Abstract

It is demonstrated that optical solitons can propagate in a dispersive (or diffractive) medium with competing quadratic [i.e., χ(2)] and cubic [i.e., χ(3)] nonlinearities. Strong interplay between the nonlinearities leads to novel effects, in particular the following: (i) stable bright solitons can still exist in a self-defocusing (owing to cubic nonlinearity) medium supported by quadratic parametric interactions and (ii) χ(2) nonlinearity can lead to instabilities of χ(3) solitons.

© 1995 Optical Society of America

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References

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  1. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, Opt. Lett. 17, 28 (1992).
    [Crossref] [PubMed]
  2. Y. N. Karamzin, A. P. Sukhorukov, JETP Lett. 20, 339 (1974); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); M. J. Werner, P. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).
  3. A. V. Buryak, Yu. S. Kivshar, Opt. Lett. 19, 1612 (1994); Phys. Lett. A 197, 407 (1995).
    [Crossref] [PubMed]
  4. L. Torner, C. R. Menyuk, G. I. Stegeman, Opt. Lett. 19, 1615 (1994).
    [Crossref] [PubMed]
  5. S. Trillo, S. Wabnitz, Opt. Lett. 17, 157 (1992).
    [Crossref]
  6. S. Trillo, A. Buryak, Yu. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 36–38.
  7. A. V. Buryak, Yu. S. Kivshar, Opt. Lett. 20, 1080 (1995)see also D. E. Pelinovsky, A. V. Buryak, Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
    [Crossref] [PubMed]
  8. A. V. Buryak, Yu. S. Kivshar, Phys. Rev. A 51, R41 (1995); S. Trillo, P. Ferro, Opt. Lett. 20, 438 (1995).
    [Crossref] [PubMed]

1995 (2)

1994 (2)

1992 (2)

1974 (1)

Y. N. Karamzin, A. P. Sukhorukov, JETP Lett. 20, 339 (1974); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); M. J. Werner, P. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).

Buryak, A.

S. Trillo, A. Buryak, Yu. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 36–38.

Buryak, A. V.

DeSalvo, R.

Hagan, D. J.

Karamzin, Y. N.

Y. N. Karamzin, A. P. Sukhorukov, JETP Lett. 20, 339 (1974); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); M. J. Werner, P. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).

Kivshar, Yu.

S. Trillo, A. Buryak, Yu. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 36–38.

Kivshar, Yu. S.

Menyuk, C. R.

Sheik-Bahae, M.

Stegeman, G.

Stegeman, G. I.

Sukhorukov, A. P.

Y. N. Karamzin, A. P. Sukhorukov, JETP Lett. 20, 339 (1974); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); M. J. Werner, P. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).

Torner, L.

Trillo, S.

S. Trillo, S. Wabnitz, Opt. Lett. 17, 157 (1992).
[Crossref]

S. Trillo, A. Buryak, Yu. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 36–38.

Van Stryland, E. W.

Wabnitz, S.

JETP Lett. (1)

Y. N. Karamzin, A. P. Sukhorukov, JETP Lett. 20, 339 (1974); R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993); M. J. Werner, P. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).

Opt. Lett. (5)

Phys. Rev. A (1)

A. V. Buryak, Yu. S. Kivshar, Phys. Rev. A 51, R41 (1995); S. Trillo, P. Ferro, Opt. Lett. 20, 438 (1995).
[Crossref] [PubMed]

Other (1)

S. Trillo, A. Buryak, Yu. Kivshar, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 36–38.

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Figures (3)

Fig. 1
Fig. 1

Bifurcation diagram of the localized solutions of Eqs. (3). Stable solitons are represented by solid curves, and unstable ones are shown by dashed curves. Note the different scales for positive and negative values of χ.

Fig. 2
Fig. 2

Characteristic profiles of the two-wave solitons of the C type at (a) χ = 0.2 (point L in Fig. 1), (b) χ = 8.0 (point M in Fig. 1), (c) χ = −0.0615 (not shown in Fig. 1).

Fig. 3
Fig. 3

Example of the two-wave solitons of the W type at χ = 8.0 (point N in Fig. 1).

Equations (4)

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i E 1 z + i δ 1 E 1 ξ + γ 1 2 E 1 ξ 2 + χ 2 E 1 * E 2 exp ( - i Δ k z ) + χ 3 ( E 1 2 + ρ E 2 2 E 1 = 0 , i E 2 z + i δ 2 E 2 ξ + γ 2 2 E 2 ξ 2 + χ 2 E 1 2 exp ( i Δ k z ) + 2 χ 3 ( E 1 2 + ρ E 1 2 E 2 = 0 ,
i w ζ + r 2 w τ 2 - w + v w * + χ ( w 2 2 σ + ρ v 2 ) w = 0 , i σ v ζ + s 2 v τ 2 - α v + w 2 2 + χ ( 2 σ v 2 + ρ w 2 ) v = 0 ,
d 2 w d τ 2 - w + w v + χ ( 1 4 w 2 + 2 v 2 ) w = 0 , d 2 v d τ 2 - 2 v + 1 2 w 2 + χ ( 4 v 2 + 2 w 2 ) v = 0 ,
P = χ - + ( w 2 + 4 v 2 ) d τ

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