# Optical Convolutional Neural Networks: Methodology and Advances (Invited)
## 2 Development of Optical Convolution Neural Network
### Optical CNN Based on Optical Interference
The rectangular diagonal matrix \(\Sigma\) can be implemented with optical attenuators or optical amplifiers. Therefore, any real-valued matrix can be realized with the dimension-matched MZI mesh. Since any real-valued matrix \(M\) is realized, parallel convolution of \(p\) real-valued kernels with \(q\) elements in each kernel can be performed with the MZI mesh. The most representative optical interference-based CNN was proposed in 2018 [85]. The rectangular architecture MZI mesh in Figure 5a was used as the kernel matrices, and the optical delay lines introduced different time delays to implement multiple convolutional layers. The classification accuracy of the handwritten digits was simulated to 97% in the MNIST database. Then, 4 \(\times\) 4 MZI-based linear optical processors were experimentally demonstrated in multiple material platforms, such as silicon-on-insulator (SOI) and silicon nitride (SiN) [86]. The triangular architecture MZI mesh has also been proposed to realize optical CNNs [87]. The fabricated SOI chip of the triangular architecture MZI mesh network is shown in Figure 5b [89] to realize three 3 \(\times\) 3 kernels. Recognition accuracies of 86.9% for the MNIST database and 79.3% for Fashion-MNIST were experimentally demonstrated. Apart from the MZI-based unitary matrix realizing the convolution operation, the optical coherent dot-product chip (OCDC) realized by the interference principle was also an important implementation of optical CNN [88]. The schematic of the chip is shown in Figure 5c, where the light wave is first divided into several branches and then sent into the dot-product chip with one as the reference and the rest to perform the dot-product operation. In each computing branch of Figure 5c, double modulators are cascaded to accomplish the dot-product. The reference branch was utilized to introduce an amplitude bias to perform real-valued computing. By reusing the chip, the AUTOMAP neural network, including matrix multiplication and convolution computing, was experimentally demonstrated and achieved image reconstruction quality comparable to that of a 32 bit digital computer. In addition to the interference of coherent light with the MZI, the combination of WDM technology and interference was another important realization of optical CNN [37; 93; 94]. Figure 5d shows the application of WDM technology in a simplified butterfly-style MZI mesh [93]. In this scheme, incoherent light was utilized to avoid additional hardware costs for phase control between input channels and the influence of phase fluctuations of optical signals in off-chip fibers when using coherent light. In their experimental demonstration, a handwritten digit recognition accuracy of 94.16% was realized. As shown in Figure 5e, a compact optical convolution processing unit (OCPU) was realized by combining a multimode interference mechanism and WDM technology [37]. In this work, the process of multiplication was accomplished with multimode interference, and the process of addition was realized with square-law detection of multiple wavelengths with photodetectors. With two 4 \(\times\) 4 multimode interference regions and four phase shifters, three correlated 2 \(\times\) 2 real-valued kernels were realized with a convolution operation precision of 5 bit. Kernels were reconfigured by adjusting phase shifters, the compute density of 12.74 TMACs/s/mm\({}^{2}\) was demonstrated, and a classification accuracy of 92.17% was realized on handwritten digits in the MNIST database. The greatest advantage of the proposed OCPU is that the number of reconfigurable units scales linearly with the scale of the kernel size, which translates into solid potential for large-scale integration.