Abstract

We study basic properties of quiescent and rotating multipole-mode solitons supported by axially symmetric Bessel lattices in a medium with defocusing cubic nonlinearity. The solitons can be found in different rings of the lattice and are stable when the propagation constant exceeds the critical value, provided that the lattice is deep enough. In a high-power limit the multipole-mode solitons feature a multi-ring structure.

© 2005 Optical Society of America

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References

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  1. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef] [PubMed]
  2. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  3. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  4. Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
    [CrossRef] [PubMed]
  5. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
    [CrossRef] [PubMed]
  6. J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
    [CrossRef] [PubMed]
  7. J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, "Necklacelike solitons in optically induced photonic lattices," Phys. Rev. Lett. 94, 113902 (2005).
    [CrossRef] [PubMed]
  8. B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642 (2003).
    [CrossRef]
  9. J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297 (2000).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  12. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable ring-profile vortex solitons in Bessel optical lattices," Phys. Rev. Lett. 94, 043902 (2005).
    [CrossRef] [PubMed]
  13. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Rotary dipole-mode solitons in Bessel optical lattices," J. Opt. B: Quantum Semiclass. Opt. 6, 444 (2004).
    [CrossRef]
  14. Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices," Phys. Rev. E 70, 065602(R) (2004).
    [CrossRef]
  15. D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable spatiotemporal solitons in Bessel optical lattices," Phys. Rev. Lett. 95, 023902 (2005).
    [CrossRef] [PubMed]
  16. A. Desyatnikov, D. Neshev, E. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. Garcia-Ripoll, and V. Perez-Garcia, "Multipole spatial vector solitons," Opt. Lett. 26, 435 (2001).
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  17. A. S. Desyatnikov, D. Neshev, E. A. Osrovskaya, Y. S. Kivshar, G. McCarthy, W. Krolikowski, and B. Luther-Davies, "Multipole composite spatial solitons: theory and experiment," J. Opt. Soc. Am. B 19, 586 (2002).
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  18. A. M. Glass and J. Strait, in "Photorefractive Materials and their Applications I," P. Günter and J. P. Huignard eds., (Springer, Berlin, 1988) pp. 237-262.

Europhys. Lett. (1)

B. B. Baizakov, B. A. Malomed, and M. Salerno, "Multidimensional solitons in periodic potentials," Europhys. Lett. 63, 642 (2003).
[CrossRef]

J. Opt. A: Pure. Appl. Opt. (1)

S. H. Tao, X.-C. Yuan, and B. S. Ahluwalia, "The generation of an array of nondiffracting beams by a single composite computer generated hologram," J. Opt. A: Pure. Appl. Opt. 7, 40 (2005).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt. (1)

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Rotary dipole-mode solitons in Bessel optical lattices," J. Opt. B: Quantum Semiclass. Opt. 6, 444 (2004).
[CrossRef]

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

Nature (1)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. Arlt and K. Dholakia, "Generation of high-order Bessel beams by use of an axicon," Opt. Commun. 177, 297 (2000).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. E (1)

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices," Phys. Rev. E 70, 065602(R) (2004).
[CrossRef]

Phys. Rev. Lett. (8)

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, "Stable spatiotemporal solitons in Bessel optical lattices," Phys. Rev. Lett. 95, 023902 (2005).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Rotary solitons in Bessel optical lattices," Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable ring-profile vortex solitons in Bessel optical lattices," Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, "Necklacelike solitons in optically induced photonic lattices," Phys. Rev. Lett. 94, 113902 (2005).
[CrossRef] [PubMed]

Other (1)

A. M. Glass and J. Strait, in "Photorefractive Materials and their Applications I," P. Günter and J. P. Huignard eds., (Springer, Berlin, 1988) pp. 237-262.

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Figures (6)

Fig. 1.
Fig. 1.

Profiles of dipole-mode solitons at b = 2.49 , p = 15 (a), and b = 0.42 , p = 15 (b). Profiles of quadrupole-mode solitons at b = 2.79 , p = 20 (c), and b = 0.58 , p = 20 (d).

Fig. 2.
Fig. 2.

(a) Energy flow vs propagation constant for the dipole-mode solitons. (b) Stability and instability (shaded) domains in the (p, b) plane. (c) The real part of the perturbation growth rate vs propagation constant at p = 15 . (d) Energy flow vs the propagation constant and (e) stability and instability domains in the (p, b) plane for the quadrupole-mode solitons. (f) The real part of the perturbation growth rate vs the propagation constant at p = 20 . Points marked by circles in (a) and (d) correspond to the profiles shown in Fig. 1.

Fig. 3.
Fig. 3.

(a) Profile of quadrupole-mode soliton at b = 1.9 , p = 20 . Real (b) and imaginary (c) parts of perturbation associated with oscillatory instability of soliton depicted in (a) with δ = 0.048 + 0.721i. (d) Profile of quadrupole-mode soliton at b = 0.4 , p = 10. (e) Real part of perturbation associated with exponential instability of soliton depicted in (d) with δ = 0.043 . Panels (b) and (c) are shown with the same vertical scale.

Fig. 4.
Fig. 4.

Evolution of an unstable (a) dipole-mode soliton for b = 0.9 , p = 15 , and (b) its quadrupole-mode counterpart for b = 0.4 , p = 10. In both cases, white noise with variance σnoise2 = 0.01 was added as initial perturbation.

Fig. 5.
Fig. 5.

Stable propagation of a dipole-mode soliton at b = 2, p = 15 (a) and quadrupole-mode one at b = 2 , p = 20 (b). In both cases, white noise with variance σnoise2 = 0.01 was added initially.

Fig. 6.
Fig. 6.

Stable clockwise rotation of a dipole-mode soliton corresponding to b = 2, p = 15 (a), and quadrupole-mode one corresponding to b = 2.79 , p = 20 (b).

Equations (4)

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i q ξ = 1 2 ( 2 q η 2 + 2 q ζ 2 ) + q q 2 pR η ζ q .
U = q 2 dηdζ .
iδu bu + 1 2 ( 2 u η 2 + 2 u ζ 2 ) w 2 v * 2 w 2 u + pRu = 0 ,
iδv bv + 1 2 ( 2 v η 2 + 2 v ζ 2 ) w 2 u * 2 w 2 v + pRv = 0 ,

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