Abstract

Internal modes and internal oscillation of necklace solitons in Bessel photonic lattices imprinted in self- defocusing and self-focusing materials are investigated. Under the same parameters, necklace solitons in self- focusing material possess larger power than that of self-defocusing material, and the stability of solitons in defocusing material is better than in focusing material. It is shown that the internal modes have both real and imaginary parts in such cases, differing from the one-dimensional case. While white noise gives rise to jitter of the intensity of stable necklace solitons, the stable solitons perform long-distance and quasi-periodic oscillation of intensity and shape under the perturbation of internal modes, and the solitons in self-defocusing material experience larger oscillation amplitude than that in self-focusing material.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  28. J. A. Gonzlez , A. Bellorn , and L. E. Guerrero , Internal modes of sine-Gordon solitons in the presence of spatiotemporal perturbations, Phys. Rev. E 65, 065601 (2002).
    [CrossRef]
  29. J. K. Yang , Internal oscillations and instability characteristics of (2+1)-dimensional solitons in a saturable nonlinear medium, Phys. Rev. E 66, 026601 (2002).
    [CrossRef]
  30. L. W. Dong , F. W. Ye , J. D. Wang , T. Cai , and Y. P. Li , Internal modes of localized optical vortex soliton in a cubic-quintic nonlinear medium, Physica D (Amsterdam) 194, 219226(2004).
    [CrossRef]
  31. Y. V. Kartashov , R. Carretero-Gonzlez , B. A. Malomed , V. A. Vysloukh , and L. Torner , Multipole-mode solitons in Bessel optical lattices, Opt. Express 13, 1070310710 (2005).
    [CrossRef] [PubMed]
  32. L. W. Dong , H. Wang , W. D. Zhou , X. Y. Yang , X. Lv , and H. Y. Chen , Necklace solitons and ring solitons in Bessel optical lattices, Opt. Express 16, 56495655 (2008).
    [CrossRef] [PubMed]

2010

J. C. Liang , Z. B. Cai , L. Yi , and H. C. Wang , Bessel solitary waves in strongly nonlocal nonlinear media with distributed parameters, Opt. Commun. 283, 386390 (2010).
[CrossRef]

2008

2007

X. S. Wang , A. Bezryadina , Z. G. Chen , K. G. Makris , D. N. Christodoulides , and G. I. Stegeman , Observation of two-dimensional surface solitons, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

2006

2005

2004

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. Lederer , Y. Min , and W. Sohler , Observation of discrete quadratic solitons, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

A. Fratalocchi , G. Assanto , K. A. Brzdakiewicz , and M. A. Karpierz , Discrete propagation and spatial solitons in nematic liquid crystals, Opt. Lett. 29, 15301532 (2004).
[CrossRef] [PubMed]

L. W. Dong , F. W. Ye , J. D. Wang , T. Cai , and Y. P. Li , Internal modes of localized optical vortex soliton in a cubic-quintic nonlinear medium, Physica D (Amsterdam) 194, 219226(2004).
[CrossRef]

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, 444447 (2004).
[CrossRef]

B. Eiermann , Th. Anker , M. Albiez , M. Taglieber , P. Treutlein , K.-P. Marzlin , and M. K. Oberthaler , Bright Bose-Einstein gap solitons of atoms with repulsive interaction, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Z. G. Chen , H. Martin , E. D. Eugenieva , J. 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]

2003

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, 147150 (2003).
[CrossRef] [PubMed]

M. Sato , B. E. Hubbard , A. J. Sievers , B. Llic , D. A. Czaplewski , and H. C. Craighead , Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array, Phys. Rev. Lett. 90, 044102 (2003).
[CrossRef] [PubMed]

2002

J. A. Gonzlez , A. Bellorn , and L. E. Guerrero , Internal modes of sine-Gordon solitons in the presence of spatiotemporal perturbations, Phys. Rev. E 65, 065601 (2002).
[CrossRef]

J. K. Yang , Internal oscillations and instability characteristics of (2+1)-dimensional solitons in a saturable nonlinear medium, Phys. Rev. E 66, 026601 (2002).
[CrossRef]

2001

A. Trombettoni and A. Smerzi , Discrete solitons and breathers with dilute Bose-Einstein condensates, Phys. Rev. Lett. 86, 23532356 (2001).
[CrossRef] [PubMed]

