Spatial ring emission and filament formation in an optical fiber with a saturable nonlinear cladding

We present numerical simulations of Gaussian beam propagation in an optical fiber with a linear core and a saturable self-focusing cladding. Cylindrical nonlinear waves are emitted from the core into the cladding and are initially localized only in the radial direction, forming rings. These rings can break their cylindrical symmetry through a transverse instability, which yields filaments localized both azimuthally and radially, most of which stay close to the core for long propagation distances.