Fig. 1. All optical nonlinear computing schemes based on second-order nonlinear frequency doubling effect. (a) Nonlinear scheme based on parametric amplification enabled by second-order nonlinearity in PPLN^[11]; (b) degenerate optical parametric oscillator formed by antisymmetric coupling between fundamental and second harmonic waves in PPLN^[13]; (c) nonlinear mapping of image data via interaction between random scattering and second harmonic generation in LN crystal^[14]

Fig. 2. All optical nonlinear schemes based on material saturable and reverse saturable absorption effects. (a) Nonlinear scheme based on rubidium atomic saturable absorption for controlling forward and backward light propagation^[15]; (b) nonlinear scheme based on saturable and reverse saturable absorption curves in metal carbides^[17]; (c) nonlinear scheme based on two-dimensional MoTe₂ flake transferred onto waveguide facet^[18]; (d) nonlinear scheme based on Bi₂Te₃ thin film saturable absorption on Si₃N₄ waveguide^[20]

Fig. 3. All-optical nonlinear schemes based on other third-order nonlinear effects. (a) Nonlinear scheme based on free-carrier dispersion in resonator^[7]; (b) tunable nonlinear scheme based on combined effects of free-carrier dispersion and thermo-optic modulation in resonator^[8]; (c) nonlinear scheme using four-wave mixing in LN to enable pump-pulse-induced modulation of input pulses^[21]

Fig. 4. All-optical nonlinear schemes based on PCM modulation. (a) On-chip optical signals alter refractive index of PCM to modulate resonator transmission spectrum and generate nonlinear activation^[26]; (b) off-chip optical pumping induces a phase transition in PCM, enabling nonlinear modulation of on-chip optical signals^[28]

Fig. 5. Opto-electro-optical nonlinear schemes based on direct modulation in on-chip waveguides. (a) Nonlinear modulation scheme based on MZI under thermal effect^[29]; (b) nonlinear modulation scheme using resonator with forward-biased voltage inducing free-carrier dispersion^[31]; (c) nonlinear modulation scheme using resonator with reverse-biased voltage inducing free-carrier dispersion^[32]; (d) nonlinear modulation scheme based on MZM exploiting electro-optic effect^[35]

Fig. 6. Opto-electro-optical nonlinear schemes based on on-chip two-dimensional material modulation. (a) Nonlinear modulation scheme based on MoS₂ opto-resistive random access memory switch^[36]; (b) nonlinear modulation scheme based on graphene/silicon heterojunction^[37]

Fig. 7. Opto-electronic nonlinear schemes based on photodetection. (a) Nonlinear scheme based on complex modulation using on-chip diffractive units and balanced photodetectors^[46]; (b) Nonlinear modulation scheme based on vertical-cavity surface-emitting lasers with homodyne detection^[47]

Fig. 8. Applications of nonlinear activation functions in feedforward neural network architectures. (a) Complex-valued photonic nonlinear activation function demonstrated on MNIST and CIFAR-10 image classification tasks using complex photonic neural networks^[37]; (b) nonlinear response of laser array output performs Fashion-MNIST and EMNIST image recognition tasks within biological neural network structure^[47]; (c) Nonlinear photonic computing unit used in coherent optical neural network architecture for vowel classification task^[33]; (d) nonlinear activation function used to simulate evolution of SSH model in photonic neural network^[20]

Fig. 9. Applications of nonlinear neurons in reservoir computing neural networks. (a) Large-scale reservoir computing neural network constructed with phase-type spatial light modulator based nonlinear neurons demonstrated on human action recognition tasks^[44]; (b) reservoir computing network based on multimode spiral waveguides applied to time series prediction^[49]; (c) photonic layered neurons based on integrated quantum dot lasers used to construct reservoir networks for image recognition tasks^[55]; (d) deep reservoir computing network built with cascaded injection-locked semiconductor laser chips and optical feedback loops for optical module nonlinear equalization^[56]

Fig. 10. Applications of nonlinear optical pulse activation in optical spiking neural networks. (a) Nonlinear optical pulse activation using FP-SA laser for digital pattern recognition^[60]; (b) nonlinear optical pulse activation using resonator structure incorporating PCM for alphabet pattern recognition^[26]