Simple Direct Measurement of the Orbital Stokes Parameters in Structured Vortex Beams

An analogy with the polarization Stokes parameters and symplectic methods of the second-order intensity moment matrix allowed us to develop a simple technique for measuring the orbital Stokes parameters followed by mapping the structured beam states onto the orbital Poincaré sphere. The measurement process involves only two shots of the beam intensity patterns in front of a cylindrical lens and in its double focus. Such a simple measurement approach is based on the reciprocity effect between the experimentally measured cross-intensity element Wxy and the orbital angular momentum of the intensity moment matrix. For experiments, we chose two types of two-parameter structured beams, namely, structured Laguerre–Gaussian beams and binomial beams. We obtained a good agreement between our theoretical background and the experiments, as well as the results of other authors.