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Article: Coupled periodic waves with opposite dispersions in a nonlinear optical fiber
Title | Coupled periodic waves with opposite dispersions in a nonlinear optical fiber |
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Authors | |
Keywords | Coupled nonlinear Schrödinger (NLS) equations Hirota method Optical fiber Periodic solutions |
Issue Date | 2005 |
Publisher | Elsevier 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? |
Abstract | Using 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 Identifier | http://hdl.handle.net/10722/75625 |
ISSN | 2015 Impact Factor: 1.48 2015 SCImago Journal Rankings: 0.778 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | Tsang, SC | en_HK |
dc.contributor.author | Nakkeeran, K | en_HK |
dc.contributor.author | Malomed, BA | en_HK |
dc.contributor.author | Chow, KW | en_HK |
dc.date.accessioned | 2010-09-06T07:13:00Z | - |
dc.date.available | 2010-09-06T07:13:00Z | - |
dc.date.issued | 2005 | en_HK |
dc.identifier.citation | Optics Communications, 2005, v. 249 n. 1-3, p. 117-128 | en_HK |
dc.identifier.issn | 0030-4018 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/75625 | - |
dc.description.abstract | Using 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.language | eng | en_HK |
dc.publisher | Elsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/optcom | en_HK |
dc.relation.ispartof | Optics Communications | en_HK |
dc.rights | Optics Communications. Copyright © Elsevier BV. | en_HK |
dc.subject | Coupled nonlinear Schrödinger (NLS) equations | en_HK |
dc.subject | Hirota method | en_HK |
dc.subject | Optical fiber | en_HK |
dc.subject | Periodic solutions | en_HK |
dc.title | Coupled periodic waves with opposite dispersions in a nonlinear optical fiber | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://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+fiber | en_HK |
dc.identifier.email | Chow, KW:kwchow@hku.hk | en_HK |
dc.identifier.authority | Chow, KW=rp00112 | en_HK |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.optcom.2004.12.042 | en_HK |
dc.identifier.scopus | eid_2-s2.0-17044364999 | en_HK |
dc.identifier.hkuros | 98217 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-17044364999&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 249 | en_HK |
dc.identifier.issue | 1-3 | en_HK |
dc.identifier.spage | 117 | en_HK |
dc.identifier.epage | 128 | en_HK |
dc.identifier.isi | WOS:000228707000014 | - |
dc.publisher.place | Netherlands | en_HK |
dc.identifier.scopusauthorid | Tsang, SC=7102255919 | en_HK |
dc.identifier.scopusauthorid | Nakkeeran, K=7004188157 | en_HK |
dc.identifier.scopusauthorid | Malomed, BA=35555126200 | en_HK |
dc.identifier.scopusauthorid | Chow, KW=13605209900 | en_HK |