Vortex beams with orbital angular momentum, helical phase wave front, and dark void intensity distribution have caught extensive attention since their discovery, and boast important application prospects in quantum entanglement, optical imaging, nonlinear optics, optical communication, and other fields. Meanwhile, their helical phase wave front can be described as exp(ilθ), where θ is the azimuth and l is the topological charge, with any rational number taken theoretically. However, the beam radius depends on the topological charge and its central dark spot will increase with the rising l value, which makes the applications of the vortex beams with large lvalue in transmission and coupling difficult. Under the maximum l limit, reducing the interval between adjacent topological loads can increase the mode types and improve the communication capacity. For example, the mode resolution Δl of orbital angular momentum (OAM) is changed from 1 to 0.1, the available modes are expanded by ten times, and the communication rate can be greatly improved. In recent years, the OAM research has gradually extended to the fractional field. The generation of fractional OAM beams and the accurate mode measurement are of significance for high-quality information transmission. Therefore, we construct an improved residual network to identify the modes of fractional vortex beams with different turbulence intensities and transmission distances. To this end, the convolutional neural network is adopted to improve the mode detection accuracy and communication reliability.

We construct a new convolutional neural network I-ResNet to identify the modes of fractional vortex beams transmitted by different distances under different turbulence intensities. I-ResNet network based on the ResNet50 network adds a deconvolution layer and maximum pooling between the last residual block and Ave Pool, deepens the number of network layers to 51 layers, and improves the operation sequence of the residual block to BN normalization, ReLU activation function, Conv, dropout layer, and until the next BN. The pre-trained model migration on the ImageNet image dataset is applied to the mode recognition task of fractional vortex beams. Compared with the existing references, our study numerically simulates the fractional vortex beam datasets of five types of mode resolutions and corresponding ten OAM modes under three turbulence intensities and three transmission distances. The number of light intensity images is greatly increased to provide sufficient sample number for I-ResNet to improve the network robustness. By learning and training a large number of samples, the built network structure can accurately identify the beam modes. Additionally, two sets of fractional vortex beams with different mode resolutions are set up to test the network, which proves that the network has strong generalization ability. Then, by comparing the training results of different network models, it is further verified that the built network can improve the recognition accuracy.

The simulation results show that the constructed network can identify the beam modes accurately with sound generalization. At a transmission distance of 500 m and Δl≥0.1, the three turbulence intensities can be identified 100% correctly [Fig. 6(a)]. When the transmission distance is 1000 m, the recognition accuracy can reach 100% with Cn2=10-14m-2/3 and Δl≥0.15, the fractional vortex beams with small mode resolution are greatly affected by the turbulence intensity, and the accuracy of Δl=0.1 is 94.7% [Fig. 6(b)]. Under the transmission distance of 1500 m, with the increasing turbulence intensity, the beam interference degree grows, which causes longer learning time, and increasing iteration number in which the accuracy and loss rate reach stability (Fig. 8). The I-ResNet network has better performance against strong turbulence than ResNet50, and the correct recognition rate is improved by 6.1 percentage points (Table 4). Under the same transmission distance, the smaller value of the mode integer part results in greater influence exerted by strong turbulence and a more obvious decline in recognition accuracy (Fig. 7). The network is proven to have strong generalization ability by the test set confusion matrix (Fig. 10).

We construct I-ResNet, improve the network structure and operation order of residual blocks based on the ResNet50 network and apply the pre-trained model on the ImageNet image dataset to the mode recognition task of fractional vortex beams. The simulation results show that the recognition accuracy of I-ResNet is improved, especially under strong turbulence, and the recognition accuracy is more significant. Under the transmission distance of 1500 m, the accuracy can reach 100% with Cn2=10-16m-2/3 and Δl≥0.05. The recognition accuracy can reach 96.5% with Cn2=10-14m-2/3 and Δl=0.15. With the increasing turbulence intensity or transmission distance, the recognition accuracy decreases. Therefore, the results have a certain guiding significance for designing free-space optical communication systems.