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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 (ϕ₀) 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, ϕ₀), from which a critical C (denoted as C(critical)) 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