As the basic physical quantity of classical mechanics and quantum mechanics, orbital angular momentum (OAM) is a natural characteristic of the spiral phase beams and has been widely studied in modern times. Meanwhile, the OAM states of different topological charges are orthogonal to each other, which can be employed as a new degree of freedom of information. Thus, OAM state has been applied to a variety of multiplexing communication systems, and the OAM state correction is the key to realize these multiplexing communication systems.

We propose a high-precision OAM state correction method based on a diffractive deep neural network (D2NN) because D2NN has almost zero energy deep learning function, and is faster and more accurate than that of the traditional deep learning network, CNN. As D2NN can realize various complex functions in traditional computer neural networks and perform parallel operations at the speed of light, the proposed method will provide a high-speed and efficient OAM state correction for realizing large-capacity and high-quality for the next-generation wireless communication.

We study a D2NN-based OAM correction method. First, the D2NN component is obtained mainly through the training dataset composed of multiple sets of OAM states and the target OAM states under different turbulence interference. Second, the designed D2NN network components are trained, and the parameters in the components are updated and optimized until the square error loss function of the OAM state and the target OAM state output from the D2NN component reaches a predetermined threshold. Then, the D2NN component is obtained, and can achieve the wavefront correction with high-speed and high-precision. The influence of the training parameters and the network iteration times on the proposed correction method is discussed, and the number of D2NN network layers and the training parameters with the best performance are presented. Finally, after the physically D2NN diffractive component is fabricated, using techniques such as 3D printing or lithography, one can perform the specific task by adopting only optical diffraction components.

We propose a fast and efficient OAM state correction method based on D2NN to significantly reduce the training time and the loss function compared with the correction method based on the traditional CNNs. Furthermore, the environment configuration required by D2NN is not high and can be widely utilized. Meanwhile, we adjust the number of diffraction layers, the training parameters, and the network iterations in the designed D2NN to find the best correction performance. Additionally, the training parameters, with only amplitude as parameters, only phase as parameters, and both the phase and amplitude as parameters are discussed. The results show that the D2NN-based correction method performs optimally under medium turbulence (atmospheric turbulence intensity of 10^-14 m^-2/3), with 8 diffraction layers (Table 4), and both the amplitude and phase used as the training parameters. As the number of network iterations increases, the loss function value in the proposed correction method will gradually decrease and converge to a constant (Figs. 8 and 9). In addition, the influence of the topological charge of the OAM state in the dataset on the correction effect is also studied. The comparison of the peak signal-to-noise ratio (PSNR) of the corrected OAM state shows that a smaller topological charge leads to a smaller distortion degree and a higher accuracy, with the PSNR greater than 30. This indicates that the OAM state has been corrected to be close to the original OAM state (Fig. 7).

The selection of iteration times, layers, and training parameters in the designed D2NN component will affect the correction speed and accuracy, and the high-precision OAM state correction can be realized through the designed D2NN component. When the atmospheric turbulence intensity is 10^-14 m^-2/3, the designed D2NN component has the best performance when the layer number is 8, and the phase and amplitude are adopted as the parameters. Meanwhile, the loss function is reduced by more than 45.45% compared with those of the D2NN compoent when the layer number is 5. For the strong atmospheric turbulence, the correction accuracy can be improved by increasing the iteration number during the network training, since the reduction rate of the loss function in 20 iterations reaches 98.03%. For weak turbulence, only phase parameters can be employed for training. For strong turbulence, the method combining the phase and the amplitude parameters is better in training. In addition, a smaller topological charge leads to a smaller corrected distortion. The proposed method has a fast and efficient learning function to provide a new implementation method for OAM state correction.