Fig. 1. General architecture of the AONN [14,15]. (a) Decomposition of the neural networks into sequential cascades of optical interference and nonlinearity units. X and Y denote the input and output signals in vectors. Wi and fi represent the weight coefficient and activation function of the i-th hidden layer. (b) Implementing the optical interference unit (OIU) structure for matrix multiplication. For linear operations, real-valued matrix M may be decomposed as M=UΣV†, where U is an m×m unitary matrix, Σ is an m×n diagonal matrix, and V† is the complex conjugate of the n×n unitary matrix V [14]. The unitary matrix can then be equated to an MZI network in a triangular or rectangular mesh [15]. (c) Implementing the ONU structure for nonlinear activation. Information propagates by an OIU followed by the application of an ONU. (d) Typical MZI structure. The 2×2 unitary matrix transformation is achieved by adjusting the phase of each MZI. (e) Typical NABA framework. The core is the energy conversion from pump light to backscattered waves, and its efficiency is related to the pump power.

Fig. 2. NABA dynamic performance. (a) Basic mechanism of BFAs. Nonlinear amplification of the signal is realized during the energy conversion process. Time-domain waveforms of the demodulated signal at two different frequencies, (b) 100 MHz and (c) 40 GHz. For observation, the data with multiple cycles is captured. Herein, the experiment and reference signals are data with and without NABA processing, respectively.

Fig. 3. NABA static performance. (a)–(c) Mapping curve of amplification factor and input power under different pump powers; all curves show obvious nonlinear effects. Nonlinear mapping model under three different pump powers of (d) 5.37 mW, (e) 9.18 mW, and (f) 37.08 mW. Clearly, there is an excellent consistency between the experimental data (dots) and theoretical analysis (curve).

Fig. 4. Performance on image classification. (a) Typical fully connected neural network frame. Learning curves for (b) MNIST and (c) Fashion-MNIST datasets under different NAFs. Herein, experiment-based nonlinear models are compared with existing NAFs. The M3 activation function is used to compute confusion matrix for (d) MNIST and (e) Fashion-MNIST datasets.

Fig. 5. Performance on regression task. (a) Data processing flowchart. In this diagram, the preprocessing module downsamples the experimental data, the fully connected ANN implements the regression function, and the error quantization module makes decisions based on the predicted data to yield the final result. SER (b) without and (c)–(e) with neural network processing. For comparison, the different activation functions including (c) M1, (d) M2, and (e) M3 are applied in ONNs.

Fig. 6. Basic principle of Brillouin scattering. The energy transfer process in Brillouin amplification can be described as a coupled three-wave interaction involving a pump wave, a Stokes wave, and an acoustic wave [40]. The Stokes wave primarily propagates in the direction opposite to that of the pump wave due to the negligible forward scattering in the fiber [40].

Fig. 7. Schematic diagram of the NABA dynamic characterization experiment. In this configuration, the signal propagates in the direction opposite to that of the pump source.

Fig. 8. Wideband response characteristics. (a) Spectral information of demodulated signals at different modulation frequencies. (b) 40-GHz signal spectrum.

Fig. 9. (a) Schematic diagram of double-balanced detection. During the experiment, all data are automatically recorded by the computer, minimizing human error in the measurements. (b) Mapping curve of amplification factor and input power under different pump powers; all curves show obvious nonlinear effects.

Fig. 10. Fitting curves of the four core parameters (a) A1, A2, (b) IS, and p versus pump power. Herein, all parameters exhibit saturation behavior.

Fig. 11. Completed pseudo-code [45]. dim is the abbreviation of dimension; x and y are the training sample and the desired output, respectively. C and θ are the loss function and learning rate, while w and b are the weight and bias vectors. m is the sample size; H and O are the number of neurons in each layer.

Fig. 12. Training data generation. (a) Schematic of the typical OTS architecture. (b) Power fading curves for different fiber lengths.

Fig. 13. Flowchart of ONN dataset generation for OTSs. (a) Complete cycle data captured by an OSC. (b) Down-sampling of the original data. In this process, the orange and blue data represent the sampled values for symbol “1” and symbol “0,” respectively. Notably, normalization is not required as the sampled values fall within the appropriate range.