  We investigate the non linear mixing of orbital angular momentum in type II
second harmonic generation with arbitrary topological charges imprinted on two
orthogonally polarized beams. Starting from the basic nonlinear equations for
the interacting fields, we derive the selection rules determining the set of
paraxial modes taking part in the interaction. Conservation of orbital angular
momentum naturally appears as the topological charge selection rule. However, a
less intuitive rule applies to the radial orders when modes carrying opposite
helicities are combined in the nonlinear crystal, an intriguing feature
confirmed by experimental measurements.
