All-optical complex-valued convolution based on four-wave mixing

Optical complex-valued convolution can extract the feature of complex-valued data by processing both amplitude and phase information, enabling a wide range of future applications in artificial intelligence and high-speed optical computation. However, because optical signals at different wavelengths cannot interfere, optical systems based on wavelength multiplexing usually can only realize real-valued computation. Here, we experimentally demonstrate an all-optical computing scheme using Kerr-based optical four-wave mixing (FWM) that can perform complex-valued convolution of multi-wavelength signals. Specifically, this all-optical complex-valued convolution operation can be implemented based on the coherent superposition of converted light generated by multiple FWM processes. The computational throughput of this scheme can be expanded by increasing the number of optical wavelengths and the signal baud rate. To exemplify the application, we successfully applied this all-optical complex-valued convolution to four different orientations of image edge extraction. Our scheme can provide a basis for wavelength-parallel optical computing systems with the demanded complex-valued computation capability.