| 1. |
- Stojanovic, M. G., et al.
(författare)
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Localized modes in linear and nonlinear octagonal-diamond lattices with two flat bands
- 2020
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Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : AMER PHYSICAL SOC. - 2469-9926 .- 2469-9934. ; 102:2
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Tidskriftsartikel (refereegranskat)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 singleoctagon 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.
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| 2. |
- Stojanović, M.G., et al.
(författare)
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Localized modes in two-dimensional octagonal-diamond lattices
- 2019
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Ingår i: Book of abstracts PHOTONICA2019. - Belgrade, Serbia : Vinča Institute of Nuclear Sciences. - 9788673061535 ; , s. 93-93
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Konferensbidrag (refereegranskat)abstract
- Two-dimensional octagonal-diamond (OD) atomic lattices have been explored in recent times to study phenomena related to topological phase transitions induced by spin-orbit interaction and gauge fields [1], and magnetic phases and metal-insulator transitions with Hubbard interaction [2,3]. It can lead to the appearance of nontrivial nearly flat band states with particular topological properties [4]. Here we study the octagonal-diamond photonic lattice formed of linearly coupled waveguides, proposed by [4] as a possible experimental realization of an artificial flat-band system.We investigated analytically and numerically the existence and stability of linear and nonlinear localized modes in a two-dimensional OD lattice. The primitive cell consists of four sites, linearly coupled with each other with the same coupling constant, including two diagonal couplings. The eigenvalue spectrum of the linear lattice consists of two flat bands and two dispersive bands [4]. The upper dispersive band intersects the upper flat band in the middle of the Brillouin zone, as well as the second flat band at the end of the Brillouin zone. In the linear case, there are two types of localized linear solutions, which are composed of eight sites each, having either monomer (+ - + - + - + -) or dimer (+ + - - + + - -) staggered phase structure [4]. In the presence of Kerr nonlinearity, both focusing and defocusing, compacton-like solutions [5] may exhibit instabilities due to intersections of the upper dispersive band and the flat bands. We also discuss the possibility of finding soliton solutions in the frequency gaps occurring between the flat bands and the isolated dispersive bands.REFERENCES[1] M. Kargarian, G. A. Fiete, Phys. Rev. B 82, 085106 (2010).[2] Y. Yamashita et al., Phys. Rev. B 88, 195104 (2013).[3] A. Bao et al., Sci. Rep. 4, 6918 (2014).[4] B. Pal, Phys. Rev. B 98, 245116 (2018).[5] R. A. Vicencio, M. Johansson, Phys. Rev. A 87, 061803(R) (2013).
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| 3. |
- Beličev, P.P., et al.
(författare)
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Light Localization in Nonlinear Binary Two-Dimensional Lieb Lattices
- 2016
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Ingår i: Abstract Book of RIAO-OPTILAS 2016. - Concepción - Chile : CEFOP-UdeC. ; , s. 80-80
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Konferensbidrag (refereegranskat)abstract
- Light localization in photonic lattices (PLs) is a well-known phenomenon which has been investigated during decades. It has been shown that light localization in the linear regime can be achieved by designing PLs with specific geometries, instead of embedding defects or disorder in otherwise periodic lattices [1]. These geometries provide conditions necessary for destructive wave interference, leading to formation of a perfectly flat (dispersionless) energy band. Eigenvectors associated to the flat-band (FB) eigenfrequencies are entirely degenerate and compact states (FB modes) and any superposition of them is nondiffracting. One of the simplest FB lattice patterns is the two-dimensional (2D) Lieb lattice [2,3] in which the primitive cell contains three sites. By appropriate spatial repetition of this fundamental block, it is possible to achieve a FB in the energy spectrum. Light confinement in PLs can also be a consequence of the interplay between nonlinearity and diffraction when these effects cancel each other, leading to formation of solitons. Recently, it has been reported that nonlinearity and “binarism” in quasi-one-dimensional FB systems can increase the range of existence and stability of FB ring modes [4].We model a 2D binary Lieb lattice with nonlinearity of Kerr type and analyse numerically and analytically the existence, stability and dynamical properties of various localized modes found to emerge in spectrum. From the derived dispersion relation we found that binarism does not affect the FB. However, due to the presence of additional periodicity, new gaps occur in the energy spectrum above and below the FB and their widths depend on the ratio between coupling constants. Like in the uniform Lieb lattice, we found eigenmodes in the form of a staggered four-peak “ring” structure, but only under certain conditions which require a particular relation between the field amplitudes in neighbouring sites. In the nonlinear regime, ring modes survive in the uniform Lieb lattice but lose their stability moving away from the FB. On the other hand, nonlinearity destroys the existence of ring solutions in the binary Lieb lattice, leading to a new class of stable localized solutions which can be found in minigaps. As in previous kagome and ladder binary nonlinear strips [4], it is shown that the binarism increases the existence range of stable nonlinear localized solutions.References[1] R. A. Vicencio, M. Johansson, Physical Review A 87, 061803(R) (2013).[2] R. A. Vicencio et al., Physical Review Letters 114, 245503 (2015).[3] D. Leykam, O. Bahat-Treidel, A. S. Desyatnikov, Physical Review A 86, 031805(R) (2012).[4] P. P. Beličev et al., Physical Review E 92, 052916 (2015).
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| 4. |
- Belicev, P. P., et al.
(författare)
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Localized gap modes in nonlinear dimerized Lieb lattices
- 2017
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Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : AMER PHYSICAL SOC. - 2469-9926 .- 2469-9934. ; 96:6
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Tidskriftsartikel (refereegranskat)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.
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| 5. |
- Belicev, P. P., et al.
(författare)
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Localized modes in nonlinear binary kagome ribbons
- 2015
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - : AMER PHYSICAL SOC. - 1539-3755 .- 1550-2376. ; 92:5, s. 052916-
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Tidskriftsartikel (refereegranskat)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.
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| 6. |
- Beličev, P.P., et al.
(författare)
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On localized modes in nonlinear binary kagome ribbons
- 2015
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)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.REFERENCES[1] R. A. Vicencio, C. Mejía-Cortés, J. Opt. 16, 015706 (2014).[2] R. A. Vicencio, M. Johansson, Phys. Rev. A 87, R061803 (2013).[3] M. Molina, Phys. Lett. A 376, 3458 (2012).[4] K. Davies et al., Opt. Lett. 21, 1729 (1996).[5] K. Itoh et al., MRS Bulletin 31, 620 (2006).
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