Detection uncertainty of fractional optical vortex with angle indeterminacy in different transformation-based OAM-sorting systems

This paper reveals and compares the detection uncertainty of fractional optical vortex (FOV) in several coordinate transformation-based OAM sorting systems. It is found that the azimuth of the phase mutation of FOV will significantly affect the output results. Hence, there will be a detection uncertainty when analyzing FOV with angle indeterminacy, but this uncertainty is not come from the FOV itself, but from the OAM sorting system. Therefore, FOV with angular uncertainty could be a tool to evaluate the robustness of the OAM sorting system. From the simulation and comparison, the features of the earliest proposed log-polar sorting method and the improved beam-copying, spiral-transformation sorting methods are studied. We conclude that the beam-copying sorting method is better for OAM spectrum analysis, and the spiral-transformation sorting with appropriate parameters performs better for average OAM detection.