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.