Fig. 10
From: Intelligent designs in nanophotonics: from optimization towards inverse creation
(a) Optical interference unit (OIU) as a key component for optical neural network (ONN). A general ONN architecture was consisted of optical inputs (‘X’), internal multiple layers, and optical outputs (‘Y’). For a single internal layer (see a zoomed-in graph of ‘layer i’), it can be decomposed into OIUs (for matrix multiplications) joined with nonlinearity units (as the nonlinear activation). (b) An ONN-based XOR gate trained by the situ backpropagation and adjoint method. Top: the neural network containing inputs of X0, two layers of 3 × 3 OIUs (two rectangles), z2 activations (two red blocks) and outputs of XL. Bottom: XOR gate properties before and after learning. The circles represent target function, and the crosses mean the true output of network. (c) A sketch of the optical scattering unit (OSU) to execute matrix multiplications. Right: training MSE errors (right corner: the targeted matrix P). Bottom: E-field distributions at wavelengths of 1.55, 1.56, 1.57, and 1.58 μm, respectively. Each sub-image corresponds to one column of the matrix P. (d) An OIU-like nanophotonic medium to execute image detection. Top: the mini-batch stochastic gradient descent-based training process. All gradients information is calculated by adjoint state method in one step. Bottom: the media appearance and field distributions at iteration of 1, 33, and 66, respectively. The disordered media patterns (denoted by multiple inclusions embedded in a rectangle host material) progressively evolves upgrading the classification accuracy from 10.1% to 77.3%. Figures reproduced with permission: (a) Ref. [115], Copyright 2017 Nature Publishing Group; (b) Ref. [116], Copyright 2018 OSA; (c) Ref. [117], Copyright 2020 Elsevier; (d) Ref. [118], Copyright 2019 OSA