Stabilization of Axisymmetric Airy Beams by Means of Diffraction and Nonlinearity Management in Two-Dimensional Fractional Nonlinear Schrödinger Equations

The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework fractional Schrödinger equation, which includes saturable or cubic self-focusing defocusing nonlinearity and Lévy index ((LI) alias for fractionality) taking values 1≤α≤2. model applies to light a chain optical cavities emulating diffraction. Management included by making diffraction and/or coefficients periodic functions distance, ζ. management format with coefficient decaying as 1/ζ considered too. These schemes maintain stable beams, their axial symmetry, contrast symmetry-breaking splitting instability ring-shaped patterns 2D Kerr media. driven supercritical collapse at all α<2 presence term eliminated, too, means management.