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Due to carrying orbital angular momentum (OAM), vortex beams are also known as OAM beams. Coherence, as another controllable parameter of the beam, and its joint control with the vortex phase greatly promote the applications of the vortex beam such as particle manipulation and anti-atmospheric turbulence. However, the OAM information, quantified by the topological charge (TC), hidden in the second-order electric field statistical function of a partially coherent vortex beam is not easily extracted experimentally. In addition, the existing TC measurement schemes for the partially coherent vortex beams are limited to the detection of the near focal plane. The above-mentioned difficulties and limitations undoubtedly limit the application of vortex beams. Here, we achieve OAM measurement of a partially coherent Laguerre Gaussian (PCLG) beam under different coherence conditions, especially at extremely low coherence, by coupling the cross phase. The cross phase can separate the original concentric dark rings in the degree of coherence function of a PCLG beam. The number of separated dark rings is equal to the magnitude of the TC which determines the OAM carried by each photon in the vortex beam. The sign of TC is determined by the arrangement direction of separated dark rings, which determines the direction of rotation of the spiral wavefront of the vortex beam. In addition, we verify the accuracy of our method experimentally, especially under the condition of extremely low coherence and during propagation. Our results can find application in OAM-based free space optical communication and information encryption.
Zhang et al. (Mon,) studied this question.