TY  - JOUR
AU  - Stojanović, Mirjana G.
AU  - Stojanović Krasić, Marija
AU  - Maluckov, Aleksandra
AU  - Johansson, Magnus M.
AU  - Salinas, I. A.
AU  - Vicencio, Rodrigo A.
AU  - Stepić, Milutin
PY  - 2020
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9664
AB  - We consider a two-dimensional octagonal-diamond network with a fine-tuned diagonal coupling inside the diamond-shaped unit cell. Its linear spectrum exhibits coexistence of two dispersive bands (DBs) and two flat bands (FBs), touching one of the DBs embedded between them. Analogous to the kagome lattice, one of the FBs will constitute the ground state of the system for a proper sign choice of the Hamiltonian. The system is characterized by two different flat-band fundamental octagonal compactons, originating from the destructive interference of fully geometric nature. In the presence of a nonlinear amplitude (on-site) perturbation, the single-octagon linear modes continue into one-parameter families of nonlinear compact modes with the same amplitude and phase structure. However, numerical stability analysis indicates that all strictly compact nonlinear modes are unstable, either purely exponentially or with oscillatory instabilities, for weak and intermediate nonlinearities and sufficiently large system sizes. Stabilization may appear in certain ranges for finite systems and, for the compacton originating from the band at the spectral edge, also in a regime of very large focusing nonlinearities. In contrast to the kagome lattice, the latter compacton family will become unstable already for arbitrarily weak defocusing nonlinearity for large enough systems. We show analytically the existence of a critical system size consisting of 12 octagon rings, such that the ground state for weak defocusing nonlinearity is a stable single compacton for smaller systems, and a continuation of a nontrivial, noncompact linear combination of single compacton modes for larger systems. Investigating generally the different nonlinear localized (noncompact) mode families in the semi-infinite gap bounded by this FB, we find that, for increasing (defocusing) nonlinearity the stable ground state will continuously develop into an exponentially localized mode with two main peaks in antiphase. At a critical nonlinearity strength a symmetry-breaking pitchfork bifurcation appears, so that the stable ground state is single peaked for larger defocusing nonlinearities. We also investigate numerically the mobility of localized modes in this regime and find that the considered modes are generally immobile both with respect to axial and diagonal phase-gradient perturbations.
T2  - Physical Review A
T1  - Localized modes in linear and nonlinear octagonal-diamond lattices with two flat bands
VL  - 102
IS  - 2
SP  - 023532
DO  - 10.1103/PhysRevA.102.023532
ER  - 

@article{
author = "Stojanović, Mirjana G. and Stojanović Krasić, Marija and Maluckov, Aleksandra and Johansson, Magnus M. and Salinas, I. A. and Vicencio, Rodrigo A. and Stepić, Milutin",
year = "2020",
abstract = "We consider a two-dimensional octagonal-diamond network with a fine-tuned diagonal coupling inside the diamond-shaped unit cell. Its linear spectrum exhibits coexistence of two dispersive bands (DBs) and two flat bands (FBs), touching one of the DBs embedded between them. Analogous to the kagome lattice, one of the FBs will constitute the ground state of the system for a proper sign choice of the Hamiltonian. The system is characterized by two different flat-band fundamental octagonal compactons, originating from the destructive interference of fully geometric nature. In the presence of a nonlinear amplitude (on-site) perturbation, the single-octagon linear modes continue into one-parameter families of nonlinear compact modes with the same amplitude and phase structure. However, numerical stability analysis indicates that all strictly compact nonlinear modes are unstable, either purely exponentially or with oscillatory instabilities, for weak and intermediate nonlinearities and sufficiently large system sizes. Stabilization may appear in certain ranges for finite systems and, for the compacton originating from the band at the spectral edge, also in a regime of very large focusing nonlinearities. In contrast to the kagome lattice, the latter compacton family will become unstable already for arbitrarily weak defocusing nonlinearity for large enough systems. We show analytically the existence of a critical system size consisting of 12 octagon rings, such that the ground state for weak defocusing nonlinearity is a stable single compacton for smaller systems, and a continuation of a nontrivial, noncompact linear combination of single compacton modes for larger systems. Investigating generally the different nonlinear localized (noncompact) mode families in the semi-infinite gap bounded by this FB, we find that, for increasing (defocusing) nonlinearity the stable ground state will continuously develop into an exponentially localized mode with two main peaks in antiphase. At a critical nonlinearity strength a symmetry-breaking pitchfork bifurcation appears, so that the stable ground state is single peaked for larger defocusing nonlinearities. We also investigate numerically the mobility of localized modes in this regime and find that the considered modes are generally immobile both with respect to axial and diagonal phase-gradient perturbations.",
journal = "Physical Review A",
title = "Localized modes in linear and nonlinear octagonal-diamond lattices with two flat bands",
volume = "102",
number = "2",
pages = "023532",
doi = "10.1103/PhysRevA.102.023532"
}

