# Optical Convolutional Neural Networks: Methodology and Advances (Invited)
## 2 Development of Optical Convolution Neural Network
### Optical CNN Based on Wavelength Division Multiplexing
Then, \(n\) wavelength-sensitive variable optical amplitude modulators serially loaded \(n\) elements of the weight vector \(W\) and completed the process of multiplication. Finally, the weighted light waves were fed to a photodetector to complete the addition function. The classical MRR-based real-valued VMM architecture on the parallel data inputting is shown in Figure 6c, where the MRR weight banks were used as the wavelength-sensitive variable optical amplitude modulator to implement the multiplication process. The wavelength components after wavelength multiplexing were loaded with data \(X\) and then divided into \(k\) channels using an optical coupler, where each channel contained \(n\) wavelength components. In each channel, \(n\) add-drop MRRs were used to couple the light waves with \(n\) wavelengths to the drop port of the MRR. The proportion of light that each microring couples to the drop port \(h_{ij}\) depends on the weight \(w_{ij}\). Then, the transfer matrix for the drop ports and through ports of MRRs can be written as  
\[H_{drop}= \begin{bmatrix}h_{11}&h_{12}&\cdots&h_{1n}\\ &\vdots\\ h_{k1}&h_{k2}&\cdots&h_{kn}\end{bmatrix} , \tag{12}\]  
\[H_{drop}= \begin{bmatrix}1-h_{11}&1-h_{12}&\cdots&1-h_{1n}\\ &\vdots\\ 1-h_{k1}&1-h_{k2}&\cdots&1-h_{kn}\end{bmatrix} . \tag{13}\]  
\(H_{drop}\) at the drop port and \(H_{throughput}\) at the through port were sent into the balanced photodetector (BPD) to make both the photoelectric conversion and difference. The transfer matrix \(H\) of the MRR weight banks coupled with BPDs can be written as  
\[ \begin{array}{llll}H&=H_{throughput}-H_{drop}\\ &=\begin{bmatrix}1-2h_{11}&1-2h_{12}&\cdots&1-2h_{1n}\\ &\vdots\\ 1-2h_{k1}&1-2h_{k2}&\cdots&1-2h_{kn}\end{bmatrix}.\end{array}  \tag{14}\]  
As seen from Equation (14), real-valued VMM can be performed by adjusting the coupling coefficient of each MRR. Additionally, WDM-based CNNs with serial data input approaches have also been reported [105; 106; 107; 108; 109; 110; 111; 103]. As shown in Figure 6d, the weight vector \(W\) was still weighted on the amplitudes of the wavelength components, and the 1D data \(X\) were serially modulated to the amplitude of the wavelength components. Owing to the delay between different wavelengths via the delay unit (single mode fiber, dispersion compensating fiber, optical tunable delay lines, etc. ), the weighted optical signal generated a time delay among the adjacent wavelength components. Following this method, the input data \(X\) were serially loaded into the light waves with a single intensity modulator, and different elements of input data \(X\) were fed to the photodetector at the same time with precise delay control. Owing to using a single modulator to load the data in the CNN system, it released the demand for full clock synchronization. In 2018, [PERSON] [99] proposed a WDM-based photonics convolutional neural network accelerator (PCNNA). Here, the MRR weight banks were the wavelength-sensitive variable optical amplitude modulators to adjust the kernels. The input data were modulated into intensities of different wavelengths. The weights were loaded while passing through the MRR weight banks, and wavelength-based weight components were summed at the photodetectors to generate the convolutional results. In Figure 7a, the analog-digital hybrid CNN computing architecture (e.g., digital electronics and analog photonics (DEAP)), as the most popular architecture, was proposed in 2019 [97]. Two MRR arrays were occupied to load the data matrix and the weight matrix. The simulation recognition accuracy on 500 images from the MNIST test dataset reached 97.6%. After that, optical tunable delay lines were introduced to serially load the input data [102; 103; 111] and were experimentally demonstrated in 2022 [101]. As shown in Figure 7b, different from other schemes, one convolution operation only needs a single wavelength component, and the WDM technology enables the multiple wavelength channel to form an on-chip photonic tensor flow processor (PTFP).