Abstract

We report experimental and numerical results that describe collisions between two-dimensional type II quadratic solitons excited in a KTP crystal by fundamental waves of orthogonal polarization. Our results provide experimental evidence of the possibility of both inelastic collision (when two quadratic solitons merge at input into a single soliton at output) and quasi-elastic collision.

© 1998 Optical Society of America

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  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]
  2. J. J. Rasmussen and K. Rypdal, Phys. Scr. 33, 481 (1986).
    [CrossRef]
  3. W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1449 (1996).
    [CrossRef]
  4. R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
    [CrossRef]
  5. L. Lefort and A. Barthelemy, IEEE Photon. Technol. Lett. 9, 1364 (1997).
    [CrossRef]
  6. M. F. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
    [CrossRef]
  7. M. J. Werner and P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).
    [CrossRef]
  8. A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
    [CrossRef] [PubMed]
  9. D. M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
    [CrossRef]
  10. C. Etrick, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
    [CrossRef]
  11. C. Balslev Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).
    [CrossRef]
  12. Y. Baek, R. Schiek, G. I. Stegeman, I. Baumann, and W. Sohler, Opt. Lett. 22, 1550 (1997).
    [CrossRef]
  13. G. Leo, G. Assanto, and W. E. Torruellas, Opt. Lett. 22, 7 (1997).
    [CrossRef] [PubMed]
  14. U. Peschel, C. Etrich, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 7704 (1997).
    [CrossRef]
  15. B. Costantini, C. De Angelis, A. Laureti Palma, A. Barthelemy, and G. Assanto, Opt. Lett. 22, 1376 (1997).
    [CrossRef]
  16. G. Leo and G. Assanto, J. Opt. Soc. Am. B 14, 3151 (1997).
    [CrossRef]

1997 (8)

L. Lefort and A. Barthelemy, IEEE Photon. Technol. Lett. 9, 1364 (1997).
[CrossRef]

M. F. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

G. Leo and G. Assanto, J. Opt. Soc. Am. B 14, 3151 (1997).
[CrossRef]

G. Leo, G. Assanto, and W. E. Torruellas, Opt. Lett. 22, 7 (1997).
[CrossRef] [PubMed]

B. Costantini, C. De Angelis, A. Laureti Palma, A. Barthelemy, and G. Assanto, Opt. Lett. 22, 1376 (1997).
[CrossRef]

Y. Baek, R. Schiek, G. I. Stegeman, I. Baumann, and W. Sohler, Opt. Lett. 22, 1550 (1997).
[CrossRef]

C. Balslev Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).
[CrossRef]

U. Peschel, C. Etrich, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 7704 (1997).
[CrossRef]

1996 (2)

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

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

1995 (4)

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]

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
[CrossRef] [PubMed]

C. Etrick, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[CrossRef]

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

1993 (1)

1986 (1)

J. J. Rasmussen and K. Rypdal, Phys. Scr. 33, 481 (1986).
[CrossRef]

Assanto, G.

Baboiu, D. M.

Baek, Y.

Balslev Clausen, C.

C. Balslev Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).
[CrossRef]

Barthelemy, A.

Baumann, I.

Buryak, A. V.

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
[CrossRef] [PubMed]

Christiansen, P. L.

C. Balslev Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).
[CrossRef]

Costantini, B.

De Angelis, C.

Drummond, P. D.

Etrich, C.

U. Peschel, C. Etrich, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 7704 (1997).
[CrossRef]

Etrick, C.

C. Etrick, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (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. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Kivshar, Y. S.

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
[CrossRef] [PubMed]

Laureti Palma, A.

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.

U. Peschel, C. Etrich, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 7704 (1997).
[CrossRef]

C. Etrick, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[CrossRef]

Lefort, L.

L. Lefort and A. Barthelemy, IEEE Photon. Technol. Lett. 9, 1364 (1997).
[CrossRef]

Leo, G.

Malomed, B.

C. Etrick, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[CrossRef]

Malomed, B. A.

U. Peschel, C. Etrich, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 7704 (1997).
[CrossRef]

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]

Peschel, U.

U. Peschel, C. Etrich, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 7704 (1997).
[CrossRef]

C. Etrick, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[CrossRef]

Rasmussen, J. J.

J. J. Rasmussen and K. Rypdal, Phys. Scr. 33, 481 (1986).
[CrossRef]

Rypdal, K.

J. J. Rasmussen and K. Rypdal, Phys. Scr. 33, 481 (1986).
[CrossRef]

Salamo, G.

M. F. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

Schiek, R.

Segev, M.

M. F. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

Shih, M. F.

M. F. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

Sohler, W.

Steblina, V. V.

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
[CrossRef] [PubMed]

Stegeman, G. I.

Y. Baek, R. Schiek, G. I. Stegeman, I. Baumann, and W. Sohler, Opt. Lett. 22, 1550 (1997).
[CrossRef]

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

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (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]

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

Torner, L.

C. Balslev Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).
[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]

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

Torruellas, W. E.

G. Leo, G. Assanto, and W. E. Torruellas, Opt. Lett. 22, 7 (1997).
[CrossRef] [PubMed]

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

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.

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]

IEEE Photon. Technol. Lett. (1)

L. Lefort and A. Barthelemy, IEEE Photon. Technol. Lett. 9, 1364 (1997).
[CrossRef]

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

Opt. Commun. (1)

C. Balslev Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (2)

C. Etrick, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[CrossRef]

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (2)

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

U. Peschel, C. Etrich, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 7704 (1997).
[CrossRef]

Phys. Rev. Lett. (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]

M. F. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

Phys. Scr. (1)

J. J. Rasmussen and K. Rypdal, Phys. Scr. 33, 481 (1986).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experiment with inelastic collision for θ=0.3 and a peak soliton intensity of 14 GW/cm2: Images at the output face of the crystal are shown (a) when the input is beam 1 (beam 2 is blocked by a screen), (b) when the input is beam 2 (beam 1 is blocked by a screen), and (c) for fusion of the two QSSW’s in the mean position. The dots are a guide for the eye.

Fig. 2
Fig. 2

Numerical z evolution of the FF1 component that describes inelastic collision for θ=0.3.

Fig. 3
Fig. 3

Experiment with interaction for θ=-0.1 and a peak soliton intensity of 14 GW/cm2; the image is at the output face of the crystal. (b) Experiment of quasi-elastic collisions for θ=0.6, for the same peak soliton intensity; the image is at the output face of the crystal.

Fig. 4
Fig. 4

Numerical z evolution of the FF1 component that describes quasi-elastic collision for θ=0.6.

Equations (1)

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U1z+12ik12U1x2+2U1y2=iΓU3U2* exp-iΔkz, U2z-ρωU2x+12ik22U2x2+2U2y2=iΓU3U1* exp-iΔkz, U3z-ρ2ωU3x+12ik32U3x2+2U3y2=2iΓU1U2 expiΔkz,

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