# A Review of Optical Neural Networks
## 3 Development Processes and Categories
### Fiber-Based Optical Neural Networks
#### 3.3.3 Time Stretch  
Photonic time stretch (PTS) has been developing for more than two decades since its introduction in the 1990s [101]. It has become a mature optical technology that can slow down, amplify, and capture ultrafast events by slowing down the optical signal in real-time to bridge the bandwidth gap between electronics and photonics. PTS consists of a dispersive optical link that uses group velocity dispersion to convert the spectrum of a broadband optical pulse into a time-stretched temporal waveform. This method is used to perform Fourier transforms of the optical signal at a high frame rate on a single transmission basis for real-time analyses of fast dynamic processes. Via dispersion, the information residing in the spectrum is stretched over time. Group delay dispersion for time stretching can be experimentally implemented using various different device designs. The main designs of the proposed devices are internal Raman amplified fibers, chirped fiber Bragg gratings, array optical waveguide gratings, multimode waveguides (fiber or a pair of planar reflectors), and curved spatially mapped chromatic dispersion devices [102; 103]. Deep learning extracts patterns and information from rich multidimensional datasets and is widely used for image recognition. Its earliest combination with PTS was for recognizing and classifying large numbers of cells. The Optical Fluid Time-Stretch Quantitative Phase Imaging (OTS-QPI) system reconstructs bright-field and quantitative phase images of flowing cells based on spectral interferograms of time-stretch light pulses, captures images of flowing cells with minimal motion distortion at rates greater than 10,000 cells/s, and extracts multiple biophysical features of individual cells, making it a powerful instrument for biomedical applications [104; 105; 106; 107; 108]. OTS-QPI was first implemented in combination with fully connected neural networks for image classification as seen in Figure 5A [104]. In addition, with the rapid development of deep learning and convolutional neural networks, combinations with generative adversarial networks and other image enhancement algorithms have been proposed to solve additional deep learning problems, combined with PTS [109; 110]. Figure 4: (**a**) CNNs project arbitrary patterns and perform transfer learning via MMF [89]. (**b**) MMF-based free-space all-optical RC system using spatial light modulators and diffractive optical elements [98]. Deep learning has evolved to the point where there is an urgent need for computationally small, low-latency datasets to reduce the computational effort associated with computational power limits and large datasets. When inputting data, nonlinear optical dynamics enables linear learning algorithms to learn nonlinear functions or determine boundaries to classify the data into correct classes. The nonlinear Schrodinger kernel, also called the Lambda kernel, is the core of this system [111, 112]. The Lambda kernel, as seen in Figure 5B, is capable of nonlinearly casting data that have been modulated onto the spectrum of femtosecond pulses into a space where data that are non-dividable in linear terms are converted to be linearly divisible in the new space. In terms of functionality, there are similarities between the Lambda kernel and the concept of \"kernel projection\" in the machine learning literature. Using this approach, the spectrum of the data is mapped onto femtosecond light pulses and projected into an implicit high-dimensional space using nonlinear optical dynamics, thereby improving the accuracy and reducing the latency in the data classification by several orders of magnitude. The nonlinear dynamics are introduced into the data before processing the output data with an optical classifier. Fiber optic imaging and nonlinear phenomena have been popular research topics in the field of optics. Control of the nonlinear propagation under spatiotemporal conditions can be achieved via mechanical perturbation of the fiber or by shaping the pumped light.