2000

A. Xie , L. Meer , W. Hoff , and R. H. Austin , Long-lived amide I vibrational modes in myoglobin, Phys. Rev. Lett. 84, 54355438(2000).
[CrossRef] [PubMed]

J. Arlt and K. Dholakia , Generation of high-order Bessel beams by use of an axicon, Opt. Commun. 177, 297301 (2000).
[CrossRef]

1998

D. E. Pelinovsky , Y. S. Kivshar , and V. V. Afanasjev , Internal modes of envelope solitons, Physica D (Amsterdam) 116, 121142 (1998).
[CrossRef]

Y. S. Kivshar , D. E. Pelinovsky , T. Cretegny , and M. Peyrard , Internal modes of solitary waves, Phys. Rev. Lett. 80, 50325035 (1998).
[CrossRef]

H. S. Eisenberg , Y. Silberberg , R. Morandotti , A. R. Boyd , and J. S. Aitchison , Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett. 81, 33833386 (1998).
[CrossRef]

1997

1989

1988

1986

D. K. Campbell , M. Peyrard , and P. Sodano , Kink-antikink interactions in the double sine-Gordon equation, Physica D (Amsterdam) 19, 165205 (1986).
[CrossRef]

1983

D. K. Campbell , J. F. Schonfeld , and C. A. Wingate , Resonance structure in kink-antikink interactions in 4 theory, Physica D (Amsterdam) 9, 132 (1983).
[CrossRef]

M. Peyrard and D. K. Campbell , Kink-antikink interactions in a modified sine-Gordon model, Physica D (Amsterdam) 9, 3351(1983).
[CrossRef]

Afanasiev, V. V.

Afanasjev, V. V.

D. E. Pelinovsky , Y. S. Kivshar , and V. V. Afanasjev , Internal modes of envelope solitons, Physica D (Amsterdam) 116, 121142 (1998).
[CrossRef]

Aguayo, S. L.

Aitchison, J. S.

H. S. Eisenberg , Y. Silberberg , R. Morandotti , A. R. Boyd , and J. S. Aitchison , Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett. 81, 33833386 (1998).
[CrossRef]

Albiez, M.

B. Eiermann , Th. Anker , M. Albiez , M. Taglieber , P. Treutlein , K.-P. Marzlin , and M. K. Oberthaler , Bright Bose-Einstein gap solitons of atoms with repulsive interaction, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Anker, Th.

B. Eiermann , Th. Anker , M. Albiez , M. Taglieber , P. Treutlein , K.-P. Marzlin , and M. K. Oberthaler , Bright Bose-Einstein gap solitons of atoms with repulsive interaction, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Arlt, J.

J. Arlt and K. Dholakia , Generation of high-order Bessel beams by use of an axicon, Opt. Commun. 177, 297301 (2000).
[CrossRef]

Assanto, G.

Austin, R. H.

A. Xie , L. Meer , W. Hoff , and R. H. Austin , Long-lived amide I vibrational modes in myoglobin, Phys. Rev. Lett. 84, 54355438(2000).
[CrossRef] [PubMed]

Bellorn, A.

J. A. Gonzlez , A. Bellorn , and L. E. Guerrero , Internal modes of sine-Gordon solitons in the presence of spatiotemporal perturbations, Phys. Rev. E 65, 065601 (2002).
[CrossRef]

Bezryadina, A.

X. S. Wang , A. Bezryadina , Z. G. Chen , K. G. Makris , D. N. Christodoulides , and G. I. Stegeman , Observation of two-dimensional surface solitons, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Z. G. Chen , H. Martin , E. D. Eugenieva , J. 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]

Boyd, A. R.

H. S. Eisenberg , Y. Silberberg , R. Morandotti , A. R. Boyd , and J. S. Aitchison , Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett. 81, 33833386 (1998).
[CrossRef]

Brzdakiewicz, K. A.

Cai, T.

L. W. Dong , F. W. Ye , J. D. Wang , T. Cai , and Y. P. Li , Internal modes of localized optical vortex soliton in a cubic-quintic nonlinear medium, Physica D (Amsterdam) 194, 219226(2004).
[CrossRef]

Cai, Z. B.

