Abstract

We numerically and experimentally show the existence of multicolor vector spatial solitons in a Kerr planar waveguide through the combined effects of cross-phase modulation, four-wave mixing, and stimulated Raman scattering. Mutual spatial guiding of the Raman–Stokes, anti-Stokes, and pump waves is achieved in the high-conversion regime mainly by cross-phase modulation and phase-matched four-wave mixing induced by a power imbalance between Stokes and anti-Stokes components, leading to the generation of a clear-cut sech-shape three-frequency spatial soliton.

© 2006 Optical Society of America

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  1. W. E. Torruellas, L. Torner, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 13, 42 (1995).
  2. G. Assanto and G. I. Stegeman, Opt. Express 10, 388 (2002).
    [PubMed]
  3. D. D. Yaruv, D. R. Walker, and M. Y. Shverdin, Phys. Rev. A 67, 041803(R) (2003).
    [CrossRef]
  4. H. T. Tran, R. A. Sammut, and W. Samir, Opt. Commun. 113, 292 (1994).
    [CrossRef]
  5. Y. Chen and J. Atai, Opt. Lett. 19, 1287 (1994).
    [CrossRef] [PubMed]
  6. P. B. Lundquist, D. R. Andersen, and Y. S. Kivshar, Phys. Rev. E 57, 3551 (1998).
    [CrossRef]
  7. V. Boucher and X. Nguyen-Phu, Appl. Opt. 41, 4390 (2002).
    [CrossRef] [PubMed]
  8. R. W. Boyd, in Nonlinear Optics (Academic, 1992), p. 371.
  9. S. Coen, D. A. Wardle, and J. D. Harvey, Phys. Rev. Lett. 89, 273901 (2002).
    [CrossRef]
  10. Y. R. Shen and N. Bloembergen, Phys. Rev. 137, 1787 (1965).
    [CrossRef]
  11. R. De la Fuente and A. Barthélémy, IEEE J. Quantum Electron. 28, 547 (1992).
    [CrossRef]
  12. J. Reintjes, R. H. Lehmberg, R. S. F. Chang, M. T. Duilgnan, and G. Calame, J. Opt. Soc. Am. B 3, 1408 (1986).
    [CrossRef]

2003 (1)

D. D. Yaruv, D. R. Walker, and M. Y. Shverdin, Phys. Rev. A 67, 041803(R) (2003).
[CrossRef]

2002 (3)

1998 (1)

P. B. Lundquist, D. R. Andersen, and Y. S. Kivshar, Phys. Rev. E 57, 3551 (1998).
[CrossRef]

1995 (1)

W. E. Torruellas, L. Torner, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 13, 42 (1995).

1994 (2)

H. T. Tran, R. A. Sammut, and W. Samir, Opt. Commun. 113, 292 (1994).
[CrossRef]

Y. Chen and J. Atai, Opt. Lett. 19, 1287 (1994).
[CrossRef] [PubMed]

1992 (1)

R. De la Fuente and A. Barthélémy, IEEE J. Quantum Electron. 28, 547 (1992).
[CrossRef]

1986 (1)

1965 (1)

Y. R. Shen and N. Bloembergen, Phys. Rev. 137, 1787 (1965).
[CrossRef]

Andersen, D. R.

P. B. Lundquist, D. R. Andersen, and Y. S. Kivshar, Phys. Rev. E 57, 3551 (1998).
[CrossRef]

Assanto, G.

Atai, J.

Barthélémy, A.

R. De la Fuente and A. Barthélémy, IEEE J. Quantum Electron. 28, 547 (1992).
[CrossRef]

Bloembergen, N.

Y. R. Shen and N. Bloembergen, Phys. Rev. 137, 1787 (1965).
[CrossRef]

Boucher, V.

Boyd, R. W.

R. W. Boyd, in Nonlinear Optics (Academic, 1992), p. 371.

Calame, G.

Chang, R. S. F.

Chen, Y.

Coen, S.

S. Coen, D. A. Wardle, and J. D. Harvey, Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

De la Fuente, R.

R. De la Fuente and A. Barthélémy, IEEE J. Quantum Electron. 28, 547 (1992).
[CrossRef]

Duilgnan, M. T.

Hagan, D. J.

W. E. Torruellas, L. Torner, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 13, 42 (1995).

Harvey, J. D.

S. Coen, D. A. Wardle, and J. D. Harvey, Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

Kivshar, Y. S.

P. B. Lundquist, D. R. Andersen, and Y. S. Kivshar, Phys. Rev. E 57, 3551 (1998).
[CrossRef]

Lehmberg, R. H.

Lundquist, P. B.

P. B. Lundquist, D. R. Andersen, and Y. S. Kivshar, Phys. Rev. E 57, 3551 (1998).
[CrossRef]

Menyuk, C. R.

