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Spatial Vector Solitons in Nonlinear Photonic Crystal Fibers
Author(s) -
Salgueiro José R.,
Kivshar Yuri S.,
Pelinovsky Dmitry E.,
Simón Verónica,
Michinel Humberto
Publication year - 2005
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2005.00324.x
Subject(s) - nonlinear system , scalar (mathematics) , physics , homogeneous , photonic crystal , scalar field , photonic crystal fiber , optics , classical mechanics , mathematical analysis , optical fiber , mathematics , quantum mechanics , geometry , statistical physics
We study spatial vector solitons in a photonic crystal fiber (PCF) made of a material with the focusing Kerr nonlinearity. We show that such two‐component localized nonlinear waves consist of two mutually trapped components confined by the PCF linear and the self‐induced nonlinear refractive indices, and they bifurcate from the corresponding scalar solitons. We demonstrate that, in a sharp contrast with an entirely homogeneous nonlinear Kerr medium where both scalar and vector spatial solitons are unstable and may collapse, the periodic structure of PCF can stabilize the otherwise unstable two‐dimensional spatial optical solitons. We apply the matrix criterion for stability of these two‐parameter solitons, and verify it by direct numerical simulations.