Abstract

We investigate experimentally the interaction of two-dimensional solitary beams in photorefractive strontium barium niobate crystal. We show that simultaneous collision of many solitons can result in complete annihilation of some of them. This effect depends on the relative phases of the solitons and may be useful for application in the formation of multiport waveguide junctions.

© 1998 Optical Society of America

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  1. M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 44, 408 (1994).
    [CrossRef]
  2. M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
    [CrossRef] [PubMed]
  3. D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
    [CrossRef]
  4. M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. D. Porto, Electron. Lett. 31, 826 (1995).
    [CrossRef]
  5. Z. Sheng, Y. Cui, N. Cheng, and Y. Wei, J. Opt. Soc. 13, 854 (1996).
  6. A. A. Zozulya, A. V. Mamaev, M. Saffman, and D. Anderson, Phys. Rev. A 54, 870 (1996); Europhys. Lett. 36, 419 (1996).
    [CrossRef]
  7. V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].
  8. S. Cowan, R. H. Enns, S. S. Rangnekar, and S. Sanghera, Can. J. Phys. 64, 311 (1986).
    [CrossRef]
  9. S. Gatz and J. Hermann, Opt. Lett. 17, 484 (1992).
    [CrossRef] [PubMed]
  10. A. W. Snyder and A. P. Sheppard, Opt. Lett. 18, 482 (1993).
    [CrossRef] [PubMed]
  11. M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996).
    [CrossRef] [PubMed]
  12. V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
    [CrossRef] [PubMed]
  13. G. S. Garcia-Quirino, M. D. Iturbe-Castillo, V. A. Vysloukh, J. J. Sánchez-Mondragón, S. I. Stepanov, G. Lugo-Martínez, and G. E. Torres-Cisneros, Opt. Lett. 22, 154 (1997).
    [CrossRef]
  14. H. Meng, G. Salamo, M.-F. Shih, and M. Segev, Opt. Lett. 22, 448 (1997).
    [CrossRef] [PubMed]
  15. W. Królikowski and S. A. Holmstrom, Opt. Lett. 22, 369 (1997).
    [CrossRef]
  16. A. W. Snyder, D. J. Mitchell, L. Poladian, and F. Ladouceur, Opt. Lett. 16, 21 (1991); A. W. Snyder, D. J. Mitchel, and Y. Kivshar, Mod. Phys. Lett. B 9, 1479 (1995).
  17. B. Luther-Davies and X. Yang, Opt. Lett. 17, 498 (1992).

1997 (3)

1996 (4)

M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996).
[CrossRef] [PubMed]

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

Z. Sheng, Y. Cui, N. Cheng, and Y. Wei, J. Opt. Soc. 13, 854 (1996).

A. A. Zozulya, A. V. Mamaev, M. Saffman, and D. Anderson, Phys. Rev. A 54, 870 (1996); Europhys. Lett. 36, 419 (1996).
[CrossRef]

1995 (2)

D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
[CrossRef]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. D. Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

1994 (2)

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 44, 408 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

1993 (1)

1992 (2)

B. Luther-Davies and X. Yang, Opt. Lett. 17, 498 (1992).

S. Gatz and J. Hermann, Opt. Lett. 17, 484 (1992).
[CrossRef] [PubMed]

1991 (1)

1986 (1)

S. Cowan, R. H. Enns, S. S. Rangnekar, and S. Sanghera, Can. J. Phys. 64, 311 (1986).
[CrossRef]

1971 (1)

V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].

Anderson, D.

A. A. Zozulya, A. V. Mamaev, M. Saffman, and D. Anderson, Phys. Rev. A 54, 870 (1996); Europhys. Lett. 36, 419 (1996).
[CrossRef]

Carvalho, M. I.

Cheng, N.

Z. Sheng, Y. Cui, N. Cheng, and Y. Wei, J. Opt. Soc. 13, 854 (1996).

Christodoulides, D. N.

Christou, J.

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

Cowan, S.

S. Cowan, R. H. Enns, S. S. Rangnekar, and S. Sanghera, Can. J. Phys. 64, 311 (1986).
[CrossRef]

Crosignani, B.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. D. Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Cui, Y.

Z. Sheng, Y. Cui, N. Cheng, and Y. Wei, J. Opt. Soc. 13, 854 (1996).

Enns, R. H.

S. Cowan, R. H. Enns, S. S. Rangnekar, and S. Sanghera, Can. J. Phys. 64, 311 (1986).
[CrossRef]

Garcia-Quirino, G. S.

Gatz, S.

Hermann, J.

Holmstrom, S. A.

Iturbe-Castillo, M. D.

G. S. Garcia-Quirino, M. D. Iturbe-Castillo, V. A. Vysloukh, J. J. Sánchez-Mondragón, S. I. Stepanov, G. Lugo-Martínez, and G. E. Torres-Cisneros, Opt. Lett. 22, 154 (1997).
[CrossRef]

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 44, 408 (1994).
[CrossRef]

Królikowski, W.

Ladouceur, F.

Lugo-Martínez, G.

