Abstract

We present experimental observations of self-trapped rings carrying zero topological charge, along with simulations that display the self-focusing dynamics of the rings and their stability features in materials with saturable nonlinearities.

© 2001 Optical Society of America

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  1. R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
    [CrossRef]
  2. G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
    [CrossRef] [PubMed]
  3. H. Hauss, Appl. Phys. Lett. 8, 128 (1966).
    [CrossRef]
  4. P. S. Lomdahl, O. H. Olsen, and P. Christiansen, Phys. Lett. A 78, 125 (1980).
    [CrossRef]
  5. V. Afanasjev, Phys. Rev. E 52, 3153 (1995).
    [CrossRef]
  6. B. S. Azimov, V. T. Platonenko, and M. Sagatov, Sov. J. Quantum Electron. 21, 291 (1991).
    [CrossRef]
  7. M. Soljacic, S. Sears, and M. Segev, Phys. Rev. Lett. 81, 4851 (1998).
    [CrossRef]
  8. P. L. Kelly, Phys. Rev. Lett. 15, 1005 (1965).
    [CrossRef]
  9. Y. Chen and A. W. Synder, Electron. Lett. 27, 565 (1991).
    [CrossRef]
  10. J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
    [CrossRef] [PubMed]
  11. J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, R3170 (1994).
    [CrossRef]
  12. V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
    [CrossRef] [PubMed]
  13. W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
    [CrossRef]
  14. Z. Chen, M. Shih, M. Segev, D. W. Wilson, R. E. Muller, and P. Maker, Opt. Lett. 22, 1751 (1997).
    [CrossRef]
  15. L. Torner and D. V. Petrov, Electron. Lett. 33, 608 (1997).
    [CrossRef]
  16. Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
    [CrossRef] [PubMed]
  17. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
    [CrossRef] [PubMed]
  18. D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
    [CrossRef]
  19. C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
    [CrossRef] [PubMed]
  20. E. Eugenieva, D. N. Christodoulides, and M. Segev, Opt. Lett. 25, 972 (2000).
    [CrossRef]

2000 (3)

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

E. Eugenieva, D. N. Christodoulides, and M. Segev, Opt. Lett. 25, 972 (2000).
[CrossRef]

1999 (1)

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

1998 (1)

M. Soljacic, S. Sears, and M. Segev, Phys. Rev. Lett. 81, 4851 (1998).
[CrossRef]

1997 (3)

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

L. Torner and D. V. Petrov, Electron. Lett. 33, 608 (1997).
[CrossRef]

Z. Chen, M. Shih, M. Segev, D. W. Wilson, R. E. Muller, and P. Maker, Opt. Lett. 22, 1751 (1997).
[CrossRef]

1996 (1)

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

1995 (2)

1994 (2)

J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, R3170 (1994).
[CrossRef]

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

1991 (3)

Y. Chen and A. W. Synder, Electron. Lett. 27, 565 (1991).
[CrossRef]

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
[CrossRef] [PubMed]

B. S. Azimov, V. T. Platonenko, and M. Sagatov, Sov. J. Quantum Electron. 21, 291 (1991).
[CrossRef]

1980 (1)

P. S. Lomdahl, O. H. Olsen, and P. Christiansen, Phys. Lett. A 78, 125 (1980).
[CrossRef]

1966 (1)

H. Hauss, Appl. Phys. Lett. 8, 128 (1966).
[CrossRef]

1965 (1)

P. L. Kelly, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Afanasjev, V.

V. Afanasjev, Phys. Rev. E 52, 3153 (1995).
[CrossRef]

Akhmediev, N. N.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
[CrossRef] [PubMed]

Anastassiou, C.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Atai, J.

J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, R3170 (1994).
[CrossRef]

Azimov, B. S.

B. S. Azimov, V. T. Platonenko, and M. Sagatov, Sov. J. Quantum Electron. 21, 291 (1991).
[CrossRef]

Carvalho, M. I.

Chen, Y.

J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, R3170 (1994).
[CrossRef]

Y. Chen and A. W. Synder, Electron. Lett. 27, 565 (1991).
[CrossRef]

Chen, Z.

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Christiansen, P.

P. S. Lomdahl, O. H. Olsen, and P. Christiansen, Phys. Lett. A 78, 125 (1980).
[CrossRef]

Christodoulides, D. N.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

E. Eugenieva, D. N. Christodoulides, and M. Segev, Opt. Lett. 25, 972 (2000).
[CrossRef]

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

Christou, J.

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

Crosignani, B.

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

DiPorto, P.

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

Eugenieva, E.

Eugenieva, E. D.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Firth, W. J.

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Hauss, H.

H. Hauss, Appl. Phys. Lett. 8, 128 (1966).
[CrossRef]

Heatley, D. R.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
[CrossRef] [PubMed]

Kelly, P. L.

P. L. Kelly, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

Kip, D.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Lomdahl, P. S.

P. S. Lomdahl, O. H. Olsen, and P. Christiansen, Phys. Lett. A 78, 125 (1980).
[CrossRef]

Luther-Davies, B.

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

Maker, P.

Muller, R. E.

Musslimani, Z. H.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

Olsen, O. H.

