Modelling and Analysis of the Influence of Astigmatic Transformations on Two-Mode Superposition of Vortex Beams

The visualization of topological charges in the superposition of two vortex Gaussian beams by introducing astigmatism based on the Fresnel transform is investigated. It is found that the introduction of astigmatism leads to a distortion of the annular structure of the beam such that the phase structure of the vortex is visually apparent in the intensity distribution and allows the topological charges of the two beams to be determined. Previously, this approach was applied, as a rule, for separate vortex beams. Note also that, unlike the approach based on the application of neural networks, this method does not require preliminary training, since the detection result is achieved on the basis of a simple analysis of the distortion geometry (counting minima along fixed directions).