J. C. Liang , Z. B. Cai , L. Yi , and H. C. Wang , Bessel solitary waves in strongly nonlocal nonlinear media with distributed parameters, Opt. Commun. 283, 386390 (2010).
[CrossRef]

Campbell, D. K.

D. K. Campbell , M. Peyrard , and P. Sodano , Kink-antikink interactions in the double sine-Gordon equation, Physica D (Amsterdam) 19, 165205 (1986).
[CrossRef]

D. K. Campbell , J. F. Schonfeld , and C. A. Wingate , Resonance structure in kink-antikink interactions in 4 theory, Physica D (Amsterdam) 9, 132 (1983).
[CrossRef]

M. Peyrard and D. K. Campbell , Kink-antikink interactions in a modified sine-Gordon model, Physica D (Amsterdam) 9, 3351(1983).
[CrossRef]

Carretero-Gonzlez, R.

Chen, H. Y.

Chen, Z. G.

X. S. Wang , A. Bezryadina , Z. G. Chen , K. G. Makris , D. N. Christodoulides , and G. I. Stegeman , Observation of two-dimensional surface solitons, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

X. S. Wang , Z. G. Chen , and J. K. Yang , Guiding light in optically induced ring lattices with a low-refractive-index core, Opt. Lett. 31, 18871889 (2006).
[CrossRef] [PubMed]

X. S. Wang , Z. G. Chen , and P. G. Kevrekidis , Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices, Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef] [PubMed]

Z. G. Chen , H. Martin , E. Eugenieva , J. J. Xu , and J. K. Yang , Formation of discrete solitons in light-induced photonic lattices, Opt. Express 13, 18161826 (2005).
[CrossRef] [PubMed]

Z. G. Chen , H. Martin , E. D. Eugenieva , J. 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]

Christodoulides, D. N.

X. S. Wang , A. Bezryadina , Z. G. Chen , K. G. Makris , D. N. Christodoulides , and G. I. Stegeman , Observation of two-dimensional surface solitons, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

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, 147150 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph , Discrete self-focusing in nonlinear arrays of coupled waveguides, Opt. Lett. 13, 794796(1988).
[CrossRef] [PubMed]

Chu, P. L.

Craighead, H. C.

M. Sato , B. E. Hubbard , A. J. Sievers , B. Llic , D. A. Czaplewski , and H. C. Craighead , Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array, Phys. Rev. Lett. 90, 044102 (2003).
[CrossRef] [PubMed]

Cretegny, T.

Y. S. Kivshar , D. E. Pelinovsky , T. Cretegny , and M. Peyrard , Internal modes of solitary waves, Phys. Rev. Lett. 80, 50325035 (1998).
[CrossRef]

Czaplewski, D. A.

M. Sato , B. E. Hubbard , A. J. Sievers , B. Llic , D. A. Czaplewski , and H. C. Craighead , Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array, Phys. Rev. Lett. 90, 044102 (2003).
[CrossRef] [PubMed]

Desyatnikov, A. S.

Dholakia, K.

J. Arlt and K. Dholakia , Generation of high-order Bessel beams by use of an axicon, Opt. Commun. 177, 297301 (2000).
[CrossRef]

Dong, L. W.

L. W. Dong , H. Wang , W. D. Zhou , X. Y. Yang , X. Lv , and H. Y. Chen , Necklace solitons and ring solitons in Bessel optical lattices, Opt. Express 16, 56495655 (2008).
[CrossRef] [PubMed]

L. W. Dong , F. W. Ye , J. D. Wang , T. Cai , and Y. P. Li , Internal modes of localized optical vortex soliton in a cubic-quintic nonlinear medium, Physica D (Amsterdam) 194, 219226(2004).
[CrossRef]

Efremidis, N. K.

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, 147150 (2003).
[CrossRef] [PubMed]

Egorov, A. A.

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, 444447 (2004).
[CrossRef]

Eiermann, B.

B. Eiermann , Th. Anker , M. Albiez , M. Taglieber , P. Treutlein , K.-P. Marzlin , and M. K. Oberthaler , Bright Bose-Einstein gap solitons of atoms with repulsive interaction, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Eisenberg, H. S.

