Transformation of polarisation singularities in nonlinear mixing of light beams with frequency conversion in a medium with cubic nonlinearity

We analyse the electric field transverse distributions in light beams with a tripled frequency and with a frequency of 2ω₁ – ω₂, which arise in the bulk of an isotropic cubic-nonlinear medium upon the propagation of nonuniformly polarised beams of fundamental radiation with a multimode transverse structure described by a superposition of Laguerre – Gaussian modes. A relation is found between the total topological indices of the circular polarisation singularity points in the transverse sections of the generated signal beams and the corresponding total indices in the beams of fundamental radiation.