Luther-Davies, B.

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

B. Luther-Davies and X. Yang, Opt. Lett. 17, 498 (1992).

Mamaev, A. V.

A. A. Zozulya, A. V. Mamaev, M. Saffman, and D. Anderson, Phys. Rev. A 54, 870 (1996); Europhys. Lett. 36, 419 (1996).
[CrossRef]

Marquez-Aguilar, P. A.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 44, 408 (1994).
[CrossRef]

Meng, H.

Mitchell, D. J.

Poladian, L.

Porto, P. D.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. D. Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Rangnekar, S. S.

S. Cowan, R. H. Enns, S. S. Rangnekar, and S. Sanghera, Can. J. Phys. 64, 311 (1986).
[CrossRef]

Saffman, M.

A. A. Zozulya, A. V. Mamaev, M. Saffman, and D. Anderson, Phys. Rev. A 54, 870 (1996); Europhys. Lett. 36, 419 (1996).
[CrossRef]

Salamo, G.

H. Meng, G. Salamo, M.-F. Shih, and M. Segev, Opt. Lett. 22, 448 (1997).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. D. Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Sánchez-Mondragón, J. J.

G. S. Garcia-Quirino, M. D. Iturbe-Castillo, V. A. Vysloukh, J. J. Sánchez-Mondragón, S. I. Stepanov, G. Lugo-Martínez, and G. E. Torres-Cisneros, Opt. Lett. 22, 154 (1997).
[CrossRef]

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 44, 408 (1994).
[CrossRef]

Sanghera, S.

S. Cowan, R. H. Enns, S. S. Rangnekar, and S. Sanghera, Can. J. Phys. 64, 311 (1986).
[CrossRef]

Segev, M.

H. Meng, G. Salamo, M.-F. Shih, and M. Segev, Opt. Lett. 22, 448 (1997).
[CrossRef] [PubMed]

M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. D. Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].

Sheng, Z.

Z. Sheng, Y. Cui, N. Cheng, and Y. Wei, J. Opt. Soc. 13, 854 (1996).

Sheppard, A. P.

Shih, M.

M. Shih and M. Segev, Opt. Lett. 21, 1538 (1996).
[CrossRef] [PubMed]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. D. Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

Shih, M.-F.

Snyder, A. W.

Stepanov, S.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 44, 408 (1994).
[CrossRef]

Stepanov, S. I.

Tikhonenko, V.

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

Torres-Cisneros, G. E.

Valley, G. C.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. D. Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Vysloukh, V.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 44, 408 (1994).
[CrossRef]

Vysloukh, V. A.

Wei, Y.

Z. Sheng, Y. Cui, N. Cheng, and Y. Wei, J. Opt. Soc. 13, 854 (1996).

Yang, X.

B. Luther-Davies and X. Yang, Opt. Lett. 17, 498 (1992).

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].

Zozulya, A. A.

A. A. Zozulya, A. V. Mamaev, M. Saffman, and D. Anderson, Phys. Rev. A 54, 870 (1996); Europhys. Lett. 36, 419 (1996).
[CrossRef]

Appl. Phys. Lett. (1)

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sánchez-Mondragón, S. Stepanov, and V. Vysloukh, Appl. Phys. Lett. 44, 408 (1994).
[CrossRef]

Can. J. Phys. (1)

S. Cowan, R. H. Enns, S. S. Rangnekar, and S. Sanghera, Can. J. Phys. 64, 311 (1986).
[CrossRef]

Electron. Lett. (1)

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. D. Porto, Electron. Lett. 31, 826 (1995).
[CrossRef]

J. Opt. Soc. (1)

Z. Sheng, Y. Cui, N. Cheng, and Y. Wei, J. Opt. Soc. 13, 854 (1996).

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

Opt. Lett. (8)

Phys. Rev. A (1)

A. A. Zozulya, A. V. Mamaev, M. Saffman, and D. Anderson, Phys. Rev. A 54, 870 (1996); Europhys. Lett. 36, 419 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

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

M. Segev, G. C. Valley, B. Crosignani, P. D. Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Zh. Eksp. Teor. Fiz. (1)

V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].

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Figures (5)

Fig. 1
Fig. 1

Schematic of the three-soliton interaction.

Fig. 2
Fig. 2

Experimental setup: BS’s, beam splitters; M1–M4, mirrors; L1, L2, lenses; PZT, piezoelectric transducer; V, voltage.

Fig. 3
Fig. 3

Light-intensity distribution of interacting beams on the exit face of the crystal; PA=PB=0.4 µW, PC=1.7 µW. (a) Relative phase between A and Cπ/2, (b) relative phase between A and C-π/2.

Fig. 4
Fig. 4

Another example of three-soliton collision: in-complete annihilation. In this case PA=PB=2.4 µW, PC=2.7 µW; the relative phase between C and A again is -π/2.

Fig. 5
Fig. 5

Light-intensity pattern on the exit face of the crystal that corresponds to the waveguide structure formed by colliding solitons. This picture was taken a moment after both side beams were blocked.

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