H. S. Eisenberg , Y. Silberberg , R. Morandotti , A. R. Boyd , and J. S. Aitchison , Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett. 81, 33833386 (1998).
[CrossRef]

Eugenieva, E.

Eugenieva, E. D.

Z. G. Chen , H. Martin , E. D. Eugenieva , J. 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]

Fischer, R.

Fleischer, J. W.

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, 147150 (2003).
[CrossRef] [PubMed]

Fratalocchi, A.

Friberg, A. T.

Gonzlez, J. A.

J. A. Gonzlez , A. Bellorn , and L. E. Guerrero , Internal modes of sine-Gordon solitons in the presence of spatiotemporal perturbations, Phys. Rev. E 65, 065601 (2002).
[CrossRef]

Guerrero, L. E.

J. A. Gonzlez , A. Bellorn , and L. E. Guerrero , Internal modes of sine-Gordon solitons in the presence of spatiotemporal perturbations, Phys. Rev. E 65, 065601 (2002).
[CrossRef]

Hoff, W.

A. Xie , L. Meer , W. Hoff , and R. H. Austin , Long-lived amide I vibrational modes in myoglobin, Phys. Rev. Lett. 84, 54355438(2000).
[CrossRef] [PubMed]

Hubbard, B. E.

M. Sato , B. E. Hubbard , A. J. Sievers , B. Llic , D. A. Czaplewski , and H. C. Craighead , Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array, Phys. Rev. Lett. 90, 044102 (2003).
[CrossRef] [PubMed]

Iwanow, R.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. Lederer , Y. Min , and W. Sohler , Observation of discrete quadratic solitons, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Joseph, R. I.

Karpierz, M. A.

Kartashov, Y. V.

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]

Y. V. Kartashov , R. Carretero-Gonzlez , B. A. Malomed , V. A. Vysloukh , and L. Torner , Multipole-mode solitons in Bessel optical lattices, Opt. Express 13, 1070310710 (2005).
[CrossRef] [PubMed]

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, 444447 (2004).
[CrossRef]

Kevrekidis, P. G.

X. S. Wang , Z. G. Chen , and P. G. Kevrekidis , Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices, Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef] [PubMed]

Kivshar, Y. S.

R. Fischer , D. N. Neshev , S. L. Aguayo , A. S. Desyatnikov , A. A. Sukhorukov , W. Krolikowski , and Y. S. Kivshar , Observation of light localization in modulated Bessel optical lattices, Opt. Express 14, 28252830 (2006).
[CrossRef] [PubMed]

D. E. Pelinovsky , Y. S. Kivshar , and V. V. Afanasjev , Internal modes of envelope solitons, Physica D (Amsterdam) 116, 121142 (1998).
[CrossRef]

Y. S. Kivshar , D. E. Pelinovsky , T. Cretegny , and M. Peyrard , Internal modes of solitary waves, Phys. Rev. Lett. 80, 50325035 (1998).
[CrossRef]

V. V. Afanasiev , P. L. Chu , and Y. S. Kivshar , Breathing spatial solitons in non-Kerr media, Opt. Lett. 22, 13881390 (1997).
[CrossRef]

Y. S. Kivshar and B. A. Malomed , Dynamics of solitons in nearly integrable systems, Rev. Mod. Phys. 61, 763915 (1989).
[CrossRef]

Krolikowski, W.

Lederer, F.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. Lederer , Y. Min , and W. Sohler , Observation of discrete quadratic solitons, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Li, Y. P.

L. W. Dong , F. W. Ye , J. D. Wang , T. Cai , and Y. P. Li , Internal modes of localized optical vortex soliton in a cubic-quintic nonlinear medium, Physica D (Amsterdam) 194, 219226(2004).
[CrossRef]

Liang, J. C.

J. C. Liang , Z. B. Cai , L. Yi , and H. C. Wang , Bessel solitary waves in strongly nonlocal nonlinear media with distributed parameters, Opt. Commun. 283, 386390 (2010).
[CrossRef]

Llic, B.

M. Sato , B. E. Hubbard , A. J. Sievers , B. Llic , D. A. Czaplewski , and H. C. Craighead , Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array, Phys. Rev. Lett. 90, 044102 (2003).
[CrossRef] [PubMed]

Lv, X.

