Abstract

We identify a new four-wave mixing process in which two nearly collinear pump beams produce phase-dependent gain into a weak bisector signal beam in a self-defocusing Kerr medium. Phase matching is achieved by weak-wave advancement caused by cross-phase modulation between the pump and signal beams. We relate this process to the inverse of spatial modulational instability and suggest a time-domain analog.

© 2002 Optical Society of America

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References

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  1. E. Fermi, J. Pasta, and H. C. Ulam, in Collected Papers of Enrico Fermi, edited by E. Segrè (The University of Chicago, Chicago, 1965), vol. 2 pp. 977–988.
  2. G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).
    [Crossref] [PubMed]
  3. G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B 19, 477 (2002).
    [Crossref]
  4. N. N. Akhmediev, “Nonlinear physics - Deja vu in optics,” Nature 413, 267 (2001).
    [Crossref] [PubMed]
  5. G. P. Agrawal, “Transverse modulation instability of copropagating optical beams in nonlinear Kerr Media,” J. Opt. Soc. Am. B 7, 1072 (1990).
    [Crossref]
  6. J. M. Hickmann, A. S. L. Gomes, and C. B. de Araújo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547 (1992).
    [Crossref] [PubMed]
  7. R. W. Boyd and G. S. Agarwal, “Preventing laser beam filamentation through use of the squeezed vacuum,” Phys. Rev. A 59, R2587 (1999).
    [Crossref]
  8. M. W. Mitchell, C. J. Hancox, and R. Y. Chiao, “Dynamics of atom-mediated photon-photon scattering,” Phys. Rev. A 62, 043819 (2000).
    [Crossref]
  9. R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158(1966).
    [Crossref]
  10. G. P. Agrawal, Nonlinear Fiber Optics, 3rded. (Academic, San Diego, 2001).
  11. R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. of Quant. Elec. QE-2467 (1966).
    [Crossref]
  12. A. J. Campillo, S. L Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628(1973).
    [Crossref]
  13. H. Wang, D. Goorskey, and M. Xiao, “Dependence of enhanced Kerr nonlinearity on coupling power in a three-level atomic system,” Opt. Lett. 27, 258(2002).
    [Crossref]
  14. K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135 (1986).
    [Crossref] [PubMed]
  15. R. Y. Chiao, “Bogoliubov dispersion relation for a ’photon fluid’: Is this a superfluid?,” Opt. Comm. 179, 157 (2000).
    [Crossref]

2002 (2)

2001 (2)

N. N. Akhmediev, “Nonlinear physics - Deja vu in optics,” Nature 413, 267 (2001).
[Crossref] [PubMed]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).
[Crossref] [PubMed]

2000 (2)

M. W. Mitchell, C. J. Hancox, and R. Y. Chiao, “Dynamics of atom-mediated photon-photon scattering,” Phys. Rev. A 62, 043819 (2000).
[Crossref]

R. Y. Chiao, “Bogoliubov dispersion relation for a ’photon fluid’: Is this a superfluid?,” Opt. Comm. 179, 157 (2000).
[Crossref]

1999 (1)

R. W. Boyd and G. S. Agarwal, “Preventing laser beam filamentation through use of the squeezed vacuum,” Phys. Rev. A 59, R2587 (1999).
[Crossref]

1992 (1)

J. M. Hickmann, A. S. L. Gomes, and C. B. de Araújo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547 (1992).
[Crossref] [PubMed]

1990 (1)

1986 (1)

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

1973 (1)

A. J. Campillo, S. L Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628(1973).
[Crossref]

1966 (2)

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158(1966).
[Crossref]

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. of Quant. Elec. QE-2467 (1966).
[Crossref]

Agarwal, G. S.

R. W. Boyd and G. S. Agarwal, “Preventing laser beam filamentation through use of the squeezed vacuum,” Phys. Rev. A 59, R2587 (1999).
[Crossref]

Agrawal, G. P.

