Spatially periodic modulation of the intersite coupling in two-dimensional (2D) nonlinear lattices modifies the eigenvalue spectrum by opening mini-gaps in it. This work aims to build stable localized modes in the new bandgaps. Numerical analysis shows that single-peak and composite two- and four-peak discrete static solitons and breathers emerge as such modes in certain parameter areas inside the mini-gaps of the 2D superlattice induced by the periodic modulation of the intersite coupling along both directions. The single-peak solitons and four-peak discrete solitons are stable in a part of their existence domain, while unstable stationary states (in particular, two-soliton complexes) may readily transform into robust localized breathers.
REFERENCES
1.
H. S.
Eisenberg
, Y.
Silberberg
, R.
Morandotti
, A. R.
Boyd
, and J. S.
Aitchison
, Phys. Rev. Lett.
81
, 3383
(1998
).2.
A. A.
Sukhorukov
, Y. S.
Kivshar
, H. S.
Eisenberg
, and Y.
Silberberg
, IEEE J. Quantum Electron.
39
, 31
(2003
).3.
D. N.
Christodoulides
, F.
Lederer
, and Y.
Silberberg
, Nature
424
, 817
(2003
).4.
J. W.
Fleischer
, M.
Segev
, N. K.
Efremidis
, and D. N.
Christodoulides
, Nature
422
, 147
(2003
).5.
J. W.
Fleischer
, T.
Carmon
, M.
Segev
, N. K.
Efremidis
, and D. N.
Christodoulides
, Phys. Rev. Lett.
90
, 023902
(2003
).6.
D.
Neshev
, E.
Ostrovskaya
, Y.
Kivshar
, and W.
Kró likowski
, Opt. Lett.
28
, 710
(2003
).7.
D. N.
Neshev
, T. J.
Alexander
, E. A.
Ostrovskaya
, Y. S.
Kivshar
, H.
Martin
, I.
Makasyuk
, and Z.
Chen
, Phys. Rev. Lett.
92
, 123903
(2004
).8.
J. W.
Fleischer
, G.
Bartal
, O.
Cohen
, O.
Manela
, M.
Segev
, J.
Hudock
, and D. N.
Christodoulides
, Phys. Rev. Lett.
92
, 123904
(2004
).9.
R.
Fischer
, D.
Trager
, D. N.
Neshev
, A. A.
Sukhorukov
, W.
Kr ólikowski
, C.
Denz
, and Y. S.
Kivshar
, Phys. Rev. Lett.
96
, 023905
(2006
);
[PubMed]
B.
Terhalle
, T.
Richter
, A. S.
Desyatnikov
, D. N.
Neshev
, W.
Królikowski
, F.
Kaiser
, C.
Denz
, and Y. S.
Kivshar
, Phys. Rev. Lett.
101
, 013903
(2008
).
[PubMed]
10.
D.
Song
, C.
Lou
, L.
Tang
, X.
Wang
, W.
Li
, X.
Chen
, K. J. H.
Law
, H.
Susanto
, P. G.
Kevrekidis
, J.
Xu
, and Z.
Chen
, Opt. Exp.
16
, 10110
(2008
).11.
J.
Hukriede
, D.
Runde
, and D.
Kip
, J. Phys. D: Appl. Phys.
36
, R1
(2003
).12.
F.
Lederer
, G. I.
Stegeman
, D. N.
Christodoulides
, G.
Assanto
, M.
Segev
, and Y.
Silberberg
, Phys. Rep.
463
, 1
(2008
).13.
M.
Heinrich
, R.
Keil
, F.
Dreisow
, A.
Tünnermann
, A.
Szameit
, and S.
Nolte
, Appl. Phys. B
104
, 469
(2011
).14.
U.
Röpke
, H.
Bartelt
, S.
Unger
, K.
Schuster
, and J.
Kobelke
, Appl. Phys. B
104
, 481
(2011
).15.
F. S.
Cataliotti
, L.
Fallani
, F.
Ferlaino
, C.
Fort
, P.
Maddaloni
, and M.
Inguscio
, New J. Phys.
5
, 71
(2003
).16.
B.
Eiermann
, Th.
Anker
, M.
Albiez
, M.
Taglieber
, P.
Treutlein
, K.-P.
Marzlin
, and M. K.
Oberthaler
, Phys. Rev. Lett.
92
, 230401
(2004
).17.
T.
Anker
, M.
Albiez
, B.
Eiermann
, M.
Taglieber
, and M.
Oberthaler
, Opt. Exp.
12
, 11
(2004
).18.
Th.
Anker
, M.
Albiez
, R.
Gati
, S.
Hunsmann
, B.
