The vortex beam carrying orbital angular momentum (OAM) has attracted great attentions in optical communication field, which can extend the channel capacity of communication system due to the orthogonality between different OAM modes. Generally, atmospheric turbulence can distort the helical phase fronts of OAM beams, which presents a critical challenge to the effective recognition of OAM modes. Recently, convolutional neural network (CNN), as a model of deep learning, has been widely applied to machine vision. In this paper, based on the CNN theory, we make a trade-off between the computational complexity of the system and the efficiency of recognition by establishing a specially designed six-layer CNN structure in CPU station to efficiently achieve the recognition of OAM mode in turbulent environment through the feature extraction of the received LG beam's intensity distributions. Furthermore, we examine the performances of our designed CNN with respect to various turbulence levels, transmission distances, mode spacings, and we have also compared the performances of recognizing single OAM mode with multiplexed OAM modes. The numerical simulation shows that basing on CNN method, the coaxial multiplexed OAM modes can obtain higher recognizing accuracy about 96.25% even under long transmission distance with strong turbulence.

Orbital angular momentum (OAM) in optical vortices (OV) beams offers a new dimension of space mode because coaxially propagating OV beams with different azimuthal OAM states are mutually orthogonal. As a result, the beams can be efficiently multiplexed and de-multiplexed to potentially increase the capacity of the optical communication system. Therefore, up to now, the azimuthal indices of the transverse spatial mode has been investigated for many times. This paper focuses on another mode, which can be called as radial indices of Laguerre–Gaussian beam. A novel OAM encoding system with high-order radial indices is established by simulation for the optical communication system. At the transmitter, a series of holograms of the Laguerre–Gaussian mode with different radial indices are used to achieve coaxial transmission of multiplexing beams, where each beam represents one data bit. At the receiver, we use the superposition of a conjugate light field corresponding to the transmitted beams for de-multiplexing the multiplexed beams. Meanwhile, the combination of the phase-shift factor and centroid algorithm can realize the simultaneous detection of the radial indices in each channel and efficient decoding of information. We also analyze the measurement deviation on the performance of an encoding system and give the corresponding discussions.

The transmission of the orbital angular momentum (OAM) beam has attracted a lot of attention in the field of free-space optical (FSO) communication. Usually, after transmitting in atmospheric turbulences, the helical phase-front of OAM beams will be severely distorted, and there will exist the intermode crosstalk. As a result, the performance of the communication system will degrade significantly. In this paper, we have investigated the influences of the level of the turbulence strength to the transmitting OAM beams by changing the refractive-index structural parameter of $C_n^2$ and the number of turbulence random phase screens of N in simulation environment. Then, by adopting the Gerchberg-Saxton (GS) algorithm, which can be used to compute the pre-compensation phase and correct the distorted OAM beams, the retrieving performances of transmitting single and multiplexed OAM beams under different turbulence strengths were also investigated. The simulation results show that with increasing the atmospheric-turbulence strength levels determined by the parameters $C_n^2$ and N, the retrieving performances decrease dramatically. When the turbulence strength level is selected within an appropriate range, the OAM beams can be effectively retrieved by adopting GS algorithm and observing the power density spectrum. Notably, the retrieving performance for the transmission of a single OAM beam is better than that of the multiplexing OAM beam.