Makris, K. G.

X. S. Wang , A. Bezryadina , Z. G. Chen , K. G. Makris , D. N. Christodoulides , and G. I. Stegeman , Observation of two-dimensional surface solitons, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Malomed, B. A.

Martin, H.

Z. G. Chen , H. Martin , E. Eugenieva , J. J. Xu , and J. K. Yang , Formation of discrete solitons in light-induced photonic lattices, Opt. Express 13, 18161826 (2005).
[CrossRef] [PubMed]

Z. G. Chen , H. Martin , E. D. Eugenieva , J. 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]

Marzlin, K.-P.

B. Eiermann , Th. Anker , M. Albiez , M. Taglieber , P. Treutlein , K.-P. Marzlin , and M. K. Oberthaler , Bright Bose-Einstein gap solitons of atoms with repulsive interaction, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Meer, L.

A. Xie , L. Meer , W. Hoff , and R. H. Austin , Long-lived amide I vibrational modes in myoglobin, Phys. Rev. Lett. 84, 54355438(2000).
[CrossRef] [PubMed]

Min, Y.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. Lederer , Y. Min , and W. Sohler , Observation of discrete quadratic solitons, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Morandotti, R.

H. S. Eisenberg , Y. Silberberg , R. Morandotti , A. R. Boyd , and J. S. Aitchison , Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett. 81, 33833386 (1998).
[CrossRef]

Neshev, D. N.

Oberthaler, M. K.

B. Eiermann , Th. Anker , M. Albiez , M. Taglieber , P. Treutlein , K.-P. Marzlin , and M. K. Oberthaler , Bright Bose-Einstein gap solitons of atoms with repulsive interaction, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Pelinovsky, D. E.

Y. S. Kivshar , D. E. Pelinovsky , T. Cretegny , and M. Peyrard , Internal modes of solitary waves, Phys. Rev. Lett. 80, 50325035 (1998).
[CrossRef]

D. E. Pelinovsky , Y. S. Kivshar , and V. V. Afanasjev , Internal modes of envelope solitons, Physica D (Amsterdam) 116, 121142 (1998).
[CrossRef]

Pertsch, T.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. Lederer , Y. Min , and W. Sohler , Observation of discrete quadratic solitons, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Peyrard, M.

Y. S. Kivshar , D. E. Pelinovsky , T. Cretegny , and M. Peyrard , Internal modes of solitary waves, Phys. Rev. Lett. 80, 50325035 (1998).
[CrossRef]

D. K. Campbell , M. Peyrard , and P. Sodano , Kink-antikink interactions in the double sine-Gordon equation, Physica D (Amsterdam) 19, 165205 (1986).
[CrossRef]

M. Peyrard and D. K. Campbell , Kink-antikink interactions in a modified sine-Gordon model, Physica D (Amsterdam) 9, 3351(1983).
[CrossRef]

Sato, M.

M. Sato , B. E. Hubbard , A. J. Sievers , B. Llic , D. A. Czaplewski , and H. C. Craighead , Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array, Phys. Rev. Lett. 90, 044102 (2003).
[CrossRef] [PubMed]

Schiek, R.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. Lederer , Y. Min , and W. Sohler , Observation of discrete quadratic solitons, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Schonfeld, J. F.

D. K. Campbell , J. F. Schonfeld , and C. A. Wingate , Resonance structure in kink-antikink interactions in 4 theory, Physica D (Amsterdam) 9, 132 (1983).
[CrossRef]

Segev, M.

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, 147150 (2003).
[CrossRef] [PubMed]

Sievers, A. J.

M. Sato , B. E. Hubbard , A. J. Sievers , B. Llic , D. A. Czaplewski , and H. C. Craighead , Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array, Phys. Rev. Lett. 90, 044102 (2003).
[CrossRef] [PubMed]

Silberberg, Y.

H. S. Eisenberg , Y. Silberberg , R. Morandotti , A. R. Boyd , and J. S. Aitchison , Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett. 81, 33833386 (1998).
[CrossRef]

Smerzi, A.

A. Trombettoni and A. Smerzi , Discrete solitons and breathers with dilute Bose-Einstein condensates, Phys. Rev. Lett. 86, 23532356 (2001).
[CrossRef] [PubMed]

Sodano, P.

