Abstract

We demonstrate that specific surface superlattice gap solitons can be supported at an interface between a one-dimensional photonic superlattice and a uniform medium with saturable nonlinearity. The solitons are stable in the semi-infinite gap but do not exist in the first gap. With the decrease of the power, the solitons jump from the surface site to the next one, and they may continue the motion into the lattices, which offers potential applications for the routing of optical signals.

© 2007 Optical Society of America

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2006

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

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 31, 2332 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, D. Mihalache, and L. Torner, Opt. Lett. 31, 2329 (2006).
[CrossRef] [PubMed]

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

M. A. Porter, P. G. Kevrekidis, R. Carretero-González, and D. J. Frantzeskakis, Phys. Lett. A 352, 210 (2006).
[CrossRef]

K. Yagasaki, I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, Europhys. Lett. 74, 1006 (2006).
[CrossRef]

J. Yang and Z. Chen, Phys. Rev. E 73, 026609 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 74, 026601 (2006).
[CrossRef]

W. H. Chen, Y. J. He, and H. Z. Wang, Opt. Express 14, 11271 (2006).
[CrossRef] [PubMed]

2005

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

P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. A 71, 023612 (2005).
[CrossRef]

B. A. Malomed, T. Mayteevarunyoo, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. E 71, 056616 (2005).
[CrossRef]

2003

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

2002

1995

Carretero-González, R.

M. A. Porter, P. G. Kevrekidis, R. Carretero-González, and D. J. Frantzeskakis, Phys. Lett. A 352, 210 (2006).
[CrossRef]

Champneys, A. R.

K. Yagasaki, I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, Europhys. Lett. 74, 1006 (2006).
[CrossRef]

Chen, W. H.

Chen, Z.

J. Yang and Z. Chen, Phys. Rev. E 73, 026609 (2006).
[CrossRef]

Z. Chen and K. McCarthy, Opt. Lett. 27, 2019 (2002).
[CrossRef]

Christodoulides, D. N.

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

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

Cronin-Golomb, M.

Efremidis, N. K.

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

Fleischer, J. W.

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

Frantzeskakis, D. J.

M. A. Porter, P. G. Kevrekidis, R. Carretero-González, and D. J. Frantzeskakis, Phys. Lett. A 352, 210 (2006).
[CrossRef]

Garanovich, I. L.

He, Y. J.

Kartashov, Y. V.

Kevrekidis, P. G.

M. A. Porter, P. G. Kevrekidis, R. Carretero-González, and D. J. Frantzeskakis, Phys. Lett. A 352, 210 (2006).
[CrossRef]

Kip, D.

Kivshar, Y. S.

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 31, 2332 (2006).
[CrossRef] [PubMed]

P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. A 71, 023612 (2005).
[CrossRef]

B. A. Malomed, T. Mayteevarunyoo, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. E 71, 056616 (2005).
[CrossRef]

Louis, P. J. Y.

P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. A 71, 023612 (2005).
[CrossRef]

Makris, K. G.

Malomed, B. A.

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 74, 026601 (2006).
[CrossRef]

K. Yagasaki, I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, Europhys. Lett. 74, 1006 (2006).
[CrossRef]

B. A. Malomed, T. Mayteevarunyoo, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. E 71, 056616 (2005).
[CrossRef]

Mayteevarunyoo, T.

B. A. Malomed, T. Mayteevarunyoo, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. E 71, 056616 (2005).
[CrossRef]

McCarthy, K.

Merhasin, I. M.

K. Yagasaki, I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, Europhys. Lett. 74, 1006 (2006).
[CrossRef]

Mihalache, D.

Molina, M. I.

Ostrovskaya, E. A.

P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. A 71, 023612 (2005).
[CrossRef]

B. A. Malomed, T. Mayteevarunyoo, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. E 71, 056616 (2005).
[CrossRef]

Porter, M. A.

