Discrete-symmetry and angular pseudo-momentum in nonlinear photonic crystals

The aim of this contribution is two-fold. We propose a new approach to the search for vortex solutions of a general nonlinear equation that describes not only both optical and Bose-Einstein condensates discrete-symmetry systems but also more general situations. A general expression for symmetric vortex solutions will be proved by showing that they are angular Bloch modes associated to the invariance under finite rotations of the discrete-symmetry system. Numerical evidence of the existence of these contraints are given using a photonic crystal fiber (PCF) as a physical example of discrete-symmetry system