Fig. 1. Chart of computational power demand for artificial intelligence models^[1]

Fig. 2. Categories of optical computing

Fig. 3. Optical implementation of differential operators. (a) All-optical implementation of image edge detection^[7]; (b) planar photonic chip implementation of multi-order differentiator^[8]; (c) target recognition and 3D object reconstruction based on all-optical metasurface ^[9]; (d) quantitative phase gradient imaging based on metasurface^[10]

Fig. 4. Optical implementation of convolution operators. (a) Convolution process implemented using angle-sensitive pixels^[12]; (b) convolution process based on Fourier transformation^[13]; (c) implementation of convolution operation with optical mask^[14]

Fig. 5. Timeline of advances in optical neural network^[20-25]

Fig. 6. Implementing linear operations based on PLC scheme. (a) Schematic diagram of linear operation based on PLC scheme^[29]; (b) all-optical diffractive neural network physical model^[24]; (c) large-scale neuromorphic optoelectronic computing with reconfigurable DPU^[30]; (d) programmable diffractive neural network based on digital-coding metasurface array^[31]; (e) implementation of intensity linear operations using incoherent light diffraction neural network^[32]; (f) implementation of complex linear operations using incoherent light diffraction neural networks^[33]

Fig. 7. Implementing linear operations based on MZI methods. (a) Basic structure of MZI unit^[36]; (b)(c) programmable MZI arrays^{[23, 38]}; (d) push-pull configuration for dot product calculation^[39-40]

Fig. 8. Implementing linear operations based on WDM. (a)Linear operation using cascaded MRRs^[40]; (b) multi-channel control for microring weight banks^[43]; (c) implementing complex valued linear operations with microring array^[44]; (d) implementing convolutional operations using optical frequency combs^[15]

Fig. 9. Implementing linear multiplication based on other methods. (a) Implementation of linear operation and photonic memory based on phase-change materials combined with WDM^[48]; (b) implementation of broadband convolution operations based on combs and PCM^[49]; (c) implementation of linear operation and photonic memory based on PCM and MRR^[50]

Fig. 10. Implementation of nonlinear operation in free-space ONN. (a) Implementing nonlinear function using microchannel plate^[53]; (b) implementing nonlinear function using surface-normal photodetector as nonlinear activation function in diffractive optical neural networks^[52]; (c) implementing nonlinear using TPT and LC modulator; (d) implementing nonlinear using photorefractive crystal SBN∶60^[64]; (e) implementing nonlinear using perovskite QDs film; (f) implementing nonlinear using electrically tunable nonlinear polaritonic metasurface^[65]

Fig. 11. Implementation of nonlinear operation in on-chip ONN. (a) Electro-absorption modulator^[70]; (b)(c) PN heterojunction MRR^[66]; (d) micro vertical-cavity surface-emitting laser (VCSEL) array; (e) photodiodes array^[74]

Fig. 12. All optical nonlinear activation function in on-chip ONN.(a) Electromagnetically induced transparency^[76], reverse saturated absorption^[76]; (b) cavity loaded MZI^[57]; (c) Ge/Si hybrid structure in MRR^[77]

Fig. 13. Analysis of offline learning^[86]. (a) Limitations of offline training; (b) comparison of impacts of different noise types on ONN

Fig. 14. Online training method for training optical neural networks. (a) Principle of online learning^[88]; (b) online training of cascade diffractive optical neural networks^[88]; (c) online training of nonlinear diffractive neural networks^[89]; (d) online training of integrated nanophotonic networks^[90]

Fig. 15. Training optical neural networks using transition methods. (a) Fundamental principle of physical adaptive training^[91]; (b) training meta-surface diffractive neural networks using physical adaptive training^[92]; (c) fundamental principle direct feedback alignment^[93]; (d) fundamental principle of dual adaptive training of photonic neural networks^[85]

Fig. 16. Application of ONN. (a) Logical operation^[100]; (b) multi-task object classification^{[87, 96]}; (c) edge extraction^[17]; (d) action recognition^[108]; (e) game’s decision making and control^[101]; (f) medical image reconstruction^[39]; (g) angular momentum-mode-switching communication^[104]; (h) super-resolution image display^[106]