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 J to the LD and the parameters associated with the external cavity mainly including optical feedback factor C , the initial external cavity length ( L0 ) and the light phase (∅0) 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 (C , ∅0), from which a critical C (denoted as Ccritical) is derived. Both simulations and experiments show that the stability can be enhanced by increasing either L0 or J . Furthermore, three regions on the plane of (C , ∅0) 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 remodeling the system by considering the bandwidth of the detection components.