Experimental Realization of Complex Tensor Convolution in Photonic Frequency Synthetic Dimensions

Tensor convolution is important for feature extraction of high-dimensional data in realistic scenarios to obtain fine, high-dimensional features. Photonic convolution in the synthesis frequency dimension, utilizing the dynamics of photons in the spectral degrees of freedom, results in highly compact devices with highly scalable and flexible configuration capabilities. We propose a complex convolution in photonic frequency synthetic dimensions and an arbitrary complex convolution kernel realizing by adding the convolution results of the even-symmetric and the odd-symmetric kernel. We experimentally demonstrate optical complex convolution kernels based on the synthesized frequency, and the complex convolution calculation with the peak speed up to 1.137 TOPS between the input frequency comb about 2000 programmable frequencies and the synthesized kernel at a rate of 2.9M frame-per-second.