| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- 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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| 5. |
- Johansson, Magnus, 1965-, et al.
(författare)
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Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains
- 2019
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Ingår i: Journal of Physics Communications. - : Institute of Physics Publishing (IOPP). - 2399-6528. ; 3:1, s. 1-17
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Tidskriftsartikel (refereegranskat)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.
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