Abstract

We study composite spatial optical solitons supported by two-wave mutual focusing induced by cross-phase modulation in Kerr-like nonlinear media. We find the families of both single- and two-hump solitons and discuss their properties and stability. We also reveal remarkable similarities between recently predicted holographic solitons in photorefractive media and parametric solitons in quadratic nonlinear crystals.

© 2003 Optical Society of America

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References

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  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).
  2. M. Vaupel, C. Seror, and R. Dykstra, Opt. Lett. 22, 1470 (1997).
    [CrossRef]
  3. O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 27, 2031 (2002).
    [CrossRef]
  4. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 53 (1988).
    [CrossRef] [PubMed]
  5. M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Lett. 18, 1406 (1993).
    [CrossRef] [PubMed]
  6. Yu. N. Karamzin and A. P. Sukhorukov, Zh. Eksp. Teor. Fiz. 68, 834 (1975) JETP 41, 414 (1975).
  7. D. E. Pelinovsky and Yu. S. Kivshar, Phys. Rev. E 62, 8668 (2000).
    [CrossRef]
  8. A. C. Yew, A. R. Champneys, and P. J. McKenna, J. Nonlin. Sci. 9, 33 (1999).
    [CrossRef]
  9. A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
    [CrossRef]

2003 (1)

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

2002 (2)

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, Opt. Lett. 27, 2031 (2002).
[CrossRef]

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[CrossRef]

2000 (1)

D. E. Pelinovsky and Yu. S. Kivshar, Phys. Rev. E 62, 8668 (2000).
[CrossRef]

1999 (1)

A. C. Yew, A. R. Champneys, and P. J. McKenna, J. Nonlin. Sci. 9, 33 (1999).
[CrossRef]

1997 (1)

1993 (1)

1988 (1)

Agrawal, G. P.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

Buryak, A. V.

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[CrossRef]

Carmon, T.

Champneys, A. R.

A. C. Yew, A. R. Champneys, and P. J. McKenna, J. Nonlin. Sci. 9, 33 (1999).
[CrossRef]

Christodoulides, D. N.

Cohen, O.

Di Trapani, P.

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[CrossRef]

Dykstra, R.

Haelterman, M.

Joseph, R. I.

Karamzin, Yu. N.

Yu. N. Karamzin and A. P. Sukhorukov, Zh. Eksp. Teor. Fiz. 68, 834 (1975) JETP 41, 414 (1975).

Kivshar, Yu. S.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

D. E. Pelinovsky and Yu. S. Kivshar, Phys. Rev. E 62, 8668 (2000).
[CrossRef]

McKenna, P. J.

A. C. Yew, A. R. Champneys, and P. J. McKenna, J. Nonlin. Sci. 9, 33 (1999).
[CrossRef]

Odoulov, S.

Pelinovsky, D. E.

D. E. Pelinovsky and Yu. S. Kivshar, Phys. Rev. E 62, 8668 (2000).
[CrossRef]

Segev, M.

Seror, C.

Sheppard, A. P.

Skryabin, D. V.

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[CrossRef]

Snyder, A. W.

Sukhorukov, A. P.

Yu. N. Karamzin and A. P. Sukhorukov, Zh. Eksp. Teor. Fiz. 68, 834 (1975) JETP 41, 414 (1975).

Trillo, S.

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[CrossRef]

Vaupel, M.

Yew, A. C.

A. C. Yew, A. R. Champneys, and P. J. McKenna, J. Nonlin. Sci. 9, 33 (1999).
[CrossRef]

J. Nonlin. Sci. (1)

A. C. Yew, A. R. Champneys, and P. J. McKenna, J. Nonlin. Sci. 9, 33 (1999).
[CrossRef]

Opt. Lett. (4)

Phys. Rep. (1)

A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).
[CrossRef]

Phys. Rev. E (1)

D. E. Pelinovsky and Yu. S. Kivshar, Phys. Rev. E 62, 8668 (2000).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

Yu. N. Karamzin and A. P. Sukhorukov, Zh. Eksp. Teor. Fiz. 68, 834 (1975) JETP 41, 414 (1975).

Other (1)

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003).

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Figures (3)

Fig. 1
Fig. 1

Top, powers P1 and P2 of the soliton components as functions of soliton parameter α2 at fixed α1=0.1. Inset, domain of existence on the parameter plane; solid line α1=α2 corresponds to the previously discussed solitons.3 The thin horizontal line indicates the bistable solutions. Bottom, examples A–C of two-component single-hump solitons supported by mutual focusing. Solid and dashed curves, the fields v and u, respectively.

Fig. 2
Fig. 2

Examples of two-component two-hump solitons supported by mutual focusing for four values of α2 as indicated and for fixed α1=0.5.

Fig. 3
Fig. 3

Collision of two in-phase vector solitons in (a) high- (α1=0.39, α2=0.59) and (b) low- (α1=0.039, α2=0.059) saturation regimes.

Equations (3)

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

iuz+2ux2+v2u1+u2+v2=0, ivz+2vx2+u2v1+u2+v2=0,
-α1U+d2Udx2+V2U1+U2+V2=0, -α2V+d2Vdx2+U2V1+U2+V2=0.
Um2>α21-α1+α2,  Vm2>α11-α1+α2·

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