Abstract

We present a study of the dynamics of multiple soliton bound states in diffractive media with second-order nonlinearity. A numerical stability analysis of these bound states reveals that wave propagation in quadratic materials exhibits spatial symmetry-breaking instabilities.

© 1997 Optical Society of America

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References

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  1. Yu. N. Karamzin and A. P. Sukhorukov, JETP Lett. 20, 339 (1974).
  2. 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]
  3. R. Schiek, Y. Baeck, and G. I. Stegeman, Phys. Rev. A 53, 1138 (1995).
  4. L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, Opt. Lett. 20, 1952 (1995).
    [CrossRef] [PubMed]
  5. D.-M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
    [CrossRef]
  6. L. Torner, J. P. Torres, and C. R. Menyuk, Opt. Lett. 21, 462 (1996).
    [CrossRef]
  7. A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).
    [CrossRef] [PubMed]
  8. H. He, M. J. Werner, and P. D. Drummond, Phys. Rev. E 54, 896 (1996).
    [CrossRef]
  9. D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
    [CrossRef]
  10. A. V. Buryak and Yu. S. Kivshar, Opt. Lett. 19, 1612 (1994); Opt. Lett. 20, 1080 (1995); Phys. Lett. A 197, 407 (1995).
    [CrossRef] [PubMed]
  11. S. Trillo and P. Ferro, Phys. Rev. E 51, 4994 (1995).
    [CrossRef]
  12. M. J. Werner and P. D. Drummond, Opt. Lett. 19, 613 (1994).
    [CrossRef] [PubMed]
  13. M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 3376 (1994).
    [CrossRef]
  14. C. Etrich, U. Preschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).
    [CrossRef]
  15. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, Orlando, Fla., 1985).

1996 (3)

H. He, M. J. Werner, and P. D. Drummond, Phys. Rev. E 54, 896 (1996).
[CrossRef]

D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

L. Torner, J. P. Torres, and C. R. Menyuk, Opt. Lett. 21, 462 (1996).
[CrossRef]

1995 (7)

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, Opt. Lett. 20, 1952 (1995).
[CrossRef] [PubMed]

D.-M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
[CrossRef]

S. Trillo and P. Ferro, Phys. Rev. E 51, 4994 (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]

R. Schiek, Y. Baeck, and G. I. Stegeman, Phys. Rev. A 53, 1138 (1995).

A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).
[CrossRef] [PubMed]

C. Etrich, U. Preschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).
[CrossRef]

1994 (3)

1974 (1)

Yu. N. Karamzin and A. P. Sukhorukov, JETP Lett. 20, 339 (1974).

Baboiu, D.-M.

Baeck, Y.

R. Schiek, Y. Baeck, and G. I. Stegeman, Phys. Rev. A 53, 1138 (1995).

Boardman, A. D.

A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).
[CrossRef] [PubMed]

Buryak, A. V.

Crasovan, L.-C.

D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Drummond, P. D.

H. He, M. J. Werner, and P. D. Drummond, Phys. Rev. E 54, 896 (1996).
[CrossRef]

M. J. Werner and P. D. Drummond, Opt. Lett. 19, 613 (1994).
[CrossRef] [PubMed]

Etrich, C.

C. Etrich, U. Preschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).
[CrossRef]

Ferro, P.

S. Trillo and P. Ferro, Phys. Rev. E 51, 4994 (1995).
[CrossRef]

Gibbs, H. M.

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, Orlando, Fla., 1985).

Haelterman, M.

M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 3376 (1994).
[CrossRef]

Hagan, D. J.

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]

He, H.

H. He, M. J. Werner, and P. D. Drummond, Phys. Rev. E 54, 896 (1996).
[CrossRef]

Karamzin, Yu. N.

Yu. N. Karamzin and A. P. Sukhorukov, JETP Lett. 20, 339 (1974).

Kivshar, Yu. S.

Lederer, F.

D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

C. Etrich, U. Preschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).
[CrossRef]

Malomed, B.

C. Etrich, U. Preschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).
[CrossRef]

Mazilu, D.

D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Menyuk, C. R.

L. Torner, J. P. Torres, and C. R. Menyuk, Opt. Lett. 21, 462 (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]

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, Opt. Lett. 20, 1952 (1995).
[CrossRef] [PubMed]

Mihalache, D.

D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Preschel, U.

