Experimental optical computing of complex vector convolution with twisted light

Fig. 1. The schematic diagram of the optical complex vector convolution $C = A * B$ , based on five-dimensional orbital-angular-momentum state vector.

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Fig. 2. Schematic of experimental layout for optical computing of complex vector convolution based on OAM eigenstates. HWP, half wave plate; SLM, spatial light modulator; L1, L2, L3, L4, L5, lenses; Mask, a phase triangular object; CCD, camera. Inset, holographic example of encoded complex vector with four OAM states in SLM1 and SLM2.

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Fig. 3. Architecture of the residual neural network.

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Fig. 4. Complex vector convolution process and experimental results of 7-dimensional OAM state vectors. The input vectors (a) $A$ and (b) $B$ convolved to get the output (c) vector $C$ , where the vector elements are $a_{n} = a_{l} \exp (i φ_{l}^{a})$ , $b_{n} = b_{l} \exp (i φ_{l}^{b})$ , and $c_{n} = c_{l} \exp (i φ_{l}^{c})$ , respectively.

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Fig. 5. The distributions of (a) proximity and (b) relative errors obtained by comparing each experimental predicted output vector with the theoretical output vector for 7-dimensional OAM state vector convolution.

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Table 1. Average proximity and mean relative error of the output vector from 7-, 9-, and 11-dimensional OAM state vector convolution.
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Table 1. Average proximity and mean relative error of the output vector from 7-, 9-, and 11-dimensional OAM state vector convolution.
Dimension of vector C $(d)$ Average proximity $(S_{avg})$ Mean relative error $({Err}_{mean})$
13 $0.9778 \pm 0.0188$ $0.0427 \pm 0.0341$
17 $0.9633 \pm 0.0192$ $0.0498 \pm 0.0403$
21 $0.9463 \pm 0.0226$ $0.0571 \pm 0.0477$

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Ling Hong, Haoxu Guo, Xiaodong Qiu, Fei Lin, Wuhong Zhang, Lixiang Chen, "Experimental optical computing of complex vector convolution with twisted light," Adv. Photon. Nexus 2, 046008 (2023)

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