Simulation of Temporally Matrix Vector Multiplication with Rayleigh Backscattering

Photonic matrix vector multiplication (MVM) has renewed interest in optical computing, which has the potential to reduce the power consumption and maintain relatively high speed. Temporally MVM (T-MVM) using distributed feedback based on the Rayleigh backscattering is one of them. Here, we established the numerical model of the T-MVM using distributed feedback based on the Rayleigh backscattering in a single-mode fiber. The feasibility of this model is proven by performing the non-linear principal component analysis (PCA). The impact of the random Rayleigh backscattering coefficient on the capability of the nonlinear PCA is also investigated. The simulation results show that the non-linear PCA can efficiently separate the points randomly distributed on 3 concentric spheres with different radii. The randomness of the Rayleigh backscattering coefficient plays an important role in improving the capability of this model.