Stojanović, M. G., Stojanović Krasić, M., Maluckov, A., Johansson, M. M., Salinas, I. A., Vicencio, R. A.,& Stepić, M.. (2020). Localized modes in linear and nonlinear octagonal-diamond lattices with two flat bands. in Physical Review A, 102(2), 023532.
https://doi.org/10.1103/PhysRevA.102.023532

Stojanović MG, Stojanović Krasić M, Maluckov A, Johansson MM, Salinas IA, Vicencio RA, Stepić M. Localized modes in linear and nonlinear octagonal-diamond lattices with two flat bands. in Physical Review A. 2020;102(2):023532.
doi:10.1103/PhysRevA.102.023532 .

Stojanović, Mirjana G., Stojanović Krasić, Marija, Maluckov, Aleksandra, Johansson, Magnus M., Salinas, I. A., Vicencio, Rodrigo A., Stepić, Milutin, "Localized modes in linear and nonlinear octagonal-diamond lattices with two flat bands" in Physical Review A, 102, no. 2 (2020):023532,
https://doi.org/10.1103/PhysRevA.102.023532 . .

TY  - JOUR
AU  - Johansson, Magnus M.
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Gulevich, Dmitry R.
AU  - Skryabin, Dmitry V.
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8815
AB  - We consider a system of generalized coupled Discrete Nonlinear Schrödinger (DNLS) equations, derived as a tight-binding model from the Gross-Pitaevskii-type equations describing a zigzag chain of weakly coupled condensates of exciton-polaritons with spin-orbit (TE-TM) coupling. We focus on the simplest case when the angles for the links in the zigzag chain are ±π/4 with respect to the chain axis, and the basis (Wannier) functions are cylindrically symmetric (zero orbital angular momenta). We analyze the properties of the fundamental nonlinear localized solutions, with particular interest in the discrete gap solitons appearing due to the simultaneous presence of spin–orbit coupling and zigzag geometry, opening a gap in the linear dispersion relation. In particular, their linear stability is analyzed. We also find that the linear dispersion relation becomes exactly flat at particular parameter values, and obtain corresponding compact solutions localized on two neighboring sites, with spin-up and spin-down parts π/2 out of phase at each site. The continuation of these compact modes into exponentially decaying gap modes for generic parameter values is studied numerically, and regions of stability are found to exist in the lower or upper half of the gap, depending on the type of gap modes. © 2019 The Author(s).
T2  - Journal of Physics Communications
T1  - Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains
VL  - 3
IS  - 1
SP  - 015001
DO  - 10.1088/2399-6528/aaf7c9
ER  - 

@article{
author = "Johansson, Magnus M. and Beličev, Petra and Gligorić, Goran and Gulevich, Dmitry R. and Skryabin, Dmitry V.",
year = "2019",
abstract = "We consider a system of generalized coupled Discrete Nonlinear Schrödinger (DNLS) equations, derived as a tight-binding model from the Gross-Pitaevskii-type equations describing a zigzag chain of weakly coupled condensates of exciton-polaritons with spin-orbit (TE-TM) coupling. We focus on the simplest case when the angles for the links in the zigzag chain are ±π/4 with respect to the chain axis, and the basis (Wannier) functions are cylindrically symmetric (zero orbital angular momenta). We analyze the properties of the fundamental nonlinear localized solutions, with particular interest in the discrete gap solitons appearing due to the simultaneous presence of spin–orbit coupling and zigzag geometry, opening a gap in the linear dispersion relation. In particular, their linear stability is analyzed. We also find that the linear dispersion relation becomes exactly flat at particular parameter values, and obtain corresponding compact solutions localized on two neighboring sites, with spin-up and spin-down parts π/2 out of phase at each site. The continuation of these compact modes into exponentially decaying gap modes for generic parameter values is studied numerically, and regions of stability are found to exist in the lower or upper half of the gap, depending on the type of gap modes. © 2019 The Author(s).",
journal = "Journal of Physics Communications",
title = "Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains",
volume = "3",
number = "1",
pages = "015001",
doi = "10.1088/2399-6528/aaf7c9"
}

Johansson, M. M., Beličev, P., Gligorić, G., Gulevich, D. R.,& Skryabin, D. V.. (2019). Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains. in Journal of Physics Communications, 3(1), 015001.
https://doi.org/10.1088/2399-6528/aaf7c9

Johansson MM, Beličev P, Gligorić G, Gulevich DR, Skryabin DV. Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains. in Journal of Physics Communications. 2019;3(1):015001.
doi:10.1088/2399-6528/aaf7c9 .

