Abstract

We introduce multipole soliton complexes in optical lattices induced by nondiffracting parabolic beams. Despite the symmetry breaking dictated by the curvature of the lattice channels, we find that complex, asymmetric higher-order states can be stable. The unique topology of parabolic lattices affords new types of soliton motion: single solitons launched into the lattice with nonzero transverse momentum perform periodic oscillations along parabolic paths.

© 2008 Optical Society of America

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References

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    [CrossRef]

2007

2006

2005

Yu. B. Gaididei, P. L. Christiansen, P. G. Kevredekidis, H. Büttner, and A. R. Bishop, New J. Phys. 7, 52 (2005).
[CrossRef]

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

C. Lopez-Mariscal, M. Bandres, J. Gutierrez-Vega, and S. Chavez-Cerda, Opt. Express 13, 2364 (2005).
[CrossRef] [PubMed]

2004

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

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

2003

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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

D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

2001

D. V. Skryabin, Phys. Rev. E 64, 055601(R) (2001).
[CrossRef]

2000

Yu. B. Gaididei, S. F. Mingaleev, and P. L. Christiansen, Phys. Rev. E 62, R53 (2000).
[CrossRef]

Nature

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

New J. Phys.

Yu. B. Gaididei, P. L. Christiansen, P. G. Kevredekidis, H. Büttner, and A. R. Bishop, New J. Phys. 7, 52 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

Yu. B. Gaididei, S. F. Mingaleev, and P. L. Christiansen, Phys. Rev. E 62, R53 (2000).
[CrossRef]

D. V. Skryabin, Phys. Rev. E 64, 055601(R) (2001).
[CrossRef]

Phys. Rev. Lett.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[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]

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

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Figures (4)

Fig. 1
Fig. 1

Parabolic lattice corresponding to a = 2 and b lin = 4 (a) and field modulus distributions for fundamental soliton (b) and (c), dipole soliton (d), and triple-mode solitons residing in the (e) first lattice channel and (f) first and second lattice channels. Propagation constant values are indicated on the plots. In all cases p = 4 .

Fig. 2
Fig. 2

(a) Energy flow versus b for fundamental solitons. The circles correspond to profiles shown in Figs. 1b, 1c. (b) Cutoffs and (c) ellipticity in low-power limit versus p for fundamental solitons. (d) Cutoffs versus p for dipole solitons. (e) Cutoffs for linear guided modes at p = 4 . (d) Energy flow versus b for soliton from the second lattice channel.

Fig. 3
Fig. 3

Stable propagation of (a) dipole soliton with b = 7.2 , (b) triple-mode soliton with b = 6 , and (c) five-hump soliton with b = 6 in the presence of noise with variance σ noise 2 = 0.01 at p = 4 . Field modulus distributions are shown at different distances.

Fig. 4
Fig. 4

(a) Maximal displacement along the ζ-axis and (b) period of soliton oscillations versus α. (c) Snapshot images showing soliton oscillations at α = 1 . Images are taken at ξ = 0 , ξ = d ξ 4 , and ξ = 3 d ξ 4 . The white line indicates the trajectory of the soliton center. In all cases the input soliton was taken at b = 6.5 and p = 2 .

Equations (2)

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i q ξ = 1 2 ( 2 q η 2 + 2 q ζ 2 ) E q q 2 + p R 1 + q 2 + p R ,
q nd = exp ( i b lin ξ ) π π A ( ϕ ) exp [ i ( 2 b lin ) 1 2 ( η cos ϕ + ζ sin ϕ ) ] d ϕ .

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