TY  - JOUR
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Maluckov, Aleksandra
AU  - Stepić, Milutin
AU  - Johansson, Magnus M.
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1885
AB  - Compact localized modes of ring type exist in many two-dimensional lattices with a flat linear band, such as the Lieb lattice. The uniform Lieb lattice is gapless, but gaps surrounding the flat band can be induced by various types of bond alternations (dimerizations) without destroying the compact linear eigenmodes. Here, we investigate the conditions under which such diffractionless modes can be formed and propagated also in the presence of a cubic on-site (Kerr) nonlinearity. For the simplest type of dimerization with a three-site unit cell, nonlinearity destroys the exact compactness, but strongly localized modes with frequencies inside the gap are still found to propagate stably for certain regimes of system parameters. By contrast, introducing a dimerization with a 12-site unit cell, compact (diffractionless) gap modes are found to exist as exact nonlinear solutions in continuation of flat band linear eigenmodes. These modes appear to be generally weakly unstable, but dynamical simulations show parameter regimes where localization would persist for propagation lengths much larger than the size of typical experimental waveguide array configurations. Our findings represent an attempt to realize conditions for full control of light propagation in photonic environments.
T2  - Physical Review A
T1  - Localized gap modes in nonlinear dimerized Lieb lattices
VL  - 96
IS  - 6
DO  - 10.1103/PhysRevA.96.063838
ER  - 

@article{
author = "Beličev, Petra and Gligorić, Goran and Maluckov, Aleksandra and Stepić, Milutin and Johansson, Magnus M.",
year = "2017",
abstract = "Compact localized modes of ring type exist in many two-dimensional lattices with a flat linear band, such as the Lieb lattice. The uniform Lieb lattice is gapless, but gaps surrounding the flat band can be induced by various types of bond alternations (dimerizations) without destroying the compact linear eigenmodes. Here, we investigate the conditions under which such diffractionless modes can be formed and propagated also in the presence of a cubic on-site (Kerr) nonlinearity. For the simplest type of dimerization with a three-site unit cell, nonlinearity destroys the exact compactness, but strongly localized modes with frequencies inside the gap are still found to propagate stably for certain regimes of system parameters. By contrast, introducing a dimerization with a 12-site unit cell, compact (diffractionless) gap modes are found to exist as exact nonlinear solutions in continuation of flat band linear eigenmodes. These modes appear to be generally weakly unstable, but dynamical simulations show parameter regimes where localization would persist for propagation lengths much larger than the size of typical experimental waveguide array configurations. Our findings represent an attempt to realize conditions for full control of light propagation in photonic environments.",
journal = "Physical Review A",
title = "Localized gap modes in nonlinear dimerized Lieb lattices",
volume = "96",
number = "6",
doi = "10.1103/PhysRevA.96.063838"
}

Beličev, P., Gligorić, G., Maluckov, A., Stepić, M.,& Johansson, M. M.. (2017). Localized gap modes in nonlinear dimerized Lieb lattices. in Physical Review A, 96(6).
https://doi.org/10.1103/PhysRevA.96.063838

Beličev P, Gligorić G, Maluckov A, Stepić M, Johansson MM. Localized gap modes in nonlinear dimerized Lieb lattices. in Physical Review A. 2017;96(6).
doi:10.1103/PhysRevA.96.063838 .

Beličev, Petra, Gligorić, Goran, Maluckov, Aleksandra, Stepić, Milutin, Johansson, Magnus M., "Localized gap modes in nonlinear dimerized Lieb lattices" in Physical Review A, 96, no. 6 (2017),
https://doi.org/10.1103/PhysRevA.96.063838 . .