Abstract

We analyze the interactions of (2+1) -dimensional parametric solitons and demonstrate nonplanar beam switching in a bulk <i>X</i><sup>(2)</sup> medium, which includes controllable soliton repulsion, spiraling, and fusion. An analytical model predicting the results of the soliton scattering is derived and verified by direct numerics.

© 1998 Optical Society of America

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  1. See, e.g., F. Reynaud and A. Barthelemy, in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), p. 319.
  2. G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Share, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).
  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).
  4. V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
  5. M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997).
  6. See, e.g., L. Poladian, A. W. Snyder, and D. J. Mitchell, Opt. Commun. 85, 59 (1991).
  7. G. I. Stegeman, D. J. Hagan, and L. Torner, J. Opt. Quantum Electron. 28, 1691 (1996).
  8. A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995); V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
  9. See also the stability analysis for the parametric three-wave mixing by A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996) ; A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).
  10. M. J. Werner and P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993) ; D. M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995) ; C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A PLRAAN 52, R3444 (1995).
  11. Y. Baek, R. Schiek, G. I. Stegeman, I. Baumann, and W. Sohler, Opt. Lett. 22, 1550 (1997).
  12. G. Leo, G. Assanto, and W. E. Torruellas, Opt. Lett. 22, 7 (1997).
  13. C. Clausen, O. Bang, and Yu. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
  14. K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981).
  15. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1980), Chap. 3.

1997

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

C. Clausen, O. Bang, and Yu. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).

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

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

1996

G. I. Stegeman, D. J. Hagan, and L. Torner, J. Opt. Quantum Electron. 28, 1691 (1996).

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).

1995

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).

1993

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Share, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

1992

See, e.g., F. Reynaud and A. Barthelemy, in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), p. 319.

1991

See, e.g., L. Poladian, A. W. Snyder, and D. J. Mitchell, Opt. Commun. 85, 59 (1991).

1981

K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981).

1980

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1980), Chap. 3.

Assanto, G.

Baboiu, D. M.

Baek, Y.

Bang, O.

C. Clausen, O. Bang, and Yu. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).

Barthelemy, A.

See, e.g., F. Reynaud and A. Barthelemy, in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), p. 319.

Baumann, I.

Buryak, A. V.

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995); V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

See also the stability analysis for the parametric three-wave mixing by A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996) ; A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).

See also the stability analysis for the parametric three-wave mixing by A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996) ; A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).

Christou, J.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).

Clausen, C.

C. Clausen, O. Bang, and Yu. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).

Crosignani, B.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Share, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Di Porto, P.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Share, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Drummond, P. D.

Duree, G. C.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Share, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Etrich, C.

Goldstein, H.

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1980), Chap. 3.

Gorshkov, K. A.

K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981).

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, J. Opt. Quantum Electron. 28, 1691 (1996).

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).

Kivshar, Yu.

C. Clausen, O. Bang, and Yu. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).

Kivshar, Yu. S.

See also the stability analysis for the parametric three-wave mixing by A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996) ; A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).

See also the stability analysis for the parametric three-wave mixing by A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996) ; A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995); V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995); V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

Lederer, F.

Leo, G.

Lisak, M.

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995); V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

Luther-Davies, B.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).

Malomed, B.

Malomed, B. A.

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995); V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

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).

Mitchell, D. J.

See, e.g., L. Poladian, A. W. Snyder, and D. J. Mitchell, Opt. Commun. 85, 59 (1991).

Neurgaonkar, R. R.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Share, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Ostrovsky, L. A.

K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981).

Peschel, U.

Poladian, L.

See, e.g., L. Poladian, A. W. Snyder, and D. J. Mitchell, Opt. Commun. 85, 59 (1991).

Reynaud, F.

See, e.g., F. Reynaud and A. Barthelemy, in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), p. 319.

Salamo, G.

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

Salamo, G. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Share, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Schiek, R.

Segev, M.

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

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Share, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Share, E. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Share, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Shih, M.

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

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Share, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Snyder, A. W.

See, e.g., L. Poladian, A. W. Snyder, and D. J. Mitchell, Opt. Commun. 85, 59 (1991).

Sohler, W.

Steblina, V. V.

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995); V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995); V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

Stegeman, G. I.

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

G. I. Stegeman, D. J. Hagan, and L. Torner, J. Opt. Quantum Electron. 28, 1691 (1996).

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).

M. J. Werner and P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993) ; D. M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995) ; C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A PLRAAN 52, R3444 (1995).

Tikhonenko, V.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, J. Opt. Quantum Electron. 28, 1691 (1996).

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).

M. J. Werner and P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993) ; D. M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995) ; C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A PLRAAN 52, R3444 (1995).

Torruellas, W. E.

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

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).

Trillo, S.

See also the stability analysis for the parametric three-wave mixing by A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996) ; A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).

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).

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).

Werner, M. J.

Yariv, A.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Share, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

J. Opt. Quantum Electron.

G. I. Stegeman, D. J. Hagan, and L. Torner, J. Opt. Quantum Electron. 28, 1691 (1996).

J. Opt. Soc. Am. B

Opt. Commun.

See, e.g., L. Poladian, A. W. Snyder, and D. J. Mitchell, Opt. Commun. 85, 59 (1991).

Opt. Lett.

Phys. Rev. A

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995); V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

Phys. Rev. Lett.

See also the stability analysis for the parametric three-wave mixing by A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996) ; A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).

C. Clausen, O. Bang, and Yu. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Share, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

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).

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).

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

Physica D

K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981).

Other

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1980), Chap. 3.

See, e.g., F. Reynaud and A. Barthelemy, in Guided Wave Nonlinear Optics, D. B. Ostrowsky and R. Reinisch, eds. (Kluwer, Dordrecht, The Netherlands, 1992), p. 319.

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