Johansson, Magnus M., Beličev, Petra, Gligorić, Goran, Gulevich, Dmitry R., Skryabin, Dmitry V., "Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains" in Journal of Physics Communications, 3, no. 1 (2019):015001,
https://doi.org/10.1088/2399-6528/aaf7c9 . .

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 . .

TY  - CONF
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Radosavljević, Ana
AU  - Maluckov, Aleksandra
AU  - Stepić, Milutin
AU  - Poblete, Rodrigo Andres Vicencio
AU  - Johansson, Magnus M.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/10954
AB  - One of the attractive two-dimensional [2D] lattice configurations is characterized by kagome geometry. The specific arrangement of its elements, i.e. waveguides, in the form of periodic hexagons renders completely flat the first energy band in linear case. As a consequence, the localized ring-like eigenmodes belonging to the lowest energy state propagate without diffraction through the system [1, 2]. Here we study kagome ribbon [3], which can be interpreted as one-dimensional counterpart of the standard 2D kagome lattice, and can be fabricated by dint of the direct femtosecond laser inscription [4, 5]. The existence, stability and dynamical properties of various localized modes in binary kagome ribbon with defocusing Kerr type of nonlinearity have been explored, both numerically and analytically. We derived the corresponding dispersion relation and the bandgap spectrum, confirmed the opening of mini-gaps in it and found several types of stable ring-like modes to exist: staggered, unstaggered and vortex. Beside these nonlinear mode configurations occurring in a semi-infinite gap, we investigated features of "hourglass" solutions, identified in [3] as interesting structures when kagome lattice dimensionality is reduced to 1D. In nonlinear binary kagome ribbon dynamically stable propagation of unstaggered rings, vortex modes with certain topological charge and hourglass solutions are observed, while the staggered ring solutions are destabilized. In addition, we examined possibility to generate stable propagating solitary modes inside the first mini-gap and found that these mode patterns localize within sites mutually coupled by smaller coupling constant. The last feature is opposite to the nonlinear localized solutions found in the semi-infinite gap.
PB  - Belgrade : Vinča Institute of Nuclear Sciences
C3  - PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade
T1  - On localized modes in nonlinear binary kagome ribbons
SP  - 68
UR  - https://hdl.handle.net/21.15107/rcub_vinar_10954
ER  - 

@conference{
author = "Beličev, Petra and Gligorić, Goran and Radosavljević, Ana and Maluckov, Aleksandra and Stepić, Milutin and Poblete, Rodrigo Andres Vicencio and Johansson, Magnus M.",
year = "2015",
abstract = "One of the attractive two-dimensional [2D] lattice configurations is characterized by kagome geometry. The specific arrangement of its elements, i.e. waveguides, in the form of periodic hexagons renders completely flat the first energy band in linear case. As a consequence, the localized ring-like eigenmodes belonging to the lowest energy state propagate without diffraction through the system [1, 2]. Here we study kagome ribbon [3], which can be interpreted as one-dimensional counterpart of the standard 2D kagome lattice, and can be fabricated by dint of the direct femtosecond laser inscription [4, 5]. The existence, stability and dynamical properties of various localized modes in binary kagome ribbon with defocusing Kerr type of nonlinearity have been explored, both numerically and analytically. We derived the corresponding dispersion relation and the bandgap spectrum, confirmed the opening of mini-gaps in it and found several types of stable ring-like modes to exist: staggered, unstaggered and vortex. Beside these nonlinear mode configurations occurring in a semi-infinite gap, we investigated features of "hourglass" solutions, identified in [3] as interesting structures when kagome lattice dimensionality is reduced to 1D. In nonlinear binary kagome ribbon dynamically stable propagation of unstaggered rings, vortex modes with certain topological charge and hourglass solutions are observed, while the staggered ring solutions are destabilized. In addition, we examined possibility to generate stable propagating solitary modes inside the first mini-gap and found that these mode patterns localize within sites mutually coupled by smaller coupling constant. The last feature is opposite to the nonlinear localized solutions found in the semi-infinite gap.",
publisher = "Belgrade : Vinča Institute of Nuclear Sciences",
journal = "PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade",
title = "On localized modes in nonlinear binary kagome ribbons",
pages = "68",
url = "https://hdl.handle.net/21.15107/rcub_vinar_10954"
}

Beličev, P., Gligorić, G., Radosavljević, A., Maluckov, A., Stepić, M., Poblete, R. A. V.,& Johansson, M. M.. (2015). On localized modes in nonlinear binary kagome ribbons. in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade
Belgrade : Vinča Institute of Nuclear Sciences., 68.
https://hdl.handle.net/21.15107/rcub_vinar_10954

Beličev P, Gligorić G, Radosavljević A, Maluckov A, Stepić M, Poblete RAV, Johansson MM. On localized modes in nonlinear binary kagome ribbons. in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade. 2015;:68.
https://hdl.handle.net/21.15107/rcub_vinar_10954 .

