Arithmetic with optical topological charges in stepwise-excited Rb vapor.

We report on experimentally observed addition, subtraction, and cancellation of orbital angular momentum (OAM) in the process of parametric four-wave mixing that results in frequency up- and down-converted emission in Rb vapor. Specific features of OAM transfer from resonant laser fields with different optical topological charges to the spatially and temporally coherent blue light (CBL) have been considered. We have observed the conservation of OAM in nonlinear wave mixing in a wide range of experimental conditions, including a noncollinear geometry of the applied laser beams, and furthermore, that the CBL accumulates the total OAM of the applied laser light. Spectral and power dependences of vortex and plane wavefront blue light beams have been compared.