534.

S. Trillo and S. Wabnitz, J. Opt. Soc. Am. B 9, 1061 (1992).
[CrossRef]

S. Trillo and S. Wabnitz, Opt. Lett. 16, 986 (1991).
[CrossRef] [PubMed]

S. Trillo and S. Wabnitz, J. Opt. Soc. Am. B 6, 238 (1989).
[CrossRef]

T. A. B. Kennedy and S. Wabnitz, Phys. Rev. A 38, 563 (1988).
[CrossRef] [PubMed]

S. Wabnitz, Phys. Rev. A 38, 2018 (1988).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986).
[CrossRef]

Winful, H. G.

Zakharov, V. E.

A. L. Berkhoer and V. E. Zakharov, Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970).]

Appl. Phys. Lett. (2)

K. Tai, A. Tomita, J. L. Jewell, and A. Hasegawa, Appl. Phys. Lett. 49, 236 (1986).
[CrossRef]

S. Trillo, S. Wabnitz, R. H. Stolen, G. Assanto, C. T. Seaton, and G. I. Stegeman, Appl. Phys. Lett. 49, 1224 (1986).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. 7, 512 (1982).

J. Fluid Mech. (1)

T. J. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

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

JETP Lett. (2)

V. I. Bespalov and V. I. Talanov, Pis’ma Zh. Eksp. Teor. Fiz. 3, 471 (1966) [JETP Lett. 3, 307 (1966)].

V. I. Karpman, JETP Lett. 6, 277 (1967).

NATO ASI Series (1)

For a review see S. Trillo and S. Wabnitz, in Guided Wave Nonlinear Optics, R. Reinish and D. Ostrowski, eds., NATO ASI Series E214 (Kluwer Academic, Dordrecht, The Netherlands, 1992), pp. 489–534.

Opt. Commun. (2)

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, Opt. Commun. 78, 137 (1990).
[CrossRef]

R. Leonhardt, S. G. Murdoch, and J. D. Harvey, Opt. Commun. 130, 25 (1996).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. (2)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

P. S. Pershan, Phys. Rev. 130, 919 (1963).
[CrossRef]

Phys. Rev. A (4)

T. A. B. Kennedy and S. Wabnitz, Phys. Rev. A 38, 563 (1988).
[CrossRef] [PubMed]

J. E. Rothenberg, Phys. Rev. A 42, 682 (1990).
[CrossRef] [PubMed]

E. Seve, P. Tchofo-Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

S. Wabnitz, Phys. Rev. A 38, 2018 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

G. Millot, E. Seve, and S. Wabnitz, Phys. Rev. Lett. 79, 661 (1997).
[CrossRef]

M. J. Ablowitz and B. M. Herbst, Phys. Rev. Lett. 62, 2065 (1989).
[CrossRef]

E. Infeld, Phys. Rev. Lett. 47, 717 (1981).
[CrossRef]

Sov. Phys. Dokl. (1)

A. A. Vedenov and L. I. Rudakov, Dok. Akad. Nauk SSSR 159, 767 (1964) [Sov. Phys. Dokl. 9, 1073 (1965)].

Sov. Phys. JETP (2)

L. A. Ostroskii, Zh. Eksp. Teor. Fiz. 51, 1189 (1966) [Sov. Phys. JETP 24, 797 (1967).]

A. L. Berkhoer and V. E. Zakharov, Zh. Eksp. Teor. Fiz. 58, 903 (1970) [Sov. Phys. JETP 31, 486 (1970).]

Other (8)

See, e.g., G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

G. P. Agrawal, Phys. Rev. Lett. 59, 880 (1987). Note that reducing the coupling of two frequencies to a set of just two incoherently coupled NLS equations involves the approximation of neglecting all four-wave mixing products; see J. E. Rothenberg, Phys. Rev. Lett. 64, 813 (1987); S. Trillo, S. Wabnitz, and T. A. B. Kennedy, Phys. Rev. A PLRAAN 50, 1732 (1994).
[CrossRef] [PubMed]

S. F. Feldman, D. A. Weinberger, and H. G. Winful, Opt. Lett. 15, 311 (1990); J. Opt. Soc. Am. B 10, 1191 (1993).
[CrossRef]