Eiermann
, A.
Trombettoni
, and M. K.
Oberthaler
, Phys. Rev. Lett.
94
, 020403
(2005
).19.
D.
Jaksch
and P.
Zoller
, Ann. Phys.
315
, 52
(2005
).20.
P.
Windpassinger
and K.
Sengstock
, Rep. Prog. Phys.
76
, 086401
(2013
).21.
M.
Sato
, B. E.
Hubbard
, and A. J.
Sievers
, Rev. Mod. Phys.
78
, 137
(2006
).22.
A.
Fratalocchi
, G.
Assanto
, K. A.
Brzdakiewicz
, and M. A.
Karpierz
, Opt. Exp.
13
, 1808
(2005
).23.
A. S.
Davydov
and N. I.
Kislukha
, Phys. Status Solidi B
59
, 465
(1973
).24.
A. C.
Scott
, Phys. Rev. A
26
, 578
(1982
).25.
P. G.
Kevrekidis
, The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations, and Physical Perspectives
(Springer
, Berlin and Heidelberg
, 2009
).26.
Y. V.
Kartashov
, V. A.
Vysloukh
, and L.
Torner
, Prog. Opt.
52
, 63
(2009
).27.
P. G.
Kevrekidis
, K. O.
Rasmussen
, and A. R.
Bishop
, Phys. Rev. E
61
, 2006
(2000
);P. G.
Kevrekidis
, H.
Susanto
, and Z.
Chen
, Phys. Rev. E
74
, 066606
(2006
).28.
G.
Gligorić
, A.
Maluckov
, M.
Stepić
, Lj.
Hadžievski
, and B. A.
Malomed
, Phys. Rev. A
81
, 013633
(2010
).29.
B. A.
Malomed
and P. G.
Kevrekidis
, Phys. Rev. E
64
, 026601
(2001
).30.
P. G.
Kevrekidis
, B. A.
Malomed
, Z.
Chen
, and D. J.
Frantzeskakis
, Phys. Rev. E
70
, 056612
(2004
).31.
M.
Öster
and M.
Johansson
, Phys. Rev. E
73
, 066608
(2006
).32.
N. K.
Efremidis
, J.
Hudock
, D. N.
Christodoulides
, J. W.
Fleischer
, O.
Cohen
, and M.
Segev
, Phys. Rev. Lett.
91
, 213906
(2003
).33.
N. K.
Efremidis
and D. N.
Christodoulides
, Phys. Rev. A
67
, 063608
(2003
).34.
A.
Gubeskys
and B. A.
Malomed
, Phys. Rev. A
76
, 043623
(2007
).35.
G.
Gligorić
, A.
Maluckov
, M.
Stepić
, Lj.
Had žievski
, and B. A.
Malomed
, J. Phys. B: At. Mol. Opt. Phys.
43
, 055303
(2010
).36.
A. A.
Sukhorukov
, Phys. Rev. Lett.
96
, 113902
(2006
).37.
G.
Gligoric
, A.
Maluckov
, Lj.
Hadžievski
, and B. A.
Malomed
, Phys. Rev. E
88
, 032905
(2013
).38.
C. P.
Collier
, T.
Vossmeyer
, and J. R.
Heath
, Ann. Rev. Phys. Chem.
49
, 371
(1998
);A.
Wacker
, Phys. Rep.
357
, 1
(2002
);A. A.
Lebedev
, Semicond. Sci. Technol.
21
, R17
(2006
).39.
V. V.
Konotop
and M.
Salerno
, Phys. Rev.
65
, 021602
(2002
).40.
P. J. Y.
Louis
, E. A.
Ostrovskaya
, and Y. S.
Kivshar
, Phys. Rev. A
71
, 023612
(2005
);M. A.
Porter
and P. G.
Kevrekidis
, SIAM J. Appl. Dyn. Syst.
4
, 783
(2005
);M.
Porter
, P. G.
Kevrekidis
, R.
Carretero-González
, and D. J.
Frantzeskakis
, Phys. Lett. A
352
, 210
(2006
);K.
Yagasaki
, I. M.
Merhasin
, B. A.
Malomed
, T.
Wagenknecht
, and A. R.
Champneys
, Europhys. Lett.
74
, 1006
(2006
).41.
H.
Susanto
, P. G.
Kevrekidis
, R.
Carretero-González
, B. A.
Malomed
, and D. J.
Frantzeskakis
, Phys. Rev. Lett.
99
, 214103
(2007
).42.
J.
Cuevas
, B. A.
Malomed
, and P. G.
Kevrekidis
, Phys. Rev. E
71
, 066614
(2005
).© 2014 AIP Publishing LLC.
2014
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