Fig. 1. The development of artificial intelligence. (a) Typical architectures of ANN^[2]; (b) comparison between total amount of AI compute and Moore's law^[10]

Fig. 2. Optical computing. (a) Classification of optical computing; (b) implementations of optical computing

Fig. 3. Evolution of PNNs^{[51,73-74,85,93-94,113-123]} during the development of ANNs^[97-112]

Fig. 4. Optical linear matrix multiplication. (a) Free-space optics; (b) integrated coherent optics; (c) WDM optics

Fig. 5. Optical linear matrix multiplications based on free-space optics. (a)-(c) SLM^[76,127-128]; (d) (e) DMD^[85,129]; (f)-(h) diffractive optics^[74,80,130]

Fig. 6. Optical linear matrix multiplications based on integrated coherent optics. (a)-(d) Programmable MZI arrays^{[73,82-83,133]}; (e) configurable push-pull modulators^[134]; (f) combination of on-chip diffractive cell and programmable MZI^[95]

Fig. 7. Optical linear matrix multiplications based on WDM optics. (a) (b) The cascaded MRRs^[46,89,122]; (c)-(e) PCMs^[51,81,92]; (f) SOA^[136]; (g) dispersion fiber^[137]; (h) (i) optical frequency combs^[93-94]

Fig. 8. Typical expressions of nonlinear activation functions in ANNs. (a) Sigmoid; (b) Tanh; (c) Relu; (d) Leaky Relu; (e) Softpuls; (f) Swish

Fig. 9. Optical nonlinear activators based on O-E-O conversion. (a)(b) Electro-optic modulators^[93-94]; (c) MRR modulator^[93-94];(d) feedback-assisted MZI^[143]

Fig. 10. All-optical nonlinear activators and the corresponding response curves. (a)-(f) Custom-defined materials^{[51,76,123,144-145]}; (g)-(i) SOAs^[146-148]; (j)-(l) MRRs^[149-152]

Fig. 11. Design process of photonic neural networks

Fig. 12. Typical applications of photonic neural networks. (a)-(e) Image processing or recognition^{[82,92-94,134,136]}; (f) vowel recognition^[73]; (g) OAM multiplexing and demultiplexing^[153]; (h) logic operation^[80]; (i) fiber nonlinearity compensation^[154]