Abstract

We address the existence of ring solitons broken by several nodes in a defocusing saturable nonlinear medium with an imprinted Bessel optical lattice. Such a multipolelike soliton is composed of two or more arc patterns with opposite phase between the adjacent components. The width of existence domain is determined only by the saturation degree of medium. The maximum number of soliton components depends on the radius of the lattice ring, where they reside. Those novel solitons can be trapped entirely on any ring of the Bessel lattice provided that the lattice is modulated deep enough. This study offers a smooth transition from the multipole soliton to necklace soliton.

© 2008 Optical Society of America

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  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  2. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  3. J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
    [CrossRef]
  4. A. Vasara, J. Turunen, and A. Friberg, J. Opt. Soc. Am. A 6, 1748 (1989).
    [CrossRef] [PubMed]
  5. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
    [CrossRef] [PubMed]
  6. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
    [CrossRef] [PubMed]
  7. Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
    [CrossRef] [PubMed]
  8. Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Express 13, 10703 (2005).
    [CrossRef] [PubMed]
  9. R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Opt. Express 14, 2825 (2006).
    [CrossRef] [PubMed]
  10. L. Dong, H. Wang, W. Zhou, X. Yang, X. Lv, and H. Chen, Opt. Express 16, 5649 (2008).
    [CrossRef] [PubMed]
  11. D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
    [CrossRef] [PubMed]
  12. X. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
    [CrossRef] [PubMed]
  13. A. S. Desyatnikov, Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, Opt. Lett. 27, 634 (2002).
    [CrossRef]
  14. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. 29, 1662 (2004).
    [CrossRef] [PubMed]
  15. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 98, 053901 (2007).
    [CrossRef] [PubMed]
  16. M. Soljačić, S. Sears, and M. Segev, Phys. Rev. Lett. 81, 4851 (1998).
    [CrossRef]
  17. T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
    [CrossRef] [PubMed]
  18. J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, Phys. Rev. Lett. 94, 113902 (2005).
    [CrossRef] [PubMed]
  19. E. Smirnov, C. E. Rüter, D. Kip, Y. V. Kartashov, and L. Torner, Opt. Lett. 32, 1950 (2007).
    [CrossRef] [PubMed]
  20. B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. E 74, 066615 (2006).
    [CrossRef]
  21. Y. Kartashov, V. Vysloukh, and L. Torner, Opt. Express 12, 2831 (2004).
    [CrossRef] [PubMed]

2008 (1)

2007 (3)

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

E. Smirnov, C. E. Rüter, D. Kip, Y. V. Kartashov, and L. Torner, Opt. Lett. 32, 1950 (2007).
[CrossRef] [PubMed]

2006 (3)

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. E 74, 066615 (2006).
[CrossRef]

X. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Opt. Express 14, 2825 (2006).
[CrossRef] [PubMed]

2005 (5)

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Express 13, 10703 (2005).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef] [PubMed]

2004 (3)

2003 (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

2002 (1)

2000 (1)

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

1998 (1)

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

1989 (1)

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Arlt, J.

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

Baizakov, B. B.

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. E 74, 066615 (2006).
[CrossRef]

Bezryadina, A.

Buccoliero, D.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

Carretero-González, R.

Chen, H.

Chen, Z.

X. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

Christodoulides, D. N.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Denz, C.

Desyatnikov, A. S.

Dholakia, K.

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

Dong, L.

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Egorov, A. A.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Ferrando, A.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Fischer, R.

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Frantzeskakis, D. J.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef] [PubMed]

Friberg, A.

Gaeta, A. L.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

Grow, T. D.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

Ishaaya, A. A.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

Kaiser, F.

Kartashov, Y.

Kartashov, Y. V.

E. Smirnov, C. E. Rüter, D. Kip, Y. V. Kartashov, and L. Torner, Opt. Lett. 32, 1950 (2007).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Express 13, 10703 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef] [PubMed]

Kevrekidis, P. G.

X. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef] [PubMed]

Kip, D.

Kivshar, Y. S.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, Opt. Express 14, 2825 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov, Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, Opt. Lett. 27, 634 (2002).
[CrossRef]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

Krolikowski, W.

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Lopez-Aguayo, S.

