Measuring the fractional and integral topological charges of the optical vortex beams using a diffraction grating

The diffraction properties of intensity and phase of the optical vortex beam through the diffraction gratings are studied. It is found that the profiles of the zero-order light spot in the center is similar to the +1 and −1 diffraction orders, and the distributions of light spots is related to the topological charges of vortex beam. For the fractional topological changes, the profiles of light spots is become long in the y direction, which parallel to the direction of slits of grating, and the patterns for positive and negative of topological charges are mirrored in the x axis. For the integral topological changes there is no difference between the patterns for positive and negative of topological charges, in this case, we can easily determined the topological charges from the patterns of phase. The results may be used to detect the fractional and integral topological charges of vortex beams.