B. Daino, G. Gregori, and S. Wabnitz, J. Appl. Phys. 58, 4512 (1985); Opt. Lett. 11, 42 (1986).
[CrossRef]

S. Trillo and S. Wabnitz, Phys. Rev. E 55, R4897 (1997); Phys. Rev. E 56, 1048 (1997).
[CrossRef]

G. Cappellini and S. Trillo, Opt. Lett. 16, 895 (1991); Phys. Rev. A 44, 7509 (1991); S. Trillo and S. Wabnitz, Phys. Lett. A PYLAAG 159, 252 (1991).
[CrossRef] [PubMed]

G. Millot, E. Seve, S. Wabnitz, and S. Trillo, in Quantum Electronics and Laser Science Conference, Vol. 12 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper QPD14; Phys. Rev. Lett. 80, 504 (1998).
[CrossRef]

C. De Angelis, M. Santagiustina, and S. Trillo, Opt. Lett. 19, 335 (1994); Phys. Rev. A 51, 774 (1995).
[CrossRef] [PubMed]

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Figures (16)

Fig. 1
Fig. 1

Solid (dashed) curves, small-signal MPI gain spectra with a pump on the fast (slow) fiber axis and input power (a) pPp/Pt=0.5, (b) p=1.5, and (c) p=2.5.

Fig. 2
Fig. 2

(a) Solid (dashed) curves, fractional pump power ηe of the spatially stable (unstable) eigenmodulations versus the mismatch κ0 for a signal power level α=5%, (b) dependence of signal power threshold α on mismatch κ0.

Fig. 3
Fig. 3

Three-wave mixing phase-plane trajectories. Solid curve, signal frequency detuning f=0.96 THz; dashed curve, f=0.9 THz; dotted–dashed curve, f=1.2 THz.

Fig. 4
Fig. 4

(a) Idler energy fraction versus signal frequency detuning and fiber length, (b) contour plot.

Fig. 5
Fig. 5

Idler energy fraction versus signal frequency detuning as in Fig. (4), at the fiber length L=6.8 m: (a) cw case; (b) pulsed case.

Fig. 6
Fig. 6

Signal power level threshold effect for the frequency-conversion efficiency at a signal detuning f=0.83 THz. Dashed curve, α=1% (low conversion); solid curve, α=1.5% (separatrix); dotted–dashed curve, α=2% (high conversion). The dashed curve inside the small loop corresponds to the same Hamiltonian level of the low-conversion trajectory.

Fig. 7
Fig. 7

Spectrum evolution of the linearly polarized components as ruled by the vector NLS [Eqs. (11) and (12)]. Here the normalized distance ζ=z/Lb, the input signal fraction α=0.01, the normalized frequency Ωb=3.41, and the power p=1.

Fig. 8
Fig. 8

Same as in Fig. 7, but for Ωb=3.43.

Fig. 9
Fig. 9

Same as in Fig. 7, but for α=0.02.

Fig. 10
Fig. 10

Schematic diagram of the experimental apparatus. MO’s, microscope objectives.

Fig. 11
Fig. 11

Experimental spectra at the fiber output for Pp=160 W: (a) spontaneous MPI (α=0); (b), (c), induced MPI with (b) α=5% and signal detuning f=1.35 THz or (c) α=5% and f=0.9 THz.

Fig. 12
Fig. 12

Output experimental spectra for the peak pump power of 160 W and the pump signal detunings (in THz) (a) f=0.6, (b) f=0.825, (c) f=0.9, (d) f=1.047, (e) f=1.2, (f) f=1.352.

Fig. 13
Fig. 13

Measured (symbols) and theoretical (solid curve) idler energy conversion versus pump signal detuning with pulsed waves for Pp=160 W and α=5%. Dashed curve, small-signal MPI gain bandwidth.

Fig. 14
Fig. 14

Measured (symbols) idler energy conversion versus pump signal frequency detuning with α=0.5%. Solid (dashed) curve, theoretical prediction for cw (pulsed) beams; dotted–dashed curve, small-signal MPI gain spectrum.

Fig. 15
Fig. 15

Experimental (left) and theoretical (right) output idler energy versus input signal fraction α for a set of pump signal detunings (in THz): (a), (b), f=0.83; (c), (d) f=1.055; (e), (f), f=1.43.

