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Jason, P. & Johansson, M. (2016). Discrete breathers for a discrete nonlinear Schrodinger ring coupled to a central site. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 93(1), 012219
Open this publication in new window or tab >>Discrete breathers for a discrete nonlinear Schrodinger ring coupled to a central site
2016 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 93, no 1, p. 012219-Article in journal (Refereed) Published
Abstract [en]

We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrodinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2016
National Category
Physical Sciences
Identifiers
urn:nbn:se:liu:diva-125683 (URN)10.1103/PhysRevE.93.012219 (DOI)000369333600003 ()26871085 (PubMedID)
Available from: 2016-03-01 Created: 2016-02-29 Last updated: 2017-11-30
Johansson, M. & Jason, P. (2015). Breather mobility and the Peierls-Nabarro potential: brief review and recent progress. In: Juan F. R. Archilla, Noé Jiménez, Victor J. Sánchez-Morcillo, Luis M. García-Raffi (Ed.), Quodons in Mica: nonlinear localized travelling excitations in crystals (pp. 147-178). Cham: Springer
Open this publication in new window or tab >>Breather mobility and the Peierls-Nabarro potential: brief review and recent progress
2015 (English)In: Quodons in Mica: nonlinear localized travelling excitations in crystals / [ed] Juan F. R. Archilla, Noé Jiménez, Victor J. Sánchez-Morcillo, Luis M. García-Raffi, Cham: Springer, 2015, p. 147-178Chapter in book (Refereed)
Abstract [en]

The question whether a nonlinear localized mode (discrete soliton/breather) can be mobile in a lattice has a standard interpretation in terms of the Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases, the PN barrier for strongly localized solutions becomes large, rendering these essentially immobile. Several ways to improve the mobility by reducing the PN-barrier have been proposed during the last decade, and the first part gives a brief review of such scenarios in 1D and 2D. We then proceed to discuss two recently discovered novel mobility scenarios. The first example is the 2D Kagome lattice, where the existence of a highly degenerate, flat linear band allows for a very small PN-barrier and mobility of highly localized modes in a small-power regime. The second example is a 1D waveguide array in an active medium with intrinsic (saturable) gain and damping, where exponentially localized, travelling discrete dissipative solitons may exist as stable attractors. Finally, using the framework of an extended Bose-Hubbard model, we show that while quantum fluctuations destroy the mobility of slowly moving, strongly localized classical modes, coherent mobility of rapidly moving states survives even in a strongly quantum regime

Place, publisher, year, edition, pages
Cham: Springer, 2015
Series
Springer Series in Materials Science, ISSN 0933-033X ; 221
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:liu:diva-123926 (URN)10.1007/978-3-319-21045-2_6 (DOI)000380538300006 ()9783319210445 (ISBN)9783319210452 (ISBN)
External cooperation:
Funder
Swedish Research Council
Available from: 2016-01-13 Created: 2016-01-13 Last updated: 2016-08-26Bibliographically approved
Jason, P. & Johansson, M. (2015). Charge Flipping Vortices in DNLS trimer and hexamer. In: Suzana Petrović , Goran Gligorić and Milutin Stepić (Ed.), PHOTONICA 2015. V International School and Conference on Photonics& COST actions: MP1204 and BM1205 & the Second international workshop "Control of light and matter waves propagation and localization in photonic lattices“, Belgrad 2015: Book of Abstracts. Paper presented at 5th International School and Conference on Photonics - PHOTONICA2015, Belgrade, Serbia, August 24 - 28, 2015 (pp. 65-65). Belgrade, Serbia: Vinča Institute of Nuclear Sciences
Open this publication in new window or tab >>Charge Flipping Vortices in DNLS trimer and hexamer
2015 (English)In: PHOTONICA 2015. V International School and Conference on Photonics& COST actions: MP1204 and BM1205 & the Second international workshop "Control of light and matter waves propagation and localization in photonic lattices“, Belgrad 2015: Book of Abstracts / [ed] Suzana Petrović , Goran Gligorić and Milutin Stepić, Belgrade, Serbia: Vinča Institute of Nuclear Sciences , 2015, p. 65-65Conference paper, Poster (with or without abstract) (Other academic)
Abstract [en]

We examine the existence and properties of Charge Flipping Vortices (CFVs), rtices which periodically flip the topological charge, in three-site (trimer) and six-site (hexamer) discrete nonlinear Schrödinger (DNLS) lattices. We demonstrate numerically that CFVs exist as exact quasiperiodic solutions in continuous families which connect two different stationary solutions without topological charge, and that it is possible to interpret the dynamics of certain CFVs as the result of perturbations of these stationary solutions. The CFVs are calculated with high numerical accuracy and we may therefore accurately determine many of their properties, such as their energy and linear stability, and the CFVs are found to be stable over large parameter regimes.