Akhmediev, N. N.

N. N. Akhmediev, “Nonlinear physics - Deja vu in optics,” Nature 413, 267 (2001).
[Crossref] [PubMed]

Boyd, R. W.

R. W. Boyd and G. S. Agarwal, “Preventing laser beam filamentation through use of the squeezed vacuum,” Phys. Rev. A 59, R2587 (1999).
[Crossref]

Campillo, A. J.

A. J. Campillo, S. L Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628(1973).
[Crossref]

Chiao, R. Y.

M. W. Mitchell, C. J. Hancox, and R. Y. Chiao, “Dynamics of atom-mediated photon-photon scattering,” Phys. Rev. A 62, 043819 (2000).
[Crossref]

R. Y. Chiao, “Bogoliubov dispersion relation for a ’photon fluid’: Is this a superfluid?,” Opt. Comm. 179, 157 (2000).
[Crossref]

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158(1966).
[Crossref]

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. of Quant. Elec. QE-2467 (1966).
[Crossref]

de Araújo, C. B.

J. M. Hickmann, A. S. L. Gomes, and C. B. de Araújo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547 (1992).
[Crossref] [PubMed]

Emplit, Ph.

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B 19, 477 (2002).
[Crossref]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).
[Crossref] [PubMed]

Fermi, E.

E. Fermi, J. Pasta, and H. C. Ulam, in Collected Papers of Enrico Fermi, edited by E. Segrè (The University of Chicago, Chicago, 1965), vol. 2 pp. 977–988.

Garmire, E.

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. of Quant. Elec. QE-2467 (1966).
[Crossref]

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158(1966).
[Crossref]

Gomes, A. S. L.

J. M. Hickmann, A. S. L. Gomes, and C. B. de Araújo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547 (1992).
[Crossref] [PubMed]

Goorskey, D.

Haelterman, M.

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B 19, 477 (2002).
[Crossref]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).
[Crossref] [PubMed]

Hancox, C. J.

M. W. Mitchell, C. J. Hancox, and R. Y. Chiao, “Dynamics of atom-mediated photon-photon scattering,” Phys. Rev. A 62, 043819 (2000).
[Crossref]

Hasegawa, A.

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

Hickmann, J. M.

J. M. Hickmann, A. S. L. Gomes, and C. B. de Araújo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547 (1992).
[Crossref] [PubMed]

Johnson, M. A.

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. of Quant. Elec. QE-2467 (1966).
[Crossref]

Kelley, P. L.

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158(1966).
[Crossref]

Krinsky, S.

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. of Quant. Elec. QE-2467 (1966).
[Crossref]

Mitchell, M. W.

M. W. Mitchell, C. J. Hancox, and R. Y. Chiao, “Dynamics of atom-mediated photon-photon scattering,” Phys. Rev. A 62, 043819 (2000).
[Crossref]

Pasta, J.

E. Fermi, J. Pasta, and H. C. Ulam, in Collected Papers of Enrico Fermi, edited by E. Segrè (The University of Chicago, Chicago, 1965), vol. 2 pp. 977–988.

Shapiro, S. L

A. J. Campillo, S. L Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628(1973).
[Crossref]

Smith, H. A.

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. of Quant. Elec. QE-2467 (1966).
[Crossref]

Suydam, B. R.

A. J. Campillo, S. L Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628(1973).
[Crossref]

Tai, K.

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

Tomita, A.

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

Townes, C. H.

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. of Quant. Elec. QE-2467 (1966).
[Crossref]

Ulam, H. C.

E. Fermi, J. Pasta, and H. C. Ulam, in Collected Papers of Enrico Fermi, edited by E. Segrè (The University of Chicago, Chicago, 1965), vol. 2 pp. 977–988.

Van Simaeys, G.

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental study of the reversible behavior of modulational instability in optical fibers,” J. Opt. Soc. Am. B 19, 477 (2002).
[Crossref]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).
[Crossref] [PubMed]

Wang, H.

