Abstract

We demonstrate that a dielectric medium with purely quadratic nonlinearity [the so-called χ(2) material] can display self-focusing phenomena through a new type of modulational instability of the interacting fundamental and second-harmonic field components and therefore can support propagation of (two-wave) optical solitons. We prove the existence of a family of such solitons, which are found numerically and, in some particular cases, also analytically. The two-wave solitons are stable in the whole parameter region in which they exist.

© 1994 Optical Society of America

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Corrections

Alexander V. Buryak and Yuri S. Kivshar, "Spatial optical solitons governed by quadratic nonlinearity: erratum," Opt. Lett. 20, 1080-1080 (1995)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-20-9-1080

References

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), Chap. 5, p. 105.
  2. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 7.
  3. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. I. Stegeman, H. Vanherzeele, Opt. Lett. 17, 28 (1992).
    [CrossRef] [PubMed]
  4. R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993).
    [CrossRef]
  5. R. Schiek, in Nonlinear Guided-Wave Phenomena, Vol. 15 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 151.
  6. K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993); errata, K. Hayata, M. Koshiba, Phys. Rev. Lett. 72, 178 (1994).
    [CrossRef] [PubMed]
  7. A. G. Kalocsai, J. W. Haus, Phys. Rev. A 49, 574 (1994).
    [CrossRef] [PubMed]
  8. M. J. Werner, P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).
    [CrossRef]
  9. R. Chaio, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
    [CrossRef]
  10. M. Haelterman, A. P. Sheppard, A. W. Snyder, Opt. Lett. 18, 479 (1993).
    [CrossRef]
  11. T. R. Taha, M. J. Ablowitz, J. Comp. Phys. 55, 203 (1984).
    [CrossRef]

1994 (1)

A. G. Kalocsai, J. W. Haus, Phys. Rev. A 49, 574 (1994).
[CrossRef] [PubMed]

1993 (4)

1992 (1)

1984 (1)

T. R. Taha, M. J. Ablowitz, J. Comp. Phys. 55, 203 (1984).
[CrossRef]

1964 (1)

R. Chaio, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Ablowitz, M. J.

T. R. Taha, M. J. Ablowitz, J. Comp. Phys. 55, 203 (1984).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), Chap. 5, p. 105.

Chaio, R.

R. Chaio, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

DeSalvo, R.

Drummond, P. D.

Garmire, E.

R. Chaio, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Haelterman, M.

Hagan, D. J.

Haus, J. W.

A. G. Kalocsai, J. W. Haus, Phys. Rev. A 49, 574 (1994).
[CrossRef] [PubMed]

Hayata, K.

K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993); errata, K. Hayata, M. Koshiba, Phys. Rev. Lett. 72, 178 (1994).
[CrossRef] [PubMed]

Kalocsai, A. G.

A. G. Kalocsai, J. W. Haus, Phys. Rev. A 49, 574 (1994).
[CrossRef] [PubMed]

Koshiba, M.

K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993); errata, K. Hayata, M. Koshiba, Phys. Rev. Lett. 72, 178 (1994).
[CrossRef] [PubMed]

Schiek, R.

R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993).
[CrossRef]

R. Schiek, in Nonlinear Guided-Wave Phenomena, Vol. 15 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 151.

Sheik-Bahae, M.

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 7.

Sheppard, A. P.

Snyder, A. W.

Stegeman, G. I.

Taha, T. R.

T. R. Taha, M. J. Ablowitz, J. Comp. Phys. 55, 203 (1984).
[CrossRef]

Townes, C. H.

R. Chaio, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Vanherzeele, H.

Werner, M. J.

J. Comp. Phys. (1)

T. R. Taha, M. J. Ablowitz, J. Comp. Phys. 55, 203 (1984).
[CrossRef]

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

Opt. Lett. (2)

Phys. Rev. A (1)

A. G. Kalocsai, J. W. Haus, Phys. Rev. A 49, 574 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

R. Chaio, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993); errata, K. Hayata, M. Koshiba, Phys. Rev. Lett. 72, 178 (1994).
[CrossRef] [PubMed]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), Chap. 5, p. 105.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 7.

R. Schiek, in Nonlinear Guided-Wave Phenomena, Vol. 15 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 151.

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Figures (3)

Fig. 1
Fig. 1

Separatrix trajectory (solid curve with arrows) corresponding to a two-wave spatial soliton in the plane (w, v). The thin solid curves show the contour plot of the effective potential U(w, v) given by Eq. (7). The other branch of the separatrix trajectory (not shown) is symmetric with respect to the change of sign of w.

Fig. 2
Fig. 2

Two characteristic profiles of the fundamental (w) and second-harmonic (v) components: (a) α = 0.4,(b) α = 4.0.

Fig. 3
Fig. 3

Ratio of the amplitude maxima of the fundamental (vm) and second-harmonic (wm) field components as a function of the dimensionless parameter α.

Equations (8)

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2 i β E ω z + 2 E ω x 2 + ( - β 2 ) E ω + χ E ω * E 2 ω = 0 , 4 i β E 2 ω z + 2 E 2 ω x 2 + 4 ( ∊′ - β 2 ) E 2 ω + 2 χ E ω 2 = 0.
E ω = ( β 2 - ) 2 χ w ,             E 2 ω = ( β 2 - ) χ v ,
i w ζ + 2 w ξ 2 - w + w * v = 0 , 2 i v ζ + 2 v ξ 2 - α v + w 2 = 0 ,
α 4 β 2 - β 2 -             ( α > 0 ) .
2 i β E ω z + 2 E ω x 2 - ( β 2 - ) E ω + χ 2 2 ( β 2 - ) E ω 2 E ω = 0 ,
w - w + w v = 0 , v - α v + w 2 = 0 ,
U ( w , v ) = 1 2 ( w 2 v - α 2 v 2 - w 2 ) .
w = v = 3 2 cosh 2 ( ξ / 2 ) ,

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