D. K. Campbell , M. Peyrard , and P. Sodano , Kink-antikink interactions in the double sine-Gordon equation, Physica D (Amsterdam) 19, 165205 (1986).
[CrossRef]

Sohler, W.

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. Lederer , Y. Min , and W. Sohler , Observation of discrete quadratic solitons, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Stegeman, G. I.

X. S. Wang , A. Bezryadina , Z. G. Chen , K. G. Makris , D. N. Christodoulides , and G. I. Stegeman , Observation of two-dimensional surface solitons, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. Lederer , Y. Min , and W. Sohler , Observation of discrete quadratic solitons, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Sukhorukov, A. A.

Taglieber, M.

B. Eiermann , Th. Anker , M. Albiez , M. Taglieber , P. Treutlein , K.-P. Marzlin , and M. K. Oberthaler , Bright Bose-Einstein gap solitons of atoms with repulsive interaction, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Torner, L.

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]

Y. V. Kartashov , R. Carretero-Gonzlez , B. A. Malomed , V. A. Vysloukh , and L. Torner , Multipole-mode solitons in Bessel optical lattices, Opt. Express 13, 1070310710 (2005).
[CrossRef] [PubMed]

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, 444447 (2004).
[CrossRef]

Treutlein, P.

B. Eiermann , Th. Anker , M. Albiez , M. Taglieber , P. Treutlein , K.-P. Marzlin , and M. K. Oberthaler , Bright Bose-Einstein gap solitons of atoms with repulsive interaction, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Trombettoni, A.

A. Trombettoni and A. Smerzi , Discrete solitons and breathers with dilute Bose-Einstein condensates, Phys. Rev. Lett. 86, 23532356 (2001).
[CrossRef] [PubMed]

Turunen, J.

Vasara, A.

Vysloukh, V. A.

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]

Y. V. Kartashov , R. Carretero-Gonzlez , B. A. Malomed , V. A. Vysloukh , and L. Torner , Multipole-mode solitons in Bessel optical lattices, Opt. Express 13, 1070310710 (2005).
[CrossRef] [PubMed]

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, 444447 (2004).
[CrossRef]

Wang, H.

Wang, H. C.

J. C. Liang , Z. B. Cai , L. Yi , and H. C. Wang , Bessel solitary waves in strongly nonlocal nonlinear media with distributed parameters, Opt. Commun. 283, 386390 (2010).
[CrossRef]

Wang, J. D.

L. W. Dong , F. W. Ye , J. D. Wang , T. Cai , and Y. P. Li , Internal modes of localized optical vortex soliton in a cubic-quintic nonlinear medium, Physica D (Amsterdam) 194, 219226(2004).
[CrossRef]

Wang, X. S.

X. S. Wang , A. Bezryadina , Z. G. Chen , K. G. Makris , D. N. Christodoulides , and G. I. Stegeman , Observation of two-dimensional surface solitons, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

X. S. Wang , Z. G. Chen , and J. K. Yang , Guiding light in optically induced ring lattices with a low-refractive-index core, Opt. Lett. 31, 18871889 (2006).
[CrossRef] [PubMed]

X. S. Wang , Z. G. Chen , and P. G. Kevrekidis , Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices, Phys. Rev. Lett. 96, 083904 (2006).
[CrossRef] [PubMed]

Wingate, C. A.

D. K. Campbell , J. F. Schonfeld , and C. A. Wingate , Resonance structure in kink-antikink interactions in 4 theory, Physica D (Amsterdam) 9, 132 (1983).
[CrossRef]

Xie, A.

A. Xie , L. Meer , W. Hoff , and R. H. Austin , Long-lived amide I vibrational modes in myoglobin, Phys. Rev. Lett. 84, 54355438(2000).
[CrossRef] [PubMed]

Xu, J. J.

Z. G. Chen , H. Martin , E. Eugenieva , J. J. Xu , and J. K. Yang , Formation of discrete solitons in light-induced photonic lattices, Opt. Express 13, 18161826 (2005).
[CrossRef] [PubMed]

Z. G. Chen , H. Martin , E. D. Eugenieva , J. 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]

Yang, J. K.