M. A. Porter, P. G. Kevrekidis, R. Carretero-González, and D. J. Frantzeskakis, Phys. Lett. A 352, 210 (2006).
[CrossRef]

Rüter, C. E.

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 74, 026601 (2006).
[CrossRef]

Segev, M.

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

Shandarov, V.

Smirnov, E.

Stegeman, G. I.

Stepic, M.

Sukhorukov, A. A.

Suntsov, S.

Torner, L.

Vysloukh, V. A.

Wagenknecht, T.

K. Yagasaki, I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, Europhys. Lett. 74, 1006 (2006).
[CrossRef]

Wang, H. Z.

Yagasaki, K.

K. Yagasaki, I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, Europhys. Lett. 74, 1006 (2006).
[CrossRef]

Yang, J.

J. Yang and Z. Chen, Phys. Rev. E 73, 026609 (2006).
[CrossRef]

Europhys. Lett.

K. Yagasaki, I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, Europhys. Lett. 74, 1006 (2006).
[CrossRef]

Nature

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

Opt. Express

Opt. Lett.

Phys. Lett. A

M. A. Porter, P. G. Kevrekidis, R. Carretero-González, and D. J. Frantzeskakis, Phys. Lett. A 352, 210 (2006).
[CrossRef]

Phys. Rev. A

P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. A 71, 023612 (2005).
[CrossRef]

Phys. Rev. E

J. Yang and Z. Chen, Phys. Rev. E 73, 026609 (2006).
[CrossRef]

B. A. Malomed, T. Mayteevarunyoo, E. A. Ostrovskaya, and Y. S. Kivshar, Phys. Rev. E 71, 056616 (2005).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 74, 026601 (2006).
[CrossRef]

Phys. Rev. Lett.

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

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Figures (4)

Fig. 1
Fig. 1

(a) Lattice intensity profile with I 0 = 3 and ϵ = 0.3 . (b) Linear spectrum of Eq. (1) in the plane of ( E 0 , μ ) ; the gray areas are Bloch bands. (c) Soliton’s total power versus μ for E 0 = 6 , with the solid and dashed segments pertaining to stable and unstable solutions, respectively. (d) Perturbation growth rate corresponding to (c).

Fig. 2
Fig. 2

SSGSs in the SI gap for ϵ = 0.3 . (a), (d) μ = 2.15 and (b), (e) μ = 2.25 : stable solitons centered at the surface site of the lattice; (c), (f) μ = 2.4 and (g), (j) μ = 2.45 : stable solitons centered at the next site; (h), (k) μ = 2.6 and (i), (l) μ = 1.8 : a stable and a weakly unstable soliton, respectively, in the depth of the lattice and the surface.

Fig. 3
Fig. 3

Spontaneous shift of a surface soliton, due to its instability, to a stable position at the next site: (a), (c) ϵ = 0.3 , μ = 2.3 , (b), (d) ϵ = 0.7 , μ = 2.35 . Instability-induced transition of the soliton from the position pinned at the second site near the surface to a state of steady motion into the lattice: (e), (g) ϵ = 0.1 , μ = 2.6 , (f), (h) ϵ = 0.3 , μ = 2.5 .

Fig. 4
Fig. 4

Areas of the soliton’s stability (gray) and instability (white) in the SI gap. At the points marked by dots (at 0.3 ϵ 0.7 ), it has been checked that the instability results in the jump of the soliton to the next site; see Figs. 3c, 3d. The squares (at 0.1 ϵ 0.3 ) show the transition of the solitons pinned the second site to steady motion across the lattice. (b) Soliton’s power versus ϵ at fixed propagation constant μ.

Equations (3)

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

i q z + 2 q x 2 E 0 1 + I L ( x ) + q 2 q = 0 ,
I L ( x ) = I 0 { ϵ sin 2 [ π ( x + π 2 ) d 1 ] + ( 1 ϵ ) sin 2 [ π ( x + π 2 ) d 2 ] }
2 f x 2 E 0 1 + I L ( x ) + f 2 f + μ f = 0 .

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