We also show that, like in earlier studies for lattices with a multiple of four sites, trimer and hexamer CFVs can be obtained by perturbing stationary constant amplitude vortices with certain linear eigenmodes. However, in contrast to the former case where the perturbation could be infinitesimal, the magnitude of the perturbations for trimers and hexamers must overcome a quite large threshold value. These CFVs may be interpreted as exact quasiperiodic CFVs, with a small perturbation applied to. The concept of a charge flipping energy barrier is introduced and discussed.

REFERENCES

[1]P. Jason, M. Johansson, Phys. Rev. E. 91, 022910 (2015).

Place, publisher, year, edition, pages
Belgrade, Serbia: Vinča Institute of Nuclear Sciences, 2015
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:liu:diva-123929 (URN)978-86-7306-131-3 (ISBN)
Conference
5th International School and Conference on Photonics - PHOTONICA2015, Belgrade, Serbia, August 24 - 28, 2015
Available from: 2016-01-13 Created: 2016-01-13 Last updated: 2016-06-21Bibliographically approved
Jason, P. & Johansson, M. (2015). Charge flipping vortices in the discrete nonlinear Schrodinger trimer and hexamer. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 91(2), 022910
Open this publication in new window or tab >>Charge flipping vortices in the discrete nonlinear Schrodinger trimer and hexamer
2015 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 91, no 2, p. 022910-Article in journal (Refereed) Published
Abstract [en]

We examine the existence and properties of charge flipping vortices (CFVs), vortices which periodically flip the topological charge, in three-site (trimer) and six-site (hexamer) discrete nonlinear Schrodinger lattices. We demonstrate numerically that CFVs exist as exact quasiperiodic solutions in continuous families which connect two different stationary solutions without topological charge, and that it is possible to interpret the dynamics of certain CFVs as the result of perturbations of these stationary solutions. The CFVs are calculated with high numerical accuracy and we may therefore accurately determine many of their properties, such as their energy and linear stability, and the CFVs are found to be stable over large parameter regimes. We also show that, like in earlier studies for lattices with a multiple of four sites, trimer and hexamer CFVs can be obtained by perturbing stationary constant amplitude vortices with certain linear eigenmodes. However, in contrast to the former case where the perturbation could be infinitesimal, the magnitude of the perturbations for trimers and hexamers must overcome a quite large threshold value. These CFVs may be interpreted as exact quasiperiodic CFVs, with a small perturbation applied. The concept of a charge flipping energy barrier is introduced and discussed.

Place, publisher, year, edition, pages
American Physical Society, 2015
National Category
Physical Sciences
Identifiers
urn:nbn:se:liu:diva-117256 (URN)10.1103/PhysRevE.91.022910 (DOI)000351205700005 ()
Note

Funding Agencies|Swedish Research Council

Available from: 2015-04-22 Created: 2015-04-21 Last updated: 2017-12-04
Johansson, M., Naether, U. & Vicencio, R. A. (2015). Compactification tuning for nonlinear localized modes in sawtooth lattices. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 92(3-1), 032912
Open this publication in new window or tab >>Compactification tuning for nonlinear localized modes in sawtooth lattices
2015 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 92, no 3-1, p. 032912-Article in journal (Refereed) Published
Abstract [en]

We discuss the properties of nonlinear localized modes in sawtooth lattices, in the framework of a discrete nonlinear Schrodinger modelwith general on-site nonlinearity. Analytic conditions for existence of exact compact three-site solutions are obtained, and explicitly illustrated for the cases of power-law (cubic) and saturable nonlinearities. These nonlinear compact modes appear as continuations of linear compact modes belonging to a flat dispersion band. While for the linear system a compact mode exists only for one specific ratio of the two different coupling constants, nonlinearity may lead to compactification of otherwise noncompact localized modes for a range of coupling ratios, at some specific power. For saturable lattices, the compactification power can be tuned by also varying the nonlinear parameter. Introducing different on-site energies and anisotropic couplings yields further possibilities for compactness tuning. The properties of strongly localized modes are investigated numerically for cubic and saturable nonlinearities, and in particular their stability over large parameter regimes is shown. Since the linear flat band is isolated, its compact modes may be continued into compact nonlinear modes both for focusing and defocusing nonlinearities. Results are discussed in relation to recent realizations of sawtooth photonic lattices.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2015
National Category
Other Physics Topics
Identifiers
urn:nbn:se:liu:diva-121892 (URN)10.1103/PhysRevE.92.032912 (DOI)000361310700008 ()26465545 (PubMedID)
Note

Funding Agencies|Swedish Research Council within the Swedish Research Links program [348-2013-6752]; Spanish government [FIS 2011-25167, FPDI-2013-18422]; Aragon project (Grupo FENOL); Programa ICM grant [RC130001]; Programa de Financiamiento Basal de CONICYT [FB0824/2008]; FONDECYT [1151444]