Yang, X. Y.

Ye, F. W.

L. W. Dong , F. W. Ye , J. D. Wang , T. Cai , and Y. P. Li , Internal modes of localized optical vortex soliton in a cubic-quintic nonlinear medium, Physica D (Amsterdam) 194, 219226(2004).
[CrossRef]

Yi, L.

J. C. Liang , Z. B. Cai , L. Yi , and H. C. Wang , Bessel solitary waves in strongly nonlocal nonlinear media with distributed parameters, Opt. Commun. 283, 386390 (2010).
[CrossRef]

Zhou, W. D.

J. Opt. B: Quantum Semiclass. Opt.

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, 444447 (2004).
[CrossRef]

J. Opt. Soc. Am. A

Nature

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, 147150 (2003).
[CrossRef] [PubMed]

Opt. Commun.

J. Arlt and K. Dholakia , Generation of high-order Bessel beams by use of an axicon, Opt. Commun. 177, 297301 (2000).
[CrossRef]

J. C. Liang , Z. B. Cai , L. Yi , and H. C. Wang , Bessel solitary waves in strongly nonlocal nonlinear media with distributed parameters, Opt. Commun. 283, 386390 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E

J. A. Gonzlez , A. Bellorn , and L. E. Guerrero , Internal modes of sine-Gordon solitons in the presence of spatiotemporal perturbations, Phys. Rev. E 65, 065601 (2002).
[CrossRef]

J. K. Yang , Internal oscillations and instability characteristics of (2+1)-dimensional solitons in a saturable nonlinear medium, Phys. Rev. E 66, 026601 (2002).
[CrossRef]

Phys. Rev. Lett.

Y. S. Kivshar , D. E. Pelinovsky , T. Cretegny , and M. Peyrard , Internal modes of solitary waves, Phys. Rev. Lett. 80, 50325035 (1998).
[CrossRef]

X. S. Wang , Z. G. Chen , and P. G. Kevrekidis , Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices, Phys. Rev. Lett. 96, 083904 (2006).
[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]

A. Xie , L. Meer , W. Hoff , and R. H. Austin , Long-lived amide I vibrational modes in myoglobin, Phys. Rev. Lett. 84, 54355438(2000).
[CrossRef] [PubMed]

R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. Lederer , Y. Min , and W. Sohler , Observation of discrete quadratic solitons, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

Z. G. Chen , H. Martin , E. D. Eugenieva , J. 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]

X. S. Wang , A. Bezryadina , Z. G. Chen , K. G. Makris , D. N. Christodoulides , and G. I. Stegeman , Observation of two-dimensional surface solitons, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

B. Eiermann , Th. Anker , M. Albiez , M. Taglieber , P. Treutlein , K.-P. Marzlin , and M. K. Oberthaler , Bright Bose-Einstein gap solitons of atoms with repulsive interaction, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

A. Trombettoni and A. Smerzi , Discrete solitons and breathers with dilute Bose-Einstein condensates, Phys. Rev. Lett. 86, 23532356 (2001).
[CrossRef] [PubMed]

M. Sato , B. E. Hubbard , A. J. Sievers , B. Llic , D. A. Czaplewski , and H. C. Craighead , Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array, Phys. Rev. Lett. 90, 044102 (2003).
[CrossRef] [PubMed]

H. S. Eisenberg , Y. Silberberg , R. Morandotti , A. R. Boyd , and J. S. Aitchison , Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett. 81, 33833386 (1998).
[CrossRef]

Physica D (Amsterdam)

D. K. Campbell , J. F. Schonfeld , and C. A. Wingate , Resonance structure in kink-antikink interactions in 4 theory, Physica D (Amsterdam) 9, 132 (1983).
[CrossRef]

M. Peyrard and D. K. Campbell , Kink-antikink interactions in a modified sine-Gordon model, Physica D (Amsterdam) 9, 3351(1983).
[CrossRef]

D. K. Campbell , M. Peyrard , and P. Sodano , Kink-antikink interactions in the double sine-Gordon equation, Physica D (Amsterdam) 19, 165205 (1986).
[CrossRef]

D. E. Pelinovsky , Y. S. Kivshar , and V. V. Afanasjev , Internal modes of envelope solitons, Physica D (Amsterdam) 116, 121142 (1998).
[CrossRef]

L. W. Dong , F. W. Ye , J. D. Wang , T. Cai , and Y. P. Li , Internal modes of localized optical vortex soliton in a cubic-quintic nonlinear medium, Physica D (Amsterdam) 194, 219226(2004).
[CrossRef]

Rev. Mod. Phys.

