Demonstration of reconfigurable and tunable all-optical matrix-vector multiplication using nonlinear wave mixing.

Recent interest has grown in processing matrix operations within the optical domain due to its potential advantages in bandwidth, latency, and parallelism. While optical implementations of matrix-vector multiplication (MVM) have been demonstrated, they still partially rely on the electronic domain to perform the matrix operation. In this paper, we demonstrate MVM using nonlinear wave mixing, enabling the matrix operation to be performed in the optical domain. Each column of the matrix is modulated onto different subcarriers, in which the column elements are serialized in time. The vector elements are encoded onto separate CW tones at different wavelengths. The MVM operation is carried out using nonlinear wave mixing in a single periodically poled lithium niobate waveguide, in which the elements of the output vector are serialized in time. We show MVM at two different clock rates (3 and 5 GHz) and for different input vectors. The resulting output vectors have error standard deviations of 2.89-3.55%, corresponding to 4.8-5.1 bits of precision.