Abstract

We numerically investigate the interaction of vectorial solitary waves propagating in a bulk crystal with a phase-matchable quadratic nonlinearity. We obtain coalescence, steering, crossing, or repulsion by controlling the launched intensities in two orthogonal polarizations without any coherent seed at the second harmonic.

© 1997 Optical Society of America

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References

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  1. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]
  2. Y. N. Karamzin and A. P. Sukhorukov, JETP Lett. 20, 339 (1974); Sov. Phys. JETP,  41, 414 (1976).
  3. K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
    [CrossRef] [PubMed]
  4. L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, Opt. Commun. 121, 149 (1995).
    [CrossRef]
  5. L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, Opt. Lett. 20, 1952 (1995); Opt. Lett. 20, 13 (1995).
    [CrossRef] [PubMed]
  6. A. V. Buriak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 160 (1995).
  7. L. Torner and E. M. Wright, J. Opt. Soc. Am. B 13, 864 (1996).
    [CrossRef]
  8. H. T. Tran, Opt. Commun. 118581 (1995); B. A. Malomed, D. Anderson, and M. Lisak, Opt. Commun. 126, 251 (1996).
  9. L. Torner, J. P. Torres, and C. R. Menyuk, Opt. Lett. 21, 462 (1996).
    [CrossRef]
  10. W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, Opt. Lett. 20, 1949 (1995).
    [CrossRef] [PubMed]
  11. W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
    [CrossRef]
  12. M. J. Werner and P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).
    [CrossRef]
  13. D.-M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
    [CrossRef]
  14. C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).
    [CrossRef]

1996 (3)

L. Torner and E. M. Wright, J. Opt. Soc. Am. B 13, 864 (1996).
[CrossRef]

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

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

1995 (8)

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

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

W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, Opt. Lett. 20, 1949 (1995).
[CrossRef] [PubMed]

H. T. Tran, Opt. Commun. 118581 (1995); B. A. Malomed, D. Anderson, and M. Lisak, Opt. Commun. 126, 251 (1996).

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

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, Opt. Commun. 121, 149 (1995).
[CrossRef]

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, Opt. Lett. 20, 1952 (1995); Opt. Lett. 20, 13 (1995).
[CrossRef] [PubMed]

A. V. Buriak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 160 (1995).

1993 (2)

1974 (1)

Y. N. Karamzin and A. P. Sukhorukov, JETP Lett. 20, 339 (1974); Sov. Phys. JETP,  41, 414 (1976).

Assanto, G.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

Baboiu, D.-M.

Buriak, A. V.

A. V. Buriak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 160 (1995).

Drummond, P. D.

Etrich, C.

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

Fuerst, R. A.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

Hagan, D. J.

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

Hayata, K.

K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Karamzin, Y. N.

Y. N. Karamzin and A. P. Sukhorukov, JETP Lett. 20, 339 (1974); Sov. Phys. JETP,  41, 414 (1976).

Kivshar, Y. S.

A. V. Buriak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 160 (1995).

Koshiba, M.

K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Lawrence, B. L.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

Lederer, F.

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

Malomed, B.

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

Mazilu, D.

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, Opt. Commun. 121, 149 (1995).
[CrossRef]

Menyuk, C. R.

Mihalache, D.

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, Opt. Commun. 121, 149 (1995).
[CrossRef]

Peschel, U.

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

Steblina, V. V.

A. V. Buriak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 160 (1995).

Stegeman, G. I.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, Opt. Commun. 121, 149 (1995).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. VanStryland, 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); Opt. Lett. 20, 13 (1995).
[CrossRef] [PubMed]

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

W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, Opt. Lett. 20, 1949 (1995).
[CrossRef] [PubMed]

Sukhorukov, A. P.

Y. N. Karamzin and A. P. Sukhorukov, JETP Lett. 20, 339 (1974); Sov. Phys. JETP,  41, 414 (1976).

Torner, L.

Torres, J. P.

Torruellas, W. E.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

L. Torner, W. E. Torruellas, G. I. Stegeman, and C. R. Menyuk, Opt. Lett. 20, 1952 (1995); Opt. Lett. 20, 13 (1995).
[CrossRef] [PubMed]

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, Opt. Commun. 121, 149 (1995).
[CrossRef]

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

W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, Opt. Lett. 20, 1949 (1995).
[CrossRef] [PubMed]

Tran, H. T.

H. T. Tran, Opt. Commun. 118581 (1995); B. A. Malomed, D. Anderson, and M. Lisak, Opt. Commun. 126, 251 (1996).

VanStryland, E. W.

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

W. E. Torruellas, Z. Wang, L. Torner, and G. I. Stegeman, Opt. Lett. 20, 1949 (1995).
[CrossRef] [PubMed]

Werner, M. J.

Wright, E. M.

L. Torner and E. M. Wright, J. Opt. Soc. Am. B 13, 864 (1996).
[CrossRef]

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, Opt. Commun. 121, 149 (1995).
[CrossRef]

Appl. Phys. Lett. (1)

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
[CrossRef]

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

JETP Lett. (1)

Y. N. Karamzin and A. P. Sukhorukov, JETP Lett. 20, 339 (1974); Sov. Phys. JETP,  41, 414 (1976).

Opt. Commun. (2)

L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas, and G. I. Stegeman, Opt. Commun. 121, 149 (1995).
[CrossRef]

H. T. Tran, Opt. Commun. 118581 (1995); B. A. Malomed, D. Anderson, and M. Lisak, Opt. Commun. 126, 251 (1996).

Opt. Lett. (4)

Phys. Rev. A (2)

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

A. V. Buriak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 160 (1995).

Phys. Rev. Lett. (2)

K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

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

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Figures (3)

Fig. 1
Fig. 1

FF intensity contour plots for the propagation of two SSW’s symmetrically launched in the ζ direction with the same imbalance δ and collision angle θ (in units of ρeω): (a) δ=15%, θ=4; (b) δ=10%, θ=4; (c) δ=0, θ=4; (d) δ=0, θ=8. The propagation distance is in diffraction lengths ld, Io+Ie=40 GW/cm2, Δk=10π m-1.

Fig. 2
Fig. 2

FF output L=10ld intensity distribution along ξψ=0 of the two SSW’s of Figs. 1(a)1(c) for various imbalances.

Fig. 3
Fig. 3

As in Fig. 1 but for two SSW’s (left and right) launched parallel along ζ (θ=0), 60 µm apart in ξ, and with imbalances (a) δR=δL=-0.5 and (b) δL=-δR=0.5.

Equations (1)

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Ee,oωζ-ρeω,oEe,oωξ+Δ2Ee,oω2ike,oω-iΓEe2ωEe,oω* exp-iΔkζ=0,Ee2ωζ-ρe2ωEe2ωξ+Δ2Ee2ω2ike2ω-i2ΓEeωEoω exp+iΔkζ=0,

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