Interaction of fractional orbital angular momentum in two-wave mixing processes

Nonlinear mixing of optical vortices carrying arbitrary fractional orbital angular momentum was studied. The selection rule for the generated field is extended for the case where non-integer vortices interacts in two-wave mixing processes. We experimentally observe, step by step, the evolution of the birth of a vortex and the formation of higher radial orders in a non-collinear two-wave mixture at the Fraunhofer zone. This is possible due the constrains on the radial order p and the topological charge l in the normalized overlap integral, allowing us to access states where both vortex and external ring are not fully formed. A theoretical model was presented together with numerical and experimental results. (paper)