Abstract

We show that resonant wave mixing that is due to quadratic nonlinearity can support stable bright spatial solitons, even in the most counterintuitive case of a bulk medium with defocusing Kerr nonlinearity. We analyze the structure and stability of such self-guided beams and demonstrate that they can be generated from a Gaussian input beam, provided that its power is above a certain threshold.

© 1997 Optical Society of America

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References

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  1. Yu. S. Kivshar and B. Luther-Davies, “Optical dark solitons: physics and applications,” Phys. Rep. (to be published).
  2. For a general overview see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum. Electron. 28, 1691 (1996).
    [CrossRef]
  3. O. Bang, J. Opt. Soc. Am. B 14, 51 (1997).
    [CrossRef]
  4. L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
    [CrossRef]
  5. A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995).
    [CrossRef] [PubMed]
  6. C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
    [CrossRef]
  7. D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
    [CrossRef] [PubMed]
  8. E. M. Wright, B. L. Lawrence, W. Torruellas, and G. I. Stegeman, Opt. Lett. 20, 2481 (1995).
    [CrossRef]
  9. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]

1997 (3)

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

O. Bang, J. Opt. Soc. Am. B 14, 51 (1997).
[CrossRef]

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
[CrossRef]

1996 (1)

For a general overview see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum. Electron. 28, 1691 (1996).
[CrossRef]

1995 (4)

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995).
[CrossRef] [PubMed]

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[CrossRef] [PubMed]

E. M. Wright, B. L. Lawrence, W. Torruellas, and G. I. Stegeman, Opt. Lett. 20, 2481 (1995).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Bang, O.

O. Bang, J. Opt. Soc. Am. B 14, 51 (1997).
[CrossRef]

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
[CrossRef]

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

Bergé, L.

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
[CrossRef]

Buryak, A. V.

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[CrossRef] [PubMed]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995).
[CrossRef] [PubMed]

Clausen, C. B.

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

Hagan, D. J.

For a general overview see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum. Electron. 28, 1691 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Kivshar, Yu. S.

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[CrossRef] [PubMed]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Opt. Lett. 20, 1961 (1995).
[CrossRef] [PubMed]

Yu. S. Kivshar and B. Luther-Davies, “Optical dark solitons: physics and applications,” Phys. Rep. (to be published).

Lawrence, B. L.

Luther-Davies, B.

Yu. S. Kivshar and B. Luther-Davies, “Optical dark solitons: physics and applications,” Phys. Rep. (to be published).

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Mezentsev, V. K.

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
[CrossRef]

Pelinovsky, D. E.

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[CrossRef] [PubMed]

Rasmussen, J. J.

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
[CrossRef]

Stegeman, G. I.

For a general overview see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum. Electron. 28, 1691 (1996).
[CrossRef]

E. M. Wright, B. L. Lawrence, W. Torruellas, and G. I. Stegeman, Opt. Lett. 20, 2481 (1995).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Torner, L.

For a general overview see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum. Electron. 28, 1691 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Torruellas, W.

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Trillo, S.

Van Stryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Wright, E. M.

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

Opt. Lett. (2)

Opt. Quantum. Electron. (1)

For a general overview see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum. Electron. 28, 1691 (1996).
[CrossRef]

Phys. Rev. E (1)

L. Bergé, O. Bang, J. J. Rasmussen, and V. K. Mezentsev, Phys. Rev. E 55, 3555 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[CrossRef] [PubMed]

Other (1)

Yu. S. Kivshar and B. Luther-Davies, “Optical dark solitons: physics and applications,” Phys. Rep. (to be published).

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Figures (5)

Fig. 1
Fig. 1

Profiles w0r=x (solid curves) and v0r=x (dotted curves) of solutions  (3) for η=2ρ=16, β=0.1, and (a) λ=0.003, (b) λ=0.006, (c) λ=0.00655.

Fig. 2
Fig. 2

Characteristics of the C solutions [Eqs.  (3)] for η=2ρ=16 and β=-0.02 (dotted curves) and β=0.1 (solid curves). (a) Amplitude versus λ for the fundamental w00 (upper curve) and the second harmonic v00 (lower curve). (b) Dimensionless power versus λ.

Fig. 3
Fig. 3

(a) Region of existence of stable (hatched) and unstable (black) solitons in the λ, β plane. (b) Power regime (hatched) of stable solitons versus β. Parameters: η=2ρ=16.

Fig. 4
Fig. 4

Evolution of a Gaussian input beam at the fundamental, wr, 0=0.1exp-r/302, with vr, 0=0 and (a) β=0.29, (b) β=0.1. Parameters: η=2ρ=16.

Fig. 5
Fig. 5

Physical power threshold versus χ˜1s3 for η=2ρ=16, λ1=1.064 µm, and values of χ˜12 of 3 pm/V (solid curves) and 5.6  pm/V (dashed curves). In each case the upper curve is for κ=-10-3 and the lower curve is for κ=10-3.

Equations (3)

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iwz+2w+w*v-w2+ρv2w=0,
2ivz+2v-βv+12w2-ηv2+ρw2v=0,
wr, z=w0rexpiλz, vr, z=v0rexp2iλz,

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