Beličev, Petra, Gligorić, Goran, Radosavljević, Ana, Maluckov, Aleksandra, Stepić, Milutin, Poblete, Rodrigo Andres Vicencio, Johansson, Magnus M., "On localized modes in nonlinear binary kagome ribbons" in PHOTONICA2015 : 5th International School and Conference on Photonics and COST actions: MP1204, BM1205 and MP1205 : book of abstracts; August 24-28, 2015; Belgrade (2015):68,
https://hdl.handle.net/21.15107/rcub_vinar_10954 .

TY  - JOUR
AU  - Beličev, Petra
AU  - Gligorić, Goran
AU  - Radosavljević, Ana
AU  - Maluckov, Aleksandra
AU  - Stepić, Milutin
AU  - Poblete, Rodrigo Andres Vicencio
AU  - Johansson, Magnus M.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/838
AB  - The localized mode propagation in binary nonlinear kagome ribbons is investigated with the premise to ensure controlled light propagation through photonic lattice media. Particularity of the linear system characterized by the dispersionless flat band in the spectrum is the opening of new minigaps due to the binarism. Together with the presence of nonlinearity, this determines the guiding mode types and properties. Nonlinearity destabilizes the staggered rings found to be nondiffracting in the linear system, but can give rise to dynamically stable ringlike solutions of several types: unstaggered rings, low-power staggered rings, hour-glass-like solutions, and vortex rings with high power. The type of solutions, i.e., the energy and angular momentum circulation through the nonlinear lattice, can be controlled by suitable initial excitation of the ribbon. In addition, by controlling the system binarism various localized modes can be generated and guided through the system, owing to the opening of the minigaps in the spectrum. All these findings offer diverse technical possibilities, especially with respect to the high-speed optical communications and high-power lasers.
PB  - American Physical Society
T2  - Physical Review E
T1  - Localized modes in nonlinear binary kagome ribbons
VL  - 92
IS  - 5
DO  - 10.1103/PhysRevE.92.052916
ER  - 

@article{
author = "Beličev, Petra and Gligorić, Goran and Radosavljević, Ana and Maluckov, Aleksandra and Stepić, Milutin and Poblete, Rodrigo Andres Vicencio and Johansson, Magnus M.",
year = "2015",
abstract = "The localized mode propagation in binary nonlinear kagome ribbons is investigated with the premise to ensure controlled light propagation through photonic lattice media. Particularity of the linear system characterized by the dispersionless flat band in the spectrum is the opening of new minigaps due to the binarism. Together with the presence of nonlinearity, this determines the guiding mode types and properties. Nonlinearity destabilizes the staggered rings found to be nondiffracting in the linear system, but can give rise to dynamically stable ringlike solutions of several types: unstaggered rings, low-power staggered rings, hour-glass-like solutions, and vortex rings with high power. The type of solutions, i.e., the energy and angular momentum circulation through the nonlinear lattice, can be controlled by suitable initial excitation of the ribbon. In addition, by controlling the system binarism various localized modes can be generated and guided through the system, owing to the opening of the minigaps in the spectrum. All these findings offer diverse technical possibilities, especially with respect to the high-speed optical communications and high-power lasers.",
publisher = "American Physical Society",
journal = "Physical Review E",
title = "Localized modes in nonlinear binary kagome ribbons",
volume = "92",
number = "5",
doi = "10.1103/PhysRevE.92.052916"
}

Beličev, P., Gligorić, G., Radosavljević, A., Maluckov, A., Stepić, M., Poblete, R. A. V.,& Johansson, M. M.. (2015). Localized modes in nonlinear binary kagome ribbons. in Physical Review E
American Physical Society., 92(5).
https://doi.org/10.1103/PhysRevE.92.052916

Beličev P, Gligorić G, Radosavljević A, Maluckov A, Stepić M, Poblete RAV, Johansson MM. Localized modes in nonlinear binary kagome ribbons. in Physical Review E. 2015;92(5).
doi:10.1103/PhysRevE.92.052916 .

Beličev, Petra, Gligorić, Goran, Radosavljević, Ana, Maluckov, Aleksandra, Stepić, Milutin, Poblete, Rodrigo Andres Vicencio, Johansson, Magnus M., "Localized modes in nonlinear binary kagome ribbons" in Physical Review E, 92, no. 5 (2015),
https://doi.org/10.1103/PhysRevE.92.052916 . .