Y. S. Kivshar and B. A. Malomed , Dynamics of solitons in nearly integrable systems, Rev. Mod. Phys. 61, 763915 (1989).
[CrossRef]

Supplementary Material (8)

» Media 1: MOV (217 KB)     
» Media 2: MOV (162 KB)     
» Media 3: MOV (338 KB)     
» Media 4: MOV (273 KB)     
» Media 5: MOV (273 KB)     
» Media 6: MOV (214 KB)     
» Media 7: MOV (130 KB)     
» Media 8: MOV (122 KB)     

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Figures (7)

Fig. 1
Fig. 1

Static solutions of ten-pearled necklace solitons in Bessel lattices for p = 40 and b = 2 . (a) Intensity distribution profile; (b) contour plot.

Fig. 2
Fig. 2

Power U conveyed by the necklace solitons versus propagation constant b for different modulation depth p.

Fig. 3
Fig. 3

(a) Instability parameter [maximum of Re ( δ ) ] versus propagation constant b. (b) The region where [ Re ( δ ) ] max = 0 corresponds to linearly stable solitons.

Fig. 4
Fig. 4

Field distribution of internal modes of ten-pearled necklace soliton in Bessel lattices with p = 30 and b = 4.5 . (a1)–(a4) In defocusing material and the related perturbation, eigenvalue is δ = - 3.075 i . (b1)–(b4) In focusing material and the related perturbation, eigenvalue is δ = 2.814 i . (a1) and (b1) Real part of eigenmode u ( u r ) . (a2) and (b2) Imaginary part of eigenmode u ( u i ) . (a3) and (b3) Real part of eigenmode v ( v r ) . (a4) and (b4) Imaginary part of eigenmode v ( v i ) .

Fig. 5
Fig. 5

Single-frame excerpts from videos of propagation of necklace solitons in unstable areas. Cases of (a) self-defocusing material and (b) self-focusing material. (a) p = 30 , b = 3.2 (Media 1). (b) p = 30 , b = 3.7 (Media 2). A white noise with variance σ 2 = 0.035 is present. Different evolution time denotes different propagation distance.

Fig. 6
Fig. 6

Single-frame excerpt from videos of propagation of the stable necklace soliton shown in Fig. 1 under perturbation of the internal modes. The initial perturbed state is given by Eq. (3). (a1) Intensity profile in the case of defocusing material (Media 3). (b1) Intensity profile in the case of focusing material (Media 4). (a2) Intensity distribution contour in the case of defocusing material (Media 5). (b2) Intensity distribution contour in the case of focusing material (Media 6).

Fig. 7
Fig. 7

Single-frame excerpt from video on propagation of the stable necklace soliton shown in Fig. 1 under the perturbation of a white noise with a variance of σ 2 = 0.035 . (a) Intensity profile in the case of defocusing material (Media 7). (b) Intensity profile in the case of focusing material (Media 8).

Equations (7)

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

i q z = - 1 2 ( 2 q x 2 + 2 q y 2 ) ± q | q | 2 + p R ( x , y ) q ,
- b w = - 1 2 ( 2 w x 2 + 2 w y 2 ) ± w 3 + p R ( x , y ) w .
w ( x , y ) = { cos ( 5 θ ) , ( when x 2 + y 2 l ) 0 , ( when x 2 + y 2 > l ) .
q = [ w + ϵ u exp ( δ z ) + ϵ v exp ( δ * z ) ] exp ( i b z ) ,
i δ u - b u + 1 2 ( 2 u x 2 + 2 u y 2 ) w 2 v * 2 w 2 u + p R u = 0 ,
i δ * v - b v + 1 2 ( 2 v x 2 + 2 v y 2 ) w 2 u * 2 w 2 v + p R v = 0 ,
u r , i 0 , v r , j 0 , when r 0 , u r , i 0 , v r , j 0 , when r .

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