Analysis of Diffractive Optical Neural Networks and Their Integration With Electronic Neural Networks

Optical machine learning offers advantages in terms of power efficiency, scalability, and computation speed. Recently, an optical machine learning method based on diffractive deep neural networks (D(2)NNs) has been introduced to execute a function as the input light diffracts through passive layers, designed by deep learning using a computer. Here, we introduce improvements to D(2)NNs by changing the training loss function and reducing the impact of vanishing gradients in the error back-propagation step. Using five phase-only diffractive layers, we numerically achieved a classification accuracy of 97.18% and 89.13% for optical recognition of handwritten digits and fashion products, respectively; using both phase and amplitude modulation (complex-valued) at each layer, our inference performance improved to 97.81% and 89.32%, respectively. Furthermore, we report the integration of D(2)NNs with electronic neural networks to create hybrid classifiers that significantly reduce the number of input pixels into an electronic network using an ultra-compact front-end (DNN)-N-2 with a layer-to-layer distance of a few wavelengths, also reducing the complexity of the successive electronic network. Using a five-layer phase-only (DNN)-N-2 jointly optimized with a single fully connected electronic layer, we achieved a classification accuracy of 98.71% and 90.04% for the recognition of handwritten digits and fashion products, respectively. Moreover, the input to the electronic network was compressed by >7.8 times down to 10 x 10 pixels. Beyond creating low-power and high-frame rate machine learning platforms, (DNN)-N-2-based hybrid neural networks will find applications in smart optical imager and sensor design.