Lv, X.

Makasyuk, I.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

Malomed, B. A.

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. E 74, 066615 (2006).
[CrossRef]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Express 13, 10703 (2005).
[CrossRef] [PubMed]

Martin, H.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef] [PubMed]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Motzek, K.

Neshev, D. N.

Rüter, C. E.

Salerno, M.

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. E 74, 066615 (2006).
[CrossRef]

Sears, S.

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

Segev, M.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

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

Smirnov, E.

Soljacic, M.

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

Sukhorukov, A. A.

Torner, L.

E. Smirnov, C. E. Rüter, D. Kip, Y. V. Kartashov, and L. Torner, Opt. Lett. 32, 1950 (2007).
[CrossRef] [PubMed]

Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Express 13, 10703 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef] [PubMed]

Y. Kartashov, V. Vysloukh, and L. Torner, Opt. Express 12, 2831 (2004).
[CrossRef] [PubMed]

Turunen, J.

Vasara, A.

Vuong, L. T.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

Vysloukh, V.

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Express 13, 10703 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef] [PubMed]

Wang, H.

Wang, X.

X. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef] [PubMed]

Weilnau, C.

Yang, J.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

Yang, X.

Zhou, W.

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

Nature (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. E (1)

B. B. Baizakov, B. A. Malomed, and M. Salerno, Phys. Rev. E 74, 066615 (2006).
[CrossRef]

Phys. Rev. Lett. (9)

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

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

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, Phys. Rev. Lett. 99, 133902 (2007).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

X. Wang, Z. Chen, and P. G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Other (1)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

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Figures (4)

Fig. 1
Fig. 1

(a) Energy flow versus propagation constant for two- (thin solid curve) and four- (thick dashed curve) pole solitons residing on the first ring of the zero-order Bessel lattice at p = 15 . (b)–(d) Profiles of broken ring solitons corresponding to the points marked by circles in (a). The concentric circles in the x y plane denote the position of the lattice ring.

Fig. 2
Fig. 2

Properties of broken ring solitons residing on the third ring of the first-order lattice. (a) and (b) Energy flow and existence domains of four-pole ring solitons at s = 1 . (c) Lower and upper cutoffs of two-pole ring solitons versus s at p = 44 . (d) Real part of perturbation growth rate versus b of four-pole solitons at s = 1 . (e) and (f) Intensity contour plots of two- and four-pole solitons at (e) z = 512 , b = 1.7 , s = 0.5 , and p = 35 and (f) b = 0.6 , s = 1 , and p = 26 . White noise with variance σ noise 2 = 0.01 was added into the initial input, and the lattices were plotted for identifying the location of solitons in (e) and (f).

Fig. 3
Fig. 3

(a) Intensity distribution of six-pole ring solitons residing on the fourth ring of the third-order lattice at b = 1.2 , s = 1.5 , p = 40 , and z = 512 . (b) Nonuniform six-pole solitons residing on the fifth ring of the fifth-order lattice at b = 2.5 , s = 0.2 , p = 100 , and z = 1600 . (c) and (d) Rotation of solitons same as (b) but under an azimuthally twist phase perturbation in the form of exp ( i 4 θ ) at (c) z = 160 and (d) 320. White noise was added into the initial input.

Fig. 4
Fig. 4

(a) Energy flow versus propagation constant for four- and 24-pole ring solitons. (b) Lower and upper cutoffs and stable area versus the number of poles N. (c) and (d) Twelve-pole soliton with b = 2.2 , U = 1035 and 40-pole soliton with b = 2.14 , U = 12.2 at z = 512 ; s = 0.8 and p = 40 in (b)–(d). The solitons reside on the second ring of the second-order lattice.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

i A z + 1 2 ( 2 A x 2 + 2 A y 2 ) A 2 1 + s A 2 A + p R A = 0 ,
λ u = 1 2 ( 2 v x 2 + 2 v y 2 ) + b v p R v + q 2 + s q 4 ( 1 + s q 2 ) 2 v ,
λ v = 1 2 ( 2 u x 2 + 2 u y 2 ) b u + p R u 3 q 2 + s q 4 ( 1 + s q 2 ) 2 u .

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