Topological charge (TC) is a key factor to characterize the orbital angular momentum (OAM) of vortex beams. Accurate determination of TC is an essential prerequisite for the applications of OAM beams in optical communication and sensing. In complex environments, wandering perturbation and opaque obstacles destroy the amplitude and phase of the optical field and put challenges to accurate measurements. In this paper, we propose a method to determine the TC of obstructed wandering vortex beams. According to the theoretical results of the propagation of two uniform off-axis multi-center vortex beams and a random off-axis wandering vortex beam through a sector-shaped opaque obstacle (SSOO), it is observed that the averaged OAM of wandering vortex beams can reveal the TC of the input field, and even wandering perturbation and large-angle SSOO are encountered. Experimental measurement of the averaged OAM is carried out based on a single cylindrical lens (CL), and the results agree with the theoretical predictions. Results show that the method proposed here works well when the methods of light intensity, Fourier transform, and phase distribution fail to determine the TC in extremely complex environment such as the angle of SSOO of 270° and large wandering perturbations.
In this work, three types of multi-center off-axis vortex beams, namely, the beams of uniform off-axis coherent superposition (UCS), uniform off-axis incoherent superposition (UIS), and random off-axis incoherent superposition (RIS), are studied both in theory and experiment. In the theory part, utilizing an equivalent matrix method (EMA), we obtain the propagation of the three types of vortex beams after the SSOO. Theoretical results of the distribution of the light intensity, Fourier intensity, and phase are presented. According to the ABCD propagation law of a tilted CL, the average OAM of the three types of beams is calculated for various input topological charges. In the experimental part, the intensity distribution is detected, and the average OAM is obtained using a single 45o-tilted CL.
In this paper, the characteristics of the average OAM, optical intensity, Fourier intensity, and phase distribution of the wandering vortex beams obstructed by SSOO are investigated theoretically and experimentally. The results show that the detection method based on the average OAM can correctly reveals the absolute value and sign of the TC of the input beam when the wandering vortex beam is obstructed by the angle of SSOO of over 180°. Moreover, this method works robustly when off-axis perturbations and vortex center misalignment are encountered.