Localized gap modes in nonlinear dimerized Lieb lattices
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 si...mulations 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.
Source:
Physical Review A, 2017, 96, 6Funding / projects:
- Photonics of micro and nano structured materials (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-45010)
- Swedish Research Council [348-2013-6752]
DOI: 10.1103/PhysRevA.96.063838
ISSN: 2469-9926; 2469-9934
WoS: 000418794800006
Scopus: 2-s2.0-85039866647
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VinčaTY - 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 . .