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Article: Coupled periodic waves with opposite dispersions in a nonlinear optical fiber

TitleCoupled periodic waves with opposite dispersions in a nonlinear optical fiber
Authors
KeywordsCoupled nonlinear Schrödinger (NLS) equations
Hirota method
Optical fiber
Periodic solutions
Issue Date2005
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/optcom
Citation
Optics Communications, 2005, v. 249 n. 1-3, p. 117-128 How to Cite?
AbstractUsing the Hirota's method and elliptic θ-functions, we obtain three families of exact periodic (cnoidal) wave solutions for two nonlinear Schrödinger (NLS) equations coupled by XPM (cross-phase-modulation) terms, with a ratio σ of the XPM and SPM (self-phase-modulation) coefficients. Unlike the previous works, we obtain the solutions for the case when the coefficients of the group-velocity-dispersion (GVD) in the coupled equations have opposite signs. In the limit of the infinite period, the solutions with σ > 1 carry over into inverted bound states of bright and dark solitons in the normal- and anomalous-GVD modes (known as "symbiotic solitons"), while the infinite-period solution with σ < 1 is an uninverted bound state (also an unstable one). The case of σ = 2 is of direct interest to fiber-optic telecommunications, as it corresponds to a scheme with a pulse stream in an anomalous-GVD payload channel stabilized by a concomitant strong periodic signal in a mate normal-GVD channel. The case of arbitrary σ may be implemented in a dual-core waveguide. To understand the stability of the coupled waves, we first analytically explore the modulational stability of CW (constant-amplitude) solutions, concluding that they may be completely stable for σ ≥ 1, provided that the absolute value of the GVD coefficient is smaller in the anomalous-GVD mode than in the normal-GVD one, and certain auxiliary conditions on the amplitudes are met. The stability of the exact cnoidal-wave solutions is tested in direct simulations. We infer that, while, strictly speaking, in the practically significant case of σ = 2 all the solutions are unstable, in many cases the instability may be strongly attenuated, rendering the above-mentioned paired channels scheme usable. In particular, the instability is milder for a smaller period of the wave pattern, and/or if the anomalous GVD is weaker than the normal GVD in the mate channel. When the instability sets in, it first initiates quasi-reversible modulations, and only at a later stage the wave pattern decays into a "turbulent" state. © 2004 Elsevier B.V. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/75625
ISSN
2015 Impact Factor: 1.48
2015 SCImago Journal Rankings: 0.778
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorTsang, SCen_HK
dc.contributor.authorNakkeeran, Ken_HK
dc.contributor.authorMalomed, BAen_HK
dc.contributor.authorChow, KWen_HK
dc.date.accessioned2010-09-06T07:13:00Z-
dc.date.available2010-09-06T07:13:00Z-
dc.date.issued2005en_HK
dc.identifier.citationOptics Communications, 2005, v. 249 n. 1-3, p. 117-128en_HK
dc.identifier.issn0030-4018en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75625-
dc.description.abstractUsing the Hirota's method and elliptic θ-functions, we obtain three families of exact periodic (cnoidal) wave solutions for two nonlinear Schrödinger (NLS) equations coupled by XPM (cross-phase-modulation) terms, with a ratio σ of the XPM and SPM (self-phase-modulation) coefficients. Unlike the previous works, we obtain the solutions for the case when the coefficients of the group-velocity-dispersion (GVD) in the coupled equations have opposite signs. In the limit of the infinite period, the solutions with σ > 1 carry over into inverted bound states of bright and dark solitons in the normal- and anomalous-GVD modes (known as "symbiotic solitons"), while the infinite-period solution with σ < 1 is an uninverted bound state (also an unstable one). The case of σ = 2 is of direct interest to fiber-optic telecommunications, as it corresponds to a scheme with a pulse stream in an anomalous-GVD payload channel stabilized by a concomitant strong periodic signal in a mate normal-GVD channel. The case of arbitrary σ may be implemented in a dual-core waveguide. To understand the stability of the coupled waves, we first analytically explore the modulational stability of CW (constant-amplitude) solutions, concluding that they may be completely stable for σ ≥ 1, provided that the absolute value of the GVD coefficient is smaller in the anomalous-GVD mode than in the normal-GVD one, and certain auxiliary conditions on the amplitudes are met. The stability of the exact cnoidal-wave solutions is tested in direct simulations. We infer that, while, strictly speaking, in the practically significant case of σ = 2 all the solutions are unstable, in many cases the instability may be strongly attenuated, rendering the above-mentioned paired channels scheme usable. In particular, the instability is milder for a smaller period of the wave pattern, and/or if the anomalous GVD is weaker than the normal GVD in the mate channel. When the instability sets in, it first initiates quasi-reversible modulations, and only at a later stage the wave pattern decays into a "turbulent" state. © 2004 Elsevier B.V. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/optcomen_HK
dc.relation.ispartofOptics Communicationsen_HK
dc.rightsOptics Communications. Copyright © Elsevier BV.en_HK
dc.subjectCoupled nonlinear Schrödinger (NLS) equationsen_HK
dc.subjectHirota methoden_HK
dc.subjectOptical fiberen_HK
dc.subjectPeriodic solutionsen_HK
dc.titleCoupled periodic waves with opposite dispersions in a nonlinear optical fiberen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0030-4018&volume=249&spage=117&epage=128&date=2005&atitle=Coupled+periodic+waves+with+opposite+dispersions+in+a+nonlinear+optical+fiberen_HK
dc.identifier.emailChow, KW:kwchow@hku.hken_HK
dc.identifier.authorityChow, KW=rp00112en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.optcom.2004.12.042en_HK
dc.identifier.scopuseid_2-s2.0-17044364999en_HK
dc.identifier.hkuros98217en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-17044364999&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume249en_HK
dc.identifier.issue1-3en_HK
dc.identifier.spage117en_HK
dc.identifier.epage128en_HK
dc.identifier.isiWOS:000228707000014-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridTsang, SC=7102255919en_HK
dc.identifier.scopusauthoridNakkeeran, K=7004188157en_HK
dc.identifier.scopusauthoridMalomed, BA=35555126200en_HK
dc.identifier.scopusauthoridChow, KW=13605209900en_HK

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