We introduce a model of dual-core waveguide with the cubic nonlinearity and group-velocity dispersion (GVD) confined to different cores, with the linear coupling between them. The model can be realized in terms of photonic-crystal fibers. It opens a way to understand how solitons are sustained by the interplay between the nonlinearity and GVD which are not “mixed” in a single nonlinear Schrödinger (NLS) equation, but are instead separated and mix indirectly, through the linear coupling between the two cores. The spectrum of the system contains two gaps, semi-infinite and finite ones. In the case of anomalous GVD in the dispersive core, the solitons fill the semi-infinite gap, leaving the finite one empty. This soliton family is entirely stable, and is qualitatively similar to the ordinary NLS solitons, although shapes of the soliton’s components in the nonlinear and dispersive cores are very different, the latter one being much weaker and broader. In the case of the normal GVD, the situation is completely different: the semi-infinite gap is empty, but the finite one is filled with a family of stable gap solitons featuring a two-tier shape, with a sharp peak on top of a broad “pedestal.” This case has no counterpart in the usual NLS model. An extended system, including weak GVD in the nonlinear core, is analyzed too. In either case, when the solitons reside in the semi-infinite or finite gap, they persist if the extra GVD is anomalous, and completely disappear if it is normal.
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September 2005
Research Article|
October 21 2005
Solitons in a linearly coupled system with separated dispersion and nonlinearity
Arik Zafrany;
Arik Zafrany
Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering,
Tel Aviv University
, Tel Aviv 69978, Israel
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Boris A. Malomed;
Boris A. Malomed
a)
Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering,
Tel Aviv University
, Tel Aviv 69978, Israel
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Ilya M. Merhasin
Ilya M. Merhasin
Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering,
Tel Aviv University
, Tel Aviv 69978, Israel
Search for other works by this author on:
Arik Zafrany
Boris A. Malomed
a)
Ilya M. Merhasin
Department of Interdisciplinary Studies, School of Electrical Engineering, Faculty of Engineering,
Tel Aviv University
, Tel Aviv 69978, Israela)
Electronic mail: [email protected]
Chaos 15, 037108 (2005)
Article history
Received:
January 25 2005
Accepted:
February 19 2005
Citation
Arik Zafrany, Boris A. Malomed, Ilya M. Merhasin; Solitons in a linearly coupled system with separated dispersion and nonlinearity. Chaos 1 September 2005; 15 (3): 037108. https://doi.org/10.1063/1.1894705
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