A Comprehensive Investigation on Enhanced Robustness for Parallel VCSEL-RC Utilizing Narrow-Band Filtered Optical Feedback

Photonic reservoir computing (RC) is a kind of artificial neural network (ANN) structure which is easy to train, with higher accuracy and speed, and has important application prospects in various fields, such as the time-series prediction, waveform recognition, speech recognition, nonlinear channel equalization, etc. In this work, we demonstrated a comprehensive numerical investigation on the characteristics and physical mechanisms of dual-channel and parallel RC based on vertical-cavity surface-emitting laser (VCSEL-RC) with filtered optical feedback (FOF). Using the dual-channel time-series prediction tasks as standard benchmark, the effects of feedback parameters (feedback strength, filter bandwidth, feedback detuning) and type on normalized mean square error (NMSE) were explored in detail. We found that: Selecting a smaller filter bandwidth can widen the range of values of feedback strength corresponding to smaller NMSE, which can effectively strengthen the robustness of parallel VCSEL-RC; When the feedback detuning varies from positive to negative value, the range of parameters space for feedback strength-filter bandwidth corresponding to lower NMSE tends to be narrowed; Compared with parallelly polarized FOF (PP-FOF), orthogonally polarized FOF (OP-POF) shows a stronger robustness enhancement; For smaller feedback strength, NMSE value is insensitive to the interior parameters of VCSEL. We also evaluated the processing rate of parallel VCSEL-RC with FOF. This study is valuable on enriching the understanding for nonlinear dynamics of FOF-based VCSEL-RC, and can provide a design guideline towards parallel, dual-channel RC with robust performance.