# Optical Convolutional Neural Networks: Methodology and Advances (Invited)
## 2 Development of Optical Convolution Neural Network
### Optical CNN Based on Wavelength Division Multiplexing  
A WDM-based CNN offers a new solution by comprehensive use of the multidimensional physical information of light waves in terms of the wavelength, amplitude, spatial, temporal, polarization, and so on. By leading into the wavelength dimension in Figure 6, VVM operation is divided into the multiplication process and the addition process, where the multiplication process is accomplished using electrooptic modulations, and the addition process is achieved via wavelength multiplexing and photoelectrical conversion at the photoelectric detector. WDM-based VVMs are familiarly split into two categories: one is the wavelength-independent weight-loaded architecture (shown in Figure 6a), and the other is the wavelength-sensitive weight-loaded architecture (Figure 6b), in which the division criteria is whether wavelength-sensitive variable optical amplitude modulators (VOAMs) are used. Figure 5: Schemes of optical CNNs based on optical interference. (**a**) Scheme of optical CNN based on rectangular architecture MZI mesh [85]. (**b**) Scheme of optical CNN based on triangular architecture MZI mesh [89]. (**c**) Scheme of optical coherent dot-product chip (OCDC) to realize optical CNN [88]. (**d**) Scheme of optical CNN based on the combination of WDM and MZI mesh [93]. (**e**) Scheme of optical CNN based on the combination of WDM and multimode interference [37]. (**a**) Reprinted from Ref. [85] with permission of the authors. (**b**,**c**,**e**) Reprinted with permission from Refs. [37; 88; 89] under a CC BY 4.0 license. (**d**) Reprinted with permission from Ref. [93]. 2022, American Chemical Society. First, for the wavelength-independent weight-loaded VVM shown in Figure 6a, \(n\) wavelength components loaded with input data vector \(X\) were parallelly sent into the computing hardware, where each light wave carried one element of the data vector \(X\). Then, wavelength components underwent amplitude modulation to load the weight vector \(W\), which was the multiplication process of elements in two vectors. As a main optical device in the WDM-based CNN, the variable optical amplitude modulators can be implemented using MZIs [95], microring resonators (MRRs) [96; 97; 98; 99; 100; 101; 102; 103], phase change materials (PCMs) [39; 104], and waveshapers [105; 106; 107; 108; 109]. The addition process was conducted using square-law photoelectric detection and the summation of the optical intensity of wavelength components at the photodetector. To obtain the summation signal of different wavelength components, the beat of optical sidebands between adjacent wavelength components should be effectively avoided. Therefore, in the WDM-based CNN system, the wavelength interval of wavelengths fed to the photodetector as well as the bandwidth for both the modulator and photodetector need to satisfy the following condition:  
\[f_{w}-2f_{m}>f_{p}, \tag{11}\]  
where \(f_{w}\) is the wavelength interval of adjacent wavelength components, \(f_{m}\) is the modulation bandwidth, and \(f_{p}\) is the bandwidth of the photodetectors. Figure 6b shows a wavelength-sensitive weight-loaded VVM architecture where the process of multiplication was performed with wavelength-sensitive variable optical amplitude modulators [97; 98; 99; 100; 101; 102]. Wavelength components loaded with data vector \(X\) were  
Figure 6: The principle of vector-vector multiplication (VVM) with WDM technology. (**a**) Wavelength-independent weight-loaded VVM architecture. (**b**) Wavelength-sensitive weight-loaded VVM architecture. (**c**) Classical MRR-based real-valued VMM architecture. (**d**) WDM-based VMM with data input serially by introducing optical delay. VOAM: variable optical amplitude modulator, MUX: multiplexing, PD: photodetector, OC: optical coupler, TIA: transimpedance amplifier, IM: intensity modulator, DCF: dispersion compensation fiber. transmitted through one physical channel by wavelength-division multiplexing.