Fig. 1. Structural overview of PNN based on diffraction optics

Fig. 2. Framework of diffractive optical neural network (DONN). (a) Conceptual diagram of metasurface performing arbitrary mathematical operations^[8]; (b) diffractive deep neural network physically constructed of multilayer diffractive metasurfaces^[10]; (c) reconfigurable diffraction processing units supporting multiple neural network models^[13]; (d) programmable DONN based on information metasurfaces^[14]

Fig. 3. Multiplexing frameworks of DONN. (a) Design framework of broadband DONN^[15]; (b) framework of polarization-multiplexed diffractive computing^[16]; (c) framework of wavelength-multiplexed broadband DONN^[17]; (d) framework of spatial-polarization multiplexed DONN^[19]

Fig. 4. On-chip DONNs. (a) On-chip DONN based on subwavelength rectangular slots^[26]; (b) schematic of on-chip DONN^[27]; (c) on-chip DONN based on SOI platform^[28]; (d) on-chip DONN in telecom bands^[29] (BE: beam expander; DMD: digital micromirror device; BS: beam splitter; SMF: single-mode fiber)

Fig. 5. Reconfigurable on-chip DONNs. (a) On-chip multimodal DONN based on tunable elements^[30] (DAC: digital-to-analog converter; ADC: analog-to-digital converter; FPGA: field programmable gate array); (b) on-chip DONN for multi-category categorization task^[31]

Fig. 6. Structural overview of PNNs based on MZI arrays

Fig. 7. PNNs based on MZI array. (a) Reck architecture^[42]; (b) Clement architecture^[43]; (c) large-scale programmable MZI array for vowel classification^[45]; (d) cascading topology architecture of diamond MZI array^[46]

Fig. 8. Improved PNNs based on MZI arrays. (a) Optical coherent dot product chip^[47]; (b) complex-valued neural network on integrated photonic chip^[48]; (c) architecture for MZI-based integrated diffractive PNN chip^[49]; (d) optical micrograph of MZI mesh^[50]

Fig. 9. PNN training methods and self-configuring architectures. (a) Training method based on adjoint variable method^[67]; (b) training method based on genetic algorithm^[68]; (c) training method based on bacterial foraging^[69]; (d) self-configuring and reconfigurable photonic signal processor architecture^[70]

Fig. 10. Structural overview of PNNs based on wavelength division multiplexing

Fig. 11. MRR weight bank and implementation of MRR-based PNN. (a) Conceptual diagram of broadcast-and-weight architecture^[77]; (b) optical micrograph of microring weight bank^[78]; (c) analysis of channel crosstalk effects in MRR weight bank^[79]; (d) comparison of computational results of optical continuous-time recurrent neural network and electrical CPU^[80]; (e) feedback control link of MRR weight bank^[81]

Fig. 12. Photonic hardware architectures based on MRR for deep learning tasks. (a) MRR-based optical signal processor^[83]; (b) digital-analog hybrid ONN architecture^[84]; (c) ONN architecture supporting large-scale complex-valued matrix operations^[85]; (d) ONN architecture enabling real-domain transformation mapping^[86] ; (e) ONN architecture for training via direct feedback alignment^[89]; (f) ONN architecture implementing matrix transpose operations with MRR crossbar arrays^[90]

Fig. 13. Photonic tensor cores and optical convolution implemented with MRR.(a) Photonic in-memory computing unit based on MRR and Ge₂Sb₂Se₅ elements^[91];(b) photonic in-memory computing unit based on MRR and phase-change material (PCM)^[92];(c) photonic tensor core enabled by multiplexing of hybrid multidimensional light waves and microwaves^[93];(d) integrated photonic tensor flow processor^[94];(e) optical convolution accelerator architecture with integrated microcomb sources^[95];(f) fully integrated photonic parallel convolution architecture^[96]

Fig. 14. Structural overview of PNNs based on cascaded modulators

Fig. 15. Illustration of principle of photonic vector dot product using cascaded modulators^[100]

Fig. 16. Smart NIC architecture^[100]

Fig. 17. Cascaded modulator architecture based on SOA-MZI. (a) Optical Sigmoid neuron^[101]; (b) optical recurrent neuron based on gating mechanisms^[105]; (c) optical recurrent neuron based on space rotator^[107]

Fig. 18. Cascaded modulator architecture based on all-optical coherent linear photonic neurons. (a) Optical linear algebra unit based on extended IQ modulators^[108]; (b) on-chip coherent linear optical neurons^[109]; (c) on-chip coherent linear PNN based on nonlinear activation functions^[111]

Fig. 19. Coherent linear PNN combining wavelength division multiplexing and crossbar structure. (a) Programmable PNN^[110]; (b) N×M optical crossbar structure^[114]; (c) schematic of N×K photonic crossbar with optical linear algebra unit and bias branch^[115]

Fig. 20. Structural overview of optical nonlinear activation function

Fig. 21. Optical nonlinear activation functions based on optoelectronic hybrid schemes. (a) Nonlinear activation function based on electro-absorption modulator^[116]; (b) nonlinear activation function based on photodetector and MZ modulator^[117]; (c) microring modulator for implementing nonlinear activation functions^[118]; (d) nonlinear activation function based on homodyne detection^[119]

Fig. 22. Optical nonlinear activation functions for all-optical schemes. (a) Comparison of line types of SOA transfer function and tanh activation function^[120]; (b) photograph of nonlinear activation computing device based on MRR-assisted MZI^[122]; (c) using saturable absorber to achieve forward and backward computations^[123]; (d) implementation of ReLU function based on nonlinear effects in waveguide^[127]