Fig. 1. Optical path compensation based on fiber optic components. (a)(b) Cross-sections and refractive index distribution diagrams of double-clad passive fibers (DCF) and erbium-doped fiber (EDF)^[12]; (c) intensity distributions of six irregular Bragg fibers (IBFs) along the fiber radius^[13]

Fig. 2. High-speed signal transmission equalization method based on FFE. (a) Schematic of FFE; (b) fractionally spaced equalization method based on FFE^[21]; (c) experimental setup of PAM4 transmission system based on FFE^[22]; (d) parallelized FFE equalization method with multiple reconstructions^[23]

Fig. 3. DFE principle and its application. (a) Principle diagram of DFE^[30]; (b) experiment flowchart of DFE equalization method based on complex-DFE^[29]; (c) block diagrams of DFE with soft-decision decoding algorithm^[27]

Fig. 4. VNLE principle and its application. (a) Structure diagram of 3rd-order VNLE, solid lines represent the second-order nonlinear terms of the Volterra series, and dotted lines represent the third-order nonlinear terms of the Volterra series; (b) comparison of computational complexity among Volterra technical solutions at different memory depths^[26]; (c) experimental setup of PAM4 transmission system for simplifying the second-order Volterra equalization scheme^[26]; (d) Volterra equalization scheme based on low-level quantization calculation^[31]; (e) comparison of bit error rates of different equalization methods under transmission distances of 20 km and 30 km^[32]

Fig. 5. Different neural network equalization methods. (a) Schematic diagram of equalization algorithm for fully connected neural networks introducing the decision feedback structure^[33]; (b) equalizer structure based on feedforward neural networks^[34]; (c) single-step and multi-step equalization flowcharts based on long short-term memory networks^[35]; (d)(e) comparison of bit error rates of different neural network equalization methods under transmission distances of 15 km and 25 km^[36]

Fig. 6. Optical neural network channel equalization method. (a) Experimental setup based on integrated optical reservoir computing^[39]; (b) experimental setup based on nonlinear vector autoregression using integrated micro-ring modulator^[42]

Fig. 7. 32-node photonic reservoir computing chip. (a) Chip layout; (b) packaged chip

Fig. 8. Real-time equalization experiment of nonlinear damage. (a) Schematic diagram of experimental device; (b) eye diagram of damage signal; (c) diagrams of original signal, damage signal, and equalized signal; (d) eye diagram of equalized signal

Fig. 9. On-chip schematic diagram of single-node highly nonlinear modulated photonic reservoir architecture

Fig. 10. Nonlinear channel equalization task based on a single-node highly nonlinear modulated photonic reservoir chip. (a) Illustration of the post-processing equalization method; (b) equalization rendering with signal-to-noise ratio of 12 dB; (c) bit error rate under different signal-to-noise ratios

Fig. 11. Prediction task for time series data^[48]. (a) Experimental schematic diagram of waveguide-type photonic reservoir for time series prediction; (b) prediction curves for FTSE in test-dataset period

Fig. 12. Modulation format recognition task^[50]. (a) Experimental schematic diagram of waveguide-type photonic reservoir for modulation format recognition; (b) recognition accuracy curves for our work and other studies; (c) confusion matrix at optical signal-to-noise ratio is 18 dB

Fig. 13. Plots of results of NARMA10 regression task