Available from: 2015-10-13 Created: 2015-10-12 Last updated: 2017-12-01
Johansson, M. (2015). Editorial Material: Comment on "Localization-delocalization transition in self-dual quasi-periodic lattices" by Sun M. L. et al. in EPL, vol 112, issue 1, pp. Europhysics letters, 112(1), 17002
Open this publication in new window or tab >>Editorial Material: Comment on "Localization-delocalization transition in self-dual quasi-periodic lattices" by Sun M. L. et al. in EPL, vol 112, issue 1, pp
2015 (English)In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 112, no 1, p. 17002-Article in journal, Editorial material (Other academic) Published
Abstract [en]

n/a

Place, publisher, year, edition, pages
EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY, 2015
National Category
Physical Sciences
Identifiers
urn:nbn:se:liu:diva-123531 (URN)10.1209/0295-5075/112/17002 (DOI)000365131500019 ()
Available from: 2015-12-22 Created: 2015-12-21 Last updated: 2017-12-01
Belicev, P. P., Gligoric, G., Radosavljevic, A., Maluckov, A., Stepic, M., Vicencio, R. A. & Johansson, M. (2015). Localized modes in nonlinear binary kagome ribbons. Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 92(5), 052916
Open this publication in new window or tab >>Localized modes in nonlinear binary kagome ribbons
Show others...
2015 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 92, no 5, p. 052916-Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2015
National Category
Physical Sciences
Identifiers
urn:nbn:se:liu:diva-123797 (URN)10.1103/PhysRevE.92.052916 (DOI)000365871500028 ()26651771 (PubMedID)
Note

Funding Agencies|Swedish Research Council within the Swedish Research Links programme [348-2013-6752]; Sweden-Chilean-Serbian trilateral project "Control of light and matter waves propagation and localization in photonic lattices"; Ministry of Education, Science and Technological Development of Republic of Serbia [III45010]; Fondecyt Grant [1151444]; Programa ICM [RC-130001]; Programa de Financiamiento Basal [FB0824]

Available from: 2016-01-11 Created: 2016-01-11 Last updated: 2017-11-30
Beličev, P., Gligorić, G., Radosavljević, A., Maluckov, A., Stepić, M., Vicencio, R. & Johansson, M. (2015). On localized modes in nonlinear binary kagome ribbons. In: : . Paper presented at 5th International School and Conference on Photonics - PHOTONICA2015, Belgrade, Serbia, August 24 - 28, 2015, (pp. 68). Belgrade, Serbia: Vinča Institute of Nuclear Sciences
Open this publication in new window or tab >>On localized modes in nonlinear binary kagome ribbons
Show others...
2015 (English)Conference paper, Poster (with or without abstract) (Other academic)
Abstract [en]

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).

Place, publisher, year, edition, pages
Belgrade, Serbia: Vinča Institute of Nuclear Sciences, 2015
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:liu:diva-123930 (URN)978-86-7306-131-3 (ISBN)
Conference
5th International School and Conference on Photonics - PHOTONICA2015, Belgrade, Serbia, August 24 - 28, 2015,
Available from: 2016-01-13 Created: 2016-01-13 Last updated: 2016-01-20Bibliographically approved
Johansson, M. (2015). Rotational energy barriers: Charge-flipping of discrete vortices and rotation of dipole discrete gap solitons. In: : . Paper presented at 2nd International workshop on Control of light and matter waves propagation and localization in photonic lattices, Belgrade, Serbia, August 28-29, 2015.
Open this publication in new window or tab >>Rotational energy barriers: Charge-flipping of discrete vortices and rotation of dipole discrete gap solitons
2015 (English)Conference paper, Oral presentation only (Other academic)
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:liu:diva-123927 (URN)
Conference
2nd International workshop on Control of light and matter waves propagation and localization in photonic lattices, Belgrade, Serbia, August 28-29, 2015
Available from: 2016-01-13 Created: 2016-01-13 Last updated: 2016-01-20Bibliographically approved
Johansson, M. (2014). Breather mobility and the PN potential - Brief review and recent progress. In: : . Paper presented at International workshop on Control of light and matter waves propagation and localization in photonic lattices, Linköping, 6-7 August 2014 (pp. 31).
Open this publication in new window or tab >>Breather mobility and the PN potential - Brief review and recent progress
2014 (English)Conference paper, Oral presentation only (Other academic)
Abstract [en]

The question whether a nonlinear localized mode (discrete soliton/breather) can be mobile in a lattice has a standard interpretation in terms of the Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases, the PN barrier for strongly localized solutions becomes large, rendering these essentially immobile. Several ways to improve the mobility by reducing the PN-barrier have been proposed during the last decade, and the first part gives a brief review of such scenarios in 1D and 2D. We then proceed to discuss two recently discovered novel mobility scenarios. The first example is the 2D Kagome lattice, where the existence of a highly degenerate, flat linear band allows for a very small PN-barrier and mobility of highly localized modes in a small-power regime. The second example is a 1D waveguide array in an active medium with intrinsic (saturable) gain and damping, where exponentially localized, travelling discrete dissipative solitons may exist as stable attractors.

National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:liu:diva-113519 (URN)
Conference
International workshop on Control of light and matter waves propagation and localization in photonic lattices, Linköping, 6-7 August 2014
Funder
Swedish Research Council, 348-2013-6752
Available from: 2015-01-20 Created: 2015-01-20 Last updated: 2015-01-26
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-6708-1560

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