W. E. Torruellas, L. Torner, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 13, 42 (1995).

Nguyen-Phu, X.

Reintjes, J.

Samir, W.

H. T. Tran, R. A. Sammut, and W. Samir, Opt. Commun. 113, 292 (1994).
[CrossRef]

Sammut, R. A.

H. T. Tran, R. A. Sammut, and W. Samir, Opt. Commun. 113, 292 (1994).
[CrossRef]

Shen, Y. R.

Y. R. Shen and N. Bloembergen, Phys. Rev. 137, 1787 (1965).
[CrossRef]

Shverdin, M. Y.

D. D. Yaruv, D. R. Walker, and M. Y. Shverdin, Phys. Rev. A 67, 041803(R) (2003).
[CrossRef]

Stegeman, G. I.

G. Assanto and G. I. Stegeman, Opt. Express 10, 388 (2002).
[PubMed]

W. E. Torruellas, L. Torner, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 13, 42 (1995).

Torner, L.

W. E. Torruellas, L. Torner, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 13, 42 (1995).

Torruellas, W. E.

W. E. Torruellas, L. Torner, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 13, 42 (1995).

Tran, H. T.

H. T. Tran, R. A. Sammut, and W. Samir, Opt. Commun. 113, 292 (1994).
[CrossRef]

Van Stryland, E. W.

W. E. Torruellas, L. Torner, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 13, 42 (1995).

Walker, D. R.

D. D. Yaruv, D. R. Walker, and M. Y. Shverdin, Phys. Rev. A 67, 041803(R) (2003).
[CrossRef]

Wang, Z.

W. E. Torruellas, L. Torner, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 13, 42 (1995).

Wardle, D. A.

S. Coen, D. A. Wardle, and J. D. Harvey, Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

Yaruv, D. D.

D. D. Yaruv, D. R. Walker, and M. Y. Shverdin, Phys. Rev. A 67, 041803(R) (2003).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

R. De la Fuente and A. Barthélémy, IEEE J. Quantum Electron. 28, 547 (1992).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

H. T. Tran, R. A. Sammut, and W. Samir, Opt. Commun. 113, 292 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. (1)

Y. R. Shen and N. Bloembergen, Phys. Rev. 137, 1787 (1965).
[CrossRef]

Phys. Rev. A (1)

D. D. Yaruv, D. R. Walker, and M. Y. Shverdin, Phys. Rev. A 67, 041803(R) (2003).
[CrossRef]

Phys. Rev. E (1)

P. B. Lundquist, D. R. Andersen, and Y. S. Kivshar, Phys. Rev. E 57, 3551 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

W. E. Torruellas, L. Torner, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, and C. R. Menyuk, Phys. Rev. Lett. 13, 42 (1995).

S. Coen, D. A. Wardle, and J. D. Harvey, Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

Other (1)

R. W. Boyd, in Nonlinear Optics (Academic, 1992), p. 371.

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Figures (5)

Fig. 1
Fig. 1

Numerical simulation of the generation of a three-frequency spatial soliton. Bottom: contour plots of (a) the pump, (b) Stokes, (c) anti-Stokes, and (d) whole beam. Top, transverse beam profiles at the waveguide input (thin solid curve), output (bold solid curve), and after a 2 cm propagation (dashed curve). The parameters are input width = 40 μ m , P sat = 0.02 W m , g r = 23.2 cm MW . P p = 1.6 P s .

Fig. 2
Fig. 2

Evolution along the waveguide of (a) powers and (b) FWHM of the pump (bold dashed curve), Raman–Stokes (bold solid curve), Raman–anti-Stokes (thin dashed curve) components, and total output beam (gray curve).

Fig. 3
Fig. 3

Experimental setup.

Fig. 4
Fig. 4

Experimental (a) output power and (b) FWHM versus input power for the pump ( × ) and the Stokes ( ) waves. Dashed curves, numerical results. The vertical dotted lines indicate the fundamental soliton mean power ( 0.8 mW ) for which scalar soliton behavior has been experimentally observed.

Fig. 5
Fig. 5

Black solid curves, experimental intensity profiles of (a) the output beam in linear regime, (b) the pump, (c) the total, and (d) Stokes output beams in the nonlinear regime. The dashed curves correspond to (a) a Gaussian and (b)–(d) to a sech-shape profile, while the dotted–dashed curve in (a) represents the experimental input profile.

Equations (2)

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E p z = i 2 β p 2 E p x 2 + i γ p [ P p + 2 P + + 2 P ] E p + 2 i γ p E p * E + E e i Δ β z g + P + E p + g P E p ,
E ± z = i 2 β ± 2 E ± x 2 + i γ ± [ P ± + 2 P p + 2 P ] E ± + i γ ± E * E p 2 e i Δ β z ± g ± P p E ± ,

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