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Data transmission with up to 100 orbital angular momentum modes via commercial multi-mode fiber and parallel neural networks

Fu Feng, Jia-An Gan, Jingpeng Nong, Peng-Fei Chen, Guangyong Chen, Changjun Min, Xiaocong Yuan, and Michael Somekh

Open Access Open Access

Abstract

This work presents an artificial intelligence enhanced orbital angular momentum (OAM) data transmission system. This system enables encoded data retrieval from speckle patterns generated by an incident beam carrying different topological charges (TCs) at the distal end of a multi-mode fiber. An appropriately trained network is shown to support up to 100 different fractional TCs in parallel with TC intervals as small as 0.01, thus overcoming the problems with previous methods that only supported a few modes and could not use small TC intervals. Additionally, an approach using multiple parallel neural networks is proposed that can increase the system’s channel capacity without increasing individual network complexity. When compared with a single network, multiple parallel networks can achieve the better performance with reduced training data requirements, which is beneficial in saving computational capacity while also expanding the network bandwidth. Finally, we demonstrate high-fidelity image transmission using a 16-bit system and four parallel 14-bit systems via OAM mode multiplexing through a 1-km-long commercial multi-mode fiber (MMF).

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Supplementary Material (1)

NameDescription
Supplement 1       revised supplementary

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (8)
Fig. 1.
Fig. 1. Experimental setup and speckle patterns. (a) Illustration of experimental setup (b) Demonstration of recorded speckle pattern variation with time under same incident topological charge (Details are discussed in Supplement 1)

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Fig. 2.
Fig. 2. Architecture of the CNN. (a) The input image size is 224 × 224 pixels. The numbers and sizes of the feature maps extracted from the hidden layers are indicated by the boxes. The conv1 box contains a 7 × 7 convolutional layer with two strides; a batch normalization layer; a rectified linear unit (ReLU) activation function layer; and a max pooling layer with two strides. (b), (c), (d), and (e) represent the “bottleneck” building blocks used in conv2_X, conv3_X, conv4_X, and conv5_X, respectively, where the number x denotes the block number. The deep residual function of the CNN is mainly dependent on the “bottleneck” building block; this has been discussed in detail by He et al. [38]. The number of convolutional kernels is denoted in each block. Down-sampling is performed by using conv3_1, conv4_1, and conv5_1 with a stride of two.

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Fig. 3.
Fig. 3. Identification of OAM modes with integer topological charges. (a) t-SNE visualization of speckle patterns in the testing set during the training process. (b) Training and testing accuracy characteristics of the CNN for speckle patterns generated with specific OAM modes. (c) Confusion matrix showing the excellent performance of the CNN in discriminating OAM modes ranging from 1 to 50.

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Fig. 4.
Fig. 4. Identification of OAM modes with fractional topological charges. (a) Dynamic range of the network. Ten central topological charges with intervals of 10 are used in this study, and each group contains 10 topological charges with values that are close to each central topological charge at intervals of 0.01. (b) Confusion matrix of the test results, where the recognition accuracy reaches 98.78%.

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Fig. 5.
Fig. 5. Parallel networks to expand the topological charge bandwidth without decreasing performance. (a) Illustration of training process of a parallel network system (b) Schematic showing how the parallel networks recognize an input speckle pattern that corresponds to a specific output. A given speckle pattern was sent to all trained networks in parallel and a corresponding value was output. (c) Performance of parallel networks in expanding the topological charge bandwidth, where each red box contains 10 topological charges with intervals of 0.01 (the axis is not to scale here).

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Fig. 6.
Fig. 6. Illustration of OAM-multiplexing information transmission system. Information is encoded into an OAM superposition state. The superposed vortex beam is then coupled into a commercial MMF and propagates through the fiber. The speckle pattern generated at the distal end of the fiber is recorded using the camera. A CNN is then used to convert the received speckle pattern into the initial data.

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Fig. 7.
Fig. 7. Details of transmission of OAM-encoded data of a color image through a commercial 1000-m-long MMF using the AI-assisted OAM multiplexing system. Each color pixel of the dog image was encoded into a weighted matrix of three groups of 16 binary bits by multiplexing 16 different fractional OAM modes. The trained CNN can then decode the information from the sequential speckle patterns. The red/green/blue (R/G/B) channels are all encoded in the same way and are transmitted in sequence.

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Fig. 8.
Fig. 8. Comparison of solo networks and parallel networks. (a) Performance of solo networks and parallel networks trained with different number of speckle patterns for each topological charge. (b) Image transmission via the 4×14-bit parallel network configuration (top) and via the single 16-bit network (bottom). Although the 4×14-bit parallel networks are trained with fewer data, they provide the better performance when compared with the single 16-bit network.

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Equations (3)

Equations on this page are rendered with MathJax. Learn more.

L c r o s s _ e n t r o p y _ l o s s = − 1 k ∑ t = 1 k ⁡ ∑ i = 1 c ⁡ y ^ t , i × l o g ( y t , i )
E l n = A n e x p ( − i l n ϕ )
E s = ∑ l = l 1 N l c n E l n
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