C. Etrich, U. Preschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).
[CrossRef]

Sangarpaul, A.

A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).
[CrossRef] [PubMed]

Schiek, R.

R. Schiek, Y. Baeck, and G. I. Stegeman, Phys. Rev. A 53, 1138 (1995).

Sheppard, A. P.

M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 3376 (1994).
[CrossRef]

Stegeman, G. I.

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]

D.-M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
[CrossRef]

R. Schiek, Y. Baeck, and G. I. Stegeman, Phys. Rev. A 53, 1138 (1995).

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, Opt. Lett. 20, 1952 (1995).
[CrossRef] [PubMed]

Sukhorukov, A. P.

Yu. N. Karamzin and A. P. Sukhorukov, JETP Lett. 20, 339 (1974).

Torner, L.

Torres, J. P.

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]

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, Opt. Lett. 20, 1952 (1995).
[CrossRef] [PubMed]

Trillo, S.

S. Trillo and P. Ferro, Phys. Rev. E 51, 4994 (1995).
[CrossRef]

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]

Werner, M. J.

H. He, M. J. Werner, and P. D. Drummond, Phys. Rev. E 54, 896 (1996).
[CrossRef]

M. J. Werner and P. D. Drummond, Opt. Lett. 19, 613 (1994).
[CrossRef] [PubMed]

Xie, K.

A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).
[CrossRef] [PubMed]

JETP Lett. (1)

Yu. N. Karamzin and A. P. Sukhorukov, JETP Lett. 20, 339 (1974).

Opt. Eng. (1)

D. Mihalache, F. Lederer, D. Mazilu, and L.-C. Crasovan, Opt. Eng. 35, 1616 (1996).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (3)

C. Etrich, U. Preschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).
[CrossRef]

R. Schiek, Y. Baeck, and G. I. Stegeman, Phys. Rev. A 53, 1138 (1995).

A. D. Boardman, K. Xie, and A. Sangarpaul, Phys. Rev. A 52, 4099 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (3)

H. He, M. J. Werner, and P. D. Drummond, Phys. Rev. E 54, 896 (1996).
[CrossRef]

S. Trillo and P. Ferro, Phys. Rev. E 51, 4994 (1995).
[CrossRef]

M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 3376 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

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]

Other (1)

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, Orlando, Fla., 1985).

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Figures (5)

Fig. 1
Fig. 1

Solitary-wave envelopes uξ (solid curves) and vξ (dotted curves) for Δ=1.95. n is the number of nodes in the fundamental field envelopes uξ.

Fig. 2
Fig. 2

(a) Soliton separation δξ in the two-soliton bound state versus the phase-mismatch parameter Δ and (b) solitary-wave second-harmonic intensity profiles corresponding to Δ=1.65 (solid curve) and Δ=1.9 (dashed curve), respectively, indicated by the arrows in (a).

Fig. 3
Fig. 3

Evolution of the fundamental field intensity profile Uξ,ζ2 for various initial conditions: (a) exact first-order soliton bound state corresponding to Δ=1.65; (b), (c) two adjacent sech2 profile beams with parameters adjusted to match the bound states of Δ=1.65 and Δ=1.8, respectively. These parameters, defined in the text, are (b) A1=0.9, A2=0.73, ξ1=2.2, ξ2=2.3, and ξ0=5; (c) A1=0.7, A2=0.69, ξ1=2.2, ξ2=2.5, and ξ0=3.5.

Fig. 4
Fig. 4

Contour lines of the fundamental field intensity Uξ,ζ2 obtained for Δ=1.8 with two sech2 beams with the parameters of Fig. 3(c) apart from a slight difference in the fundamental field amplitude of the right-hand-side beam. This amplitude is (a) AIRHS=0.707 and (b) A1 RHS=0.603.

Fig. 5
Fig. 5

Fundamental field intensity profiles Uξ,ζ2 of two colliding π-out-of-phase parametric solitons. The incident angles of the solitons are (a) θ=0.05, (b) θ=0.1, and (c) θ=0.2. The symmetry breaking is seeded by a small positive phase shift Δϕ=0.01 of the left-hand-side soliton.

Equations (3)

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iζU+½ρρ2U+U*V=0,
iσζV+½ρρ2V+σδV+½U2=0.
u=2u-2uv, v=2σ2-Δv-u2,

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