Abstract

We introduce a novel class of stable nonlinear modes trapped in a lower-index film core sandwiched between two optical lattices, or in the cylindrical core of a radial lattice, imprinted in defocusing media. Such a family of nonlinear modes transforms into defect lattice solitons when the core width is sufficiently small or into an array of kinks when the width is large enough. We find that higher-order modes with multiple zeros inside the guiding core can be stable in one-dimensional settings.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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2007 (2)

2006 (10)

Y. Kominis and K. Hizanidis, Opt. Lett. 31, 2888 (2006).
[CrossRef] [PubMed]

X. Wang, Z. Chen, and J. Yang, Opt. Lett. 31, 1887 (2006).
[CrossRef] [PubMed]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, Nature 440, 1166 (2006).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

E. Smirnov, M. Stepic, C. E. Rüter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 14, 12365 (2006).
[CrossRef] [PubMed]

2005 (4)

2003 (2)

P. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

J. C. Knight, Nature 424, 847 (2003).
[CrossRef] [PubMed]

2002 (1)

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 510 (2002).
[CrossRef] [PubMed]

1999 (1)

Bartal, G.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, Nature 440, 1166 (2006).
[CrossRef] [PubMed]

Chen, Z.

Christodoulides, D. N.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, Nature 440, 1166 (2006).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

Darmanyan, S.

Efremidis, N. K.

Fedele, F.

Fink, Y.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 510 (2002).
[CrossRef] [PubMed]

Fleischer, J. W.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, Nature 440, 1166 (2006).
[CrossRef] [PubMed]

Frantzeskakis, D. J.

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, Phys. Lett. A 341, 145 (2005).
[CrossRef]

Freedman, B.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, Nature 440, 1166 (2006).
[CrossRef] [PubMed]

Hache, A.

Haché, A.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Hart, S. D.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 510 (2002).
[CrossRef] [PubMed]

Hizanidis, K.

Hoq, Q. E.

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, Phys. Lett. A 341, 145 (2005).
[CrossRef]

Hudock, J.

Joannopoulos, J. D.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 510 (2002).
[CrossRef] [PubMed]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 14, 12365 (2006).
[CrossRef] [PubMed]

Kevrekidis, P. G.

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, Phys. Lett. A 341, 145 (2005).
[CrossRef]

Kip, D.

Kivshar, Y. S.

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Knight, J. C.

Kobyakov, A.

Kominis, Y.

Krolikowski, W.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Lederer, F.

Lifshitz, R.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, Nature 440, 1166 (2006).
[CrossRef] [PubMed]

Makris, K. G.

Malomed, B. A.

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, Phys. Lett. A 341, 145 (2005).
[CrossRef]

Manela, O.

Maskaly, G. R.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 510 (2002).
[CrossRef] [PubMed]

Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Molina, M. I.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

Morandotti, R.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Neshev, D. N.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Papadopoulos, A.

Pertsch, T.

Prideaux, P. H.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 510 (2002).
[CrossRef] [PubMed]

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Russell, P.

P. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

Rüter, C. E.

Salamo, G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Segev, M.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, Nature 440, 1166 (2006).
[CrossRef] [PubMed]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
[CrossRef] [PubMed]

Shandarov, V.

Skryabin, D. V.

Smirnov, E.

Sorel, M.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Stegeman, G. I.

Stepic, M.

Suntsov, S.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

Temelkuran, B.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 510 (2002).
[CrossRef] [PubMed]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 14, 12365 (2006).
[CrossRef] [PubMed]

Vicencio, R. A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 14, 12365 (2006).
[CrossRef] [PubMed]

Wang, X.

Yang, H.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Yang, J.

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

Nature (2)

J. C. Knight, Nature 424, 847 (2003).
[CrossRef] [PubMed]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, Nature 440, 1166 (2006).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (7)

Phys. Lett. A (1)

Q. E. Hoq, P. G. Kevrekidis, D. J. Frantzeskakis, and B. A. Malomed, Phys. Lett. A 341, 145 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Science (2)

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, Science 296, 510 (2002).
[CrossRef] [PubMed]

P. Russell, Science 299, 358 (2003).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Bandgap lattice spectrum at Ω = 2 . (b) Profiles of fundamental (black curve) and dipole (gray curve) nonlinear modes at b = 0.6 , p = 4 , n = 7 , Ω = 2 . (c) Existence regions at ( p , b ) plane for n = 7 and n = 1 at Ω = 2 . (d) Energy flow versus b for p = 4 and Ω = 2 . (e) Mixed-gap modes at b = 2 (1) and b = 2.7 (2) for p = 14 , Ω 1 = 2 , and Ω 2 = 5 . (f) Existence regions at Ω 1 = 2 for Ω 2 = 4 and Ω 2 = 5 . In (e) and (f) the core width is 4 π Ω 1 + 4 π Ω 2 . Light gray (green online) lines in (c) and (f) show gap edges.

Fig. 2
Fig. 2

Stable propagation of (a) fundamental and (b) dipole 1D modes at b = 0.6 , p = 4 , n = 7 , Ω = 2 and (c) mixed-gap mode at b = 1 , p = 20 , Ω 1 = 2 , Ω 2 = 4 . (d) Dynamics of unstable fundamental mode at b = 1.44 , p = 2 , n = 7 , Ω = 2 . Stable propagation of 2D domain soliton in lattice with n = 5 and Ω = 2 at b = 0.7 , p = 4 . In (e) and (f) field modulus distributions are shown at different distances.

Fig. 3
Fig. 3

(a) Fundamental mode profiles in circular lattices at b = 0.6 and p = 4 . (b) Existence region on the ( p , b ) plane for n = 2 and n = 5 . (c) Energy flow versus b at n = 5 . (d) Real part of perturbation growth rate versus b at p = 1.5 , n = 5 . In all cases Ω = 2 .

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i q ξ = 1 2 2 q η 2 + q 2 q p R ( η ) q .

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