Fig. 16
Fig. 16

Output pump pulse profile with Pp=160 W and α=5%: (a) theory, (b) experiment.

Equations (30)

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Exz+δ2 Ext+i β22 2Ext2=iγ[(|Ex|2+23|Ey|2)Ex+13Ex*Ey2 exp(2iΔβz)],
Eyz-δ2 Eyt+i β22 2Eyt2=iγ[(|Ey|2+23|Ex|2)Ey+13Ey*Ex2 exp(-2iΔβz)],
-i Epz=HEp*=βpEp+γp|Ep|2+23 (|Es|2+|Ea|2)Ep+2γp3 EsEaEp*,
-i Esz=HEs*=βsEs+γs|Es|2+2|Ea|2+23 |Ep|2Es+γs3 Ea*Ep2,
-i Eaz=HEa*=βaEa+γa|Ea|2+2|Es|2+23 |Ep|2Es+γa3 Es*Ep2,
H=j=p,s,aβj|Ej|2+γj,k=p,s,adjk|Ej|2|Ek|2+γ3 Ea*Es*Ep2+c.c.,
H=j=p,s,aβj|Aj|2+γ¯j,k=p,s,adjkωjωk|Aj|2|Ak|2+γ¯3 ωp2ωaωsAa*As*Ap2+c.c.
dηdξ=Hrϕ=-2η[(1-η)2-α2]1/2 sin ϕ,
dϕdξ=-Hrη=(κ+5)-7η-2 1+2η2-3η-α2[(1-η)2-α2]1/2 cos ϕ,
Hr=2η[(1-η)2-α2]1/2 cos ϕ-(κ+5)η+72η2,
ξ=z/Lnl,κ=ΔkLnl,α=|Ea|2-|Es|2Ptot.
η0=1-α-2.
fd=12π 2|Δβ|β2.
i uxζ-12 2uxτ2+πux+3πp|ux|2+23 |uy|2ux+13 uy2ux*=0,
i uyζ-12 2uyτ2-πuy+3πp|uy|2+23 |ux|2uy+13 ux2uy*=0.
i uk,±ζ-12 2uk,±τ2+πuk,+2πp(|uk,±|2
+2|uk,|2)uk,±=0,k=1,, N.
2ηe[(1-ηe)2-α2]1/2cos ϕe-[κ0(1-α)+5]ηe+72ηe2He(ηe, α, κ)=-[κ0(1-α)+5](1-α)+72(1-α)2H0(η0=1-α, α, κ),
ηe=1α=0(κ0=κ)ϕe=cos-1κ02-1for0<κ0<4,
ηe=0α=κ0+32κ0-72ϕe=cos-1κ0(1-α)+521-α2for-<κ0<-21332.
p(x)=(33κ04-693κ03+3399κ02-7623κ0+1089)x4+(-66κ04+1947κ03-13266κ02+40887κ0-16632)x3+(-16κ04-654κ03+11885κ02-65667κ0+39447)x2+(-320κ03-854κ02+41853κ0-34554)x-1600κ02-9050κ0+10650,
α=q(ηe, κ0)r(ηe, κ0),
q(ηe, κ0)=(-132κ02+1155κ0-1353)ηe3+(28κ03-84κ02-2882κ0+4293)ηe2+(-28κ03+484κ02+2171κ0-4527)ηe-268κ02-444κ0+1587,
r(ηe, κ0)=(28κ03-390κ02+805κ0-1353)ηe2+(-28κ03+560κ02-893κ0+2016)ηe-268κ02+256κ0-863.
H=j=p1,p2,s,aβj|Aj|2+γ¯j,k=p1,p2,s,adjkωjωk|Aj|2|Ak|2+2γ¯dω2Aa*As*Ap1Ap2+c.c.,
dηdξ=Hrϕ,dϕdξ=-Hrη,
Hr(η, ϕ)=2{η(η-α2)[(1-2η+α2)2-α12]}1/2×cos ϕ-(κ+a)η+(b/2)η2,
Hr(η, ϕ)=2η(1-η)2-α12 cos ϕ-(κ+a)η+(b/4)η2,
κ=β2(2πf)2-δ2πfγP0=-1.
αc=12 1+3κ5-15 5-9κ2

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