Dynamic stability analysis for a self-mixing interferometry system

A self-mixing interferometry (SMI) system is a laser diode (LD) with an external cavity formed by a moving external target. The behavior of an SMI system is governed by the injection current 퐽 to the LD and the parameters associated with the external cavity mainly including optical feedback factor 퐶, the initial external cavity length (퐿0) and the light phase (휙0) which is mapped to the movement of the target. In this paper, we investigate the dynamic behavior of an SMI system by using the Lang-Kobayashi model. The stability boundary of such system is presented in the plane of (퐶, 휙0), from which a critical 퐶 (denoted as 퐶푐푟푖푡푖푐푎푙) is derived. Both simulations and experiments show that the stability can be enhanced by increasing either 퐿0 or 퐽. Furthermore, three regions on the plane of (퐶, 휙0) are proposed to characterize the behavior of an SMI system, including stable, semi-stable and unstable regions. We found that the existing SMI model is only valid for the stable region, and the semi-stable region has potential applications on sensing and measurement but needs re-modeling the system by considering the bandwidth of the detection components.