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

Abstract

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.