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

Full Article  |  PDF Article

References

  • View by:
  • |

  1. E. Fermi, J. Pasta, and H. C. Ulam, in Collected Papers of Enrico Fermi, edited by E. Segre (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 Araujo, �??Observation of spatial cross-phase modulation e.ects 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 .lamentation 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 .laments,�?? IEEE J. Quantum Electron. QE-2 467 (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. Commun. 179, 157 (2000).
    [CrossRef]

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. Quantum Electron. (1)

R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith, C. H. Townes, and E. Garmire, �??A new class of trapped light .laments,�?? IEEE J. Quantum Electron. QE-2 467 (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. Commun. (1)

R. Y. Chiao, �??Bogoliubov dispersion relation for a �??photon fluid�??: Is this a superfluid?,�?? Opt. Commun. 179, 157 (2000).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

R. W. Boyd, and G. S. Agarwal, �??Preventing laser beam .lamentation 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 Araujo, �??Observation of spatial cross-phase modulation e.ects 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. Segre (The University of Chicago, Chicago, 1965), vol. 2 pp. 977-988.

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

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.

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)

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

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 .

Metrics