Xiao, M.

Appl. Phys. Lett. (1)

A. J. Campillo, S. L Shapiro, and B. R. Suydam, “Periodic breakup of optical beams due to self-focusing,” Appl. Phys. Lett. 23, 628(1973).
[Crossref]

IEEE J. of Quant. Elec. (1)

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, “A new class of trapped light filaments,” IEEE J. of Quant. Elec. QE-2467 (1966).
[Crossref]

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

Nature (1)

N. N. Akhmediev, “Nonlinear physics - Deja vu in optics,” Nature 413, 267 (2001).
[Crossref] [PubMed]

Opt. Comm. (1)

R. Y. Chiao, “Bogoliubov dispersion relation for a ’photon fluid’: Is this a superfluid?,” Opt. Comm. 179, 157 (2000).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (2)

R. W. Boyd and G. S. Agarwal, “Preventing laser beam filamentation through use of the squeezed vacuum,” Phys. Rev. A 59, R2587 (1999).
[Crossref]

M. W. Mitchell, C. J. Hancox, and R. Y. Chiao, “Dynamics of atom-mediated photon-photon scattering,” Phys. Rev. A 62, 043819 (2000).
[Crossref]

Phys. Rev. Lett. (4)

R. Y. Chiao, P. L. Kelley, and E. Garmire, “Stimulated four-photon interaction and its influence on stimulated Rayleigh-wing scattering,” Phys. Rev. Lett. 17, 1158(1966).
[Crossref]

G. Van Simaeys, Ph. Emplit, and M. Haelterman, “Experimental demonstration of the Fermi-Pasta-Ulam recurrence in a modulationally unstable optical wave,” Phys. Rev. Lett. 87, 033902 (2001).
[Crossref] [PubMed]

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

J. M. Hickmann, A. S. L. Gomes, and C. B. de Araújo, “Observation of spatial cross-phase modulation effects in a self-defocusing nonlinear medium,” Phys. Rev. Lett. 68, 3547 (1992).
[Crossref] [PubMed]

Other (2)

E. Fermi, J. Pasta, and H. C. Ulam, in Collected Papers of Enrico Fermi, edited by E. Segrè (The University of Chicago, Chicago, 1965), vol. 2 pp. 977–988.

G. P. Agrawal, Nonlinear Fiber Optics, 3rded. (Academic, San Diego, 2001).

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Figures (3)

Fig. 1.
Fig. 1.

Wave vector configuration for weak-wave advancement.

Fig. 2.
Fig. 2.

Signal beam gain as a function of collision half-angle α for λ = 700nm. Note that Δk = 2|k⁽ 1|(1 - cos α).

Fig. 3.
Fig. 3.

Logarithm of signal beam amplitude as a function of propagation distance.

Equations (9)

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P 4 = 3 χ xxxx ( 3 ) { E 4 2 E 4 + 2 ( E 1 2 + E 2 2 + E 3 2 ) E 4
+ E 1 E 2 E 4 * exp ( i ( k 1 + k 2 k 3 k 4 ) · z i ( ω 1 + ω 2 ω 3 ω 4 ) t ) }
Δ n = 3 4 n 0 Re [ χ xxxx ( 3 ) ] ( E 1 2 + E 2 2 )
E 4 z = i 4 γ P ( E 4 + 0.5 E 4 * e i ( 6 γ P Δ k ) z e i ( ϕ 1 + ϕ 2 ) )
E 4 = Ae gz e i ( 3 γ P Δ k 2 ) z e i ϕ 4
0 Δ k 6 γP
g = 3 ( γP ) 2 ( γP ) Δ k 0.25 ( Δ k ) 2 .
Δϕ ϕ 1 + ϕ 2 2 ϕ 4 = π 2
γP k Δ k 6 k = 1 3 ( 1 cos α ) 5 × 10 5 .

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