Bright vortex bullets in a parametric band-gap system

Summary form only given. It is well known that multi-dimensional bright and dark soliton solutions exist in a parametric system with a one-dimensional volume grating. An optical vortex is a soliton-like object that contains a phase singularity, around which the phase of the electric field changes by an integer multiple of 2m/spl pi/ where integer m is the topological charge of the phase singularity. Two-dimensional vortex solutions have been found in conventional parametric system without band-gaps. They can be classified into two categories, dark vortices and bright vortices. Dark vortices appear like a dark hole in a uniform bright background. By contrast, a bright vortex is like a hollow cone on a dark background. Here we look for stationary bright vortices localized in all three dimensions in the band-gap system, which are described by the normalised equations.