Multidimensional Convolution Operation with Synthetic Frequency Dimensions in Photonics

Abstract

The convolution operation is widely used in signal and image processing and represents the most computationally intensive step in convolutional neural networks. We introduce a scheme to achieve arbitrary convolution kernels in the synthetic frequency dimension with a simple setup consisting of a ring resonator incorporating a phase and an amplitude modulator. This scheme can be used to perform multidimensional convolutions. We provide an analytic approach that determines the required modulation profile for any convolution kernel. Our work points to a direction of using optical computing to remove the computational bottleneck in traditional electronic circuits and may be useful in improving machine-learning hardware in artificial-intelligence applications.