Compactification tuning for nonlinear localized modes in sawtooth lattices

We discuss the properties of nonlinear localized modes in sawtooth lattices, in the framework of a discrete nonlinear Schrödinger model with general on-site nonlinearity. Analytic conditions for existence of exact compact three-site solutions are obtained, and explicitly illustrated for the cases of...

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Autores: Johansson, Magnus, Naether, Uta, Vicencio, Rodrigo A.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/147574
Acceso en línea:http://hdl.handle.net/10261/147574
Access Level:acceso abierto
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spelling Compactification tuning for nonlinear localized modes in sawtooth latticesJohansson, MagnusNaether, UtaVicencio, Rodrigo A.We discuss the properties of nonlinear localized modes in sawtooth lattices, in the framework of a discrete nonlinear Schrödinger model with 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.The research has been performed with support from the Swedish Research Council within the Swedish Research Links program, 348-2013-6752. U.N. appreciates the Spanish government projects FIS 2011-25167 and FPDI-2013-18422 as well as the Aragon project (Grupo FENOL). R.A.V. acknowledges support from Programa ICM grant RC130001, Programa de Financiamiento Basal de CONICYT (FB0824/2008), and FONDECYT Grant No. 1151444.Peer ReviewedAmerican Physical SocietyComisión Nacional de Investigación Científica y Tecnológica (Chile)Fondo Nacional de Desarrollo Científico y Tecnológico (Chile)Swedish Research CouncilMinisterio de Ciencia e Innovación (España)Ministerio de Economía y Competitividad (España)Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]2017201720152017info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10261/147574reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Ingléshttp://dx.doi.org/10.1103/PhysRevE.92.032912Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1475742026-05-22T06:33:51Z
dc.title.none.fl_str_mv Compactification tuning for nonlinear localized modes in sawtooth lattices
title Compactification tuning for nonlinear localized modes in sawtooth lattices
spellingShingle Compactification tuning for nonlinear localized modes in sawtooth lattices
Johansson, Magnus
title_short Compactification tuning for nonlinear localized modes in sawtooth lattices
title_full Compactification tuning for nonlinear localized modes in sawtooth lattices
title_fullStr Compactification tuning for nonlinear localized modes in sawtooth lattices
title_full_unstemmed Compactification tuning for nonlinear localized modes in sawtooth lattices
title_sort Compactification tuning for nonlinear localized modes in sawtooth lattices
dc.creator.none.fl_str_mv Johansson, Magnus
Naether, Uta
Vicencio, Rodrigo A.
author Johansson, Magnus
author_facet Johansson, Magnus
Naether, Uta
Vicencio, Rodrigo A.
author_role author
author2 Naether, Uta
Vicencio, Rodrigo A.
author2_role author
author
dc.contributor.none.fl_str_mv Comisión Nacional de Investigación Científica y Tecnológica (Chile)
Fondo Nacional de Desarrollo Científico y Tecnológico (Chile)
Swedish Research Council
Ministerio de Ciencia e Innovación (España)
Ministerio de Economía y Competitividad (España)
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
description We discuss the properties of nonlinear localized modes in sawtooth lattices, in the framework of a discrete nonlinear Schrödinger model with 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.
publishDate 2015
dc.date.none.fl_str_mv 2015
2017
2017
2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/147574
url http://hdl.handle.net/10261/147574
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv http://dx.doi.org/10.1103/PhysRevE.92.032912
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.811543

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