Coupling of noncanonical optical vortices

Abstract

When canonical vortices with different topological charges coexist in an optical beam, they inevitably become noncanonical during propagation. The noncanonical nature of optical vortices can be expressed in terms of morphological parameters, which can be represented in terms of a spinor, similar to the Jones vectors for polarization. This allows one to express the prefactor for a Gaussian beam containing two arbitrary vortices in terms of two terms. One is a product of two linearly propagating vortices. The other one, which is called the coupling term, represents the interaction between the vortices. The coupling term is independent of the vortex positions but depends on their initial morphological parameters. There are two situations where the interaction is zero. One is when the vortices are canonical with the same topological charge, and the other is when the vortices have the same anisotropy but with orthogonal orientations. The former situation is well known. The noninteraction of the latter situation is confirmed by a numerical simulation.