The Abbe-Rayleigh diffraction limit of traditional optical equipment has always been an obstacle to the study of micro-/nano-scale objects [1, 2]. Near-field microscopic imaging techniques, such as contact photography [3] and scanning near-field imaging (SNOM) [4, 5], capture evanescent fields by placing a probe or light-sensitive material extremely close to the object to achieve nanoscale resolution, which is not possible for imaging inside biological samples or encapsulated micro-/nano-structures. Far-field microscopic imaging technology is not restricted by the above bottlenecks. Some typical far-field microscopic imaging techniques, such as single-molecule localization (SML) microscopy [6, 7] or stimulated emission depletion (STED) [8, 9], have demonstrated the possibility of nanoscale imaging without capturing evanescent fields. However, SML microscopy and STED typically require intense beams to excite, deplete, or bleach fluorophores in a sample that produces photobleaching and phototoxicity in living samples. Optical super-oscillations are rapid sub-wavelength spatial variations of light intensity and phase that occur in complex electromagnetic fields formed by the precise interference of coherent waves, which provide an advanced method for far-field super-resolution imaging beyond the diffraction limit [10, 11]. To generate optical super-oscillation, the complicated lens design methods [12-14] or Fresnel zone plate (FZP) optimization design methods, including optimizing algorithms [15-18] or optimization-free algorithms [19, 20], have been proposed.

Electroencephalography (EEG) analysis extracts critical information from brain signals, which has provided fundamental support for various applications, including brain-disease diagnosis and brain-computer interface. However, the real-time processing of large-scale EEG signals at high energy efficiency has placed great challenges for electronic processors on edge computing devices. Here, we propose the EEG opto-processor based on diffractive photonic computing units (DPUs) to effectively process the extracranial and intracranial EEG signals and perform epileptic seizure detection. The signals of EEG channels within a second-time window are optically encoded as inputs to the constructed diffractive neural networks for classification, which monitors the brain state to determine whether it's the symptom of an epileptic seizure or not. We developed both the free-space and integrated DPUs as edge computing systems and demonstrated their applications for real-time epileptic seizure detection with the benchmark datasets, i.e., the CHB-MIT extracranial EEG dataset and Epilepsy-iEEG-Multicenter intracranial EEG dataset, at high computing performance. Along with the channel selection mechanism, both the numerical evaluations and experimental results validated the sufficient high classification accuracies of the proposed opto-processors for supervising the clinical diagnosis. Our work opens up a new research direction of utilizing photonic computing techniques for processing large-scale EEG signals in promoting its broader applications.

Photonic neural network (PNN) is a remarkable analog artificial intelligence (AI) accelerator that computes with photons instead of electrons to feature low latency, high energy efficiency, and high parallelism. However, the existing training approaches cannot address the extensive accumulation of systematic errors in large-scale PNNs, resulting in a significant decrease in model performance in physical systems. Here, we propose dual adaptive training (DAT) that allows the PNN model to adapt to substantial systematic errors and preserves its performance during the deployment. By introducing the systematic error prediction networks with task-similarity joint optimization, DAT achieves the high similarity mapping between the PNN numerical models and physical systems and high-accurate gradient calculations during the dual backpropagation training. We validated the effectiveness of DAT by using diffractive PNNs and interference-based PNNs on image classification tasks. DAT successfully trained large-scale PNNs under major systematic errors and preserved the model classification accuracies comparable to error-free systems. The results further demonstrated its superior performance over the state-of-the-art in situ training approaches. DAT provides critical support for constructing large-scale PNNs to achieve advanced architectures and can be generalized to other types of AI systems with analog computing errors.

Increasing the layer number of on-chip photonic neural networks (PNNs) is essential to improve its model performance. However, the successively cascading of network hidden layers results in larger integrated photonic chip areas. To address this issue, we propose the optical neural ordinary differential equations (ON-ODE) architecture that parameterizes the continuous dynamics of hidden layers with optical ODE solvers. The ON-ODE comprises the PNNs followed by the photonic integrator and optical feedback loop, which can be configured to represent residual neural networks (ResNet) and recurrent neural networks with effectively reduced chip area occupancy. For the interference-based optoelectronic nonlinear hidden layer, the numerical experiments demonstrate that the single hidden layer ON-ODE can achieve approximately the same accuracy as the two-layer optical ResNet in image classification tasks. Besides, the ONODE improves the model classification accuracy for the diffraction-based all-optical linear hidden layer. The time-dependent dynamics property of ON-ODE is further applied for trajectory prediction with high accuracy.