# A Review of Optical Neural Networks
## 3 Development Processes and Categories
### Fiber-Based Optical Neural Networks
#### 3.3.2 Multimode Fibers  
Since the 1980s, researchers have been studying the effect of scattering media on imaging systems and have found it possible to conduct imaging using the scattering media itself. The results indicate that imaging via scattering media not only improves the resolution of the imaging system but also eliminates image noise. Single-fiber imaging can be achieved if an optical fiber is treated as a scattering medium [84]. A multimode fiber (MMF) is a highly scattering medium that disrupts the light propagating through it and outputs speckle patterns that the human eye cannot decode. These patterns are called scattered spots. The behavior of a system consisting of input patterns has deterministic propagation through an MMF and a detector [85]. Multiple studies have shown that image sending or imaging through an MMF can be performed by simulating phase conjugation. With the development of digital holography and the increasing maturity of spatial light modulation devices and digital micromirror devices, beam wavefront and phase adjustments are becoming increasingly flexible and precise [86]. The proposed systems suffer from overly complex optical components and image distortion, resulting from variations in the path length experienced by the various modes of light propagation in optical fibers. Such problems can be effectively solved using neural networks. The idea of combining MMF imaging with neural networks for image classification has been around for more than three decades [87; 88].  
Currently, deep learning applications can solve more complex problems, and MMFs are becoming one of the choices available for optically implemented neural networks, as seen in Figure 4. The concept of combining a complex fix mapping with a simple programmable processor to achieve a powerful overall system has been applied to a variety of deep learning algorithms. Optical neural networks based on MMFs learn the nonlinear relationship between the amplitude of the scatter pattern obtained at the fiber output and the phase or amplitude at the fiber input [89; 90; 91]. In addition, optical reservoir computing (RC) systems have been shown to significantly improve the computational performance [92]. The reservoir layer of an all-optical reservoir computing system consists of an optical fiber and other optical process devices, and nonlinearity is reflected in the system. No electro-optical conversions are required in the reservoir layer, which dramatically reduces the problem of time consumption [93; 94; 95; 96; 97; 98; 99]. What is more, a picosecond-pulsed fiber laser is used to illuminate the subject, and the spatial information of the detected image is expanded in the time domain by using the inter-mode dispersion property of the multimode fiber. Time domain information is accordingly detected using a single-pixel detector, and the resulting two-dimensional image information can then ultimately be recovered from the one-dimensional time domain information with a neural network training method [100].  
Figure 3: Comparison of photons with biological neurons and synapses [80]. **(A,B)** is biological synapse and photonic synapse, respectively.  
The key challenge when designing a viable optical neuromorphic computer is to combine the linear part of the optical system with the nonlinear elements and input-output interfaces while maintaining the speed and power efficiency of the optical interconnect. It is possible to combine the linear and nonlinear portions of an optical system in the shared body of an MMF. At the same time, a large number of spatial modes are densely supported in the MMF, maintaining the traditional high parallelism of optics while retaining the compact form factor. Therefore, it appears that MMF-based analog optical computers can be highly energy-efficient and versatile while having performance comparable to digital computers.