Probing the vortex beams with fractional and integral topological charges using weak random scattering screen

By use of the numerical calculation based on the Kirchhoff Green's integral theorem, we study the intensity distributions of speckle fields behind the weak random scattering screens illuminated by the Laguerre-Gaussian beams. It is found that the profile of bright spot similar to the peacock-feather-like in intensity distributions of speckle field, those bright spots show uniform distribution around the central dark spots, and the number of bright spots is related to the topological charges of the vortex beams. We are able to probe the topological charges of Laguerre-Gaussian beams directly by observing the bright spots in the intensity distributions patterns.