J.R. Salgueiro, Yu.S. Kivshar, D.E. Pelinovsky, V. Simon, and H. Michinel
Spatial vector solitons in nonlinear photonic crystal fibers
Studies in Applied Mathematics 115, 157-171 (2005)
Abstract:
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.
Keywords:
COUPLED NONLINEAR SCHRODINGER EQUATIONS, PERIODIC POTENTIALS WITH DEFECTS,
PHOTONIC OPTICAL FIBERS, BIFURCATIONS OF VECTOR SOLITONS, STABILITY OF VECTORS SOLITONS.