P. S. Lomdahl, O. H. Olsen, and P. Christiansen, Phys. Lett. A 78, 125 (1980).
[CrossRef]

Petrov, D. V.

L. Torner and D. V. Petrov, Electron. Lett. 33, 608 (1997).
[CrossRef]

Platonenko, V. T.

B. S. Azimov, V. T. Platonenko, and M. Sagatov, Sov. J. Quantum Electron. 21, 291 (1991).
[CrossRef]

Sagatov, M.

B. S. Azimov, V. T. Platonenko, and M. Sagatov, Sov. J. Quantum Electron. 21, 291 (1991).
[CrossRef]

Sears, S.

M. Soljacic, S. Sears, and M. Segev, Phys. Rev. Lett. 81, 4851 (1998).
[CrossRef]

Segev, M.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

E. Eugenieva, D. N. Christodoulides, and M. Segev, Opt. Lett. 25, 972 (2000).
[CrossRef]

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

M. Soljacic, S. Sears, and M. Segev, Phys. Rev. Lett. 81, 4851 (1998).
[CrossRef]

Z. Chen, M. Shih, M. Segev, D. W. Wilson, R. E. Muller, and P. Maker, Opt. Lett. 22, 1751 (1997).
[CrossRef]

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

Shih, M.

Skryabin, D. V.

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Soljacic, M.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

M. Soljacic, S. Sears, and M. Segev, Phys. Rev. Lett. 81, 4851 (1998).
[CrossRef]

Soto-Crespo, J. M.

J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, R3170 (1994).
[CrossRef]

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
[CrossRef] [PubMed]

Stegeman, G. I.

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Synder, A. W.

Y. Chen and A. W. Synder, Electron. Lett. 27, 565 (1991).
[CrossRef]

Tikhonenko, V.

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

Torner, L.

L. Torner and D. V. Petrov, Electron. Lett. 33, 608 (1997).
[CrossRef]

Torres, J. P.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Valley, G. C.

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

Wilson, D. W.

Wright, E. M.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
[CrossRef] [PubMed]

Yariv, A.

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

Appl. Phys. Lett. (1)

H. Hauss, Appl. Phys. Lett. 8, 128 (1966).
[CrossRef]

Electron. Lett. (2)

Y. Chen and A. W. Synder, Electron. Lett. 27, 565 (1991).
[CrossRef]

L. Torner and D. V. Petrov, Electron. Lett. 33, 608 (1997).
[CrossRef]

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

Opt. Lett. (2)

Phys. Lett. A (1)

P. S. Lomdahl, O. H. Olsen, and P. Christiansen, Phys. Lett. A 78, 125 (1980).
[CrossRef]

Phys. Rev. A (2)

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright, and N. N. Akhmediev, Phys. Rev. A 44, 636 (1991).
[CrossRef] [PubMed]

J. Atai, Y. Chen, and J. M. Soto-Crespo, Phys. Rev. A 49, R3170 (1994).
[CrossRef]

Phys. Rev. E (1)

V. Afanasjev, Phys. Rev. E 52, 3153 (1995).
[CrossRef]

Phys. Rev. Lett. (8)

R. Y. Chiao, E. Garmire, and C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

M. Soljacic, S. Sears, and M. Segev, Phys. Rev. Lett. 81, 4851 (1998).
[CrossRef]

P. L. Kelly, Phys. Rev. Lett. 15, 1005 (1965).
[CrossRef]

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

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

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

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, Phys. Rev. Lett. 85, 4888 (2000).
[CrossRef] [PubMed]

Science (1)

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Sov. J. Quantum Electron. (1)

B. S. Azimov, V. T. Platonenko, and M. Sagatov, Sov. J. Quantum Electron. 21, 291 (1991).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Numerical simulations of ring solitons in a saturable nonlinear medium at high (top) and low (bottom) saturation. Intensity cross sections during propagation are shown. The ring undergoes compression in both cases. I0 is the maximum intensity upon the ring. The ring radius, R, is 13. In dimensional units (representing typical parameters in photorefractives), these results correspond, for example, to R=43 μm and a ring width of 8 μm for λ=0.488 μm, n=2.37, and Δnmax=0.0002. Propagation distance z=54 corresponds to 18  mm.

Fig. 2
Fig. 2

Same as Fig.  1 but for R=25. The high saturation (top) shrinks, and the low saturation (bottom) suffers azimuthal instability. In dimensional units, R=86 μm and the ring width is 8 μm for λ=0.488 μm, n=2.37, and Δnmax=0.0002. Propagation distance z=69 corresponds to 22.5  mm.

Fig. 3
Fig. 3

Experimental results for a photorefractive SBN:60 crystal. (a) Input ring of 12μm FWHM and a radius of 55 μm at an intensity ratio of 20. (b) Diffraction output. (c) Self-trapped output with nonlinearity on. (d), (e) Unstable soliton output for intensity ratios 0.33 and 0.10, respectively. (f) Same as (c) but with the c axis is rotated by 90°. The experiment is in the parameter regime of the simulation of Fig.  1.

Equations (1)

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iΨz+122Ψr2+1rΨr+1r22Ψϕ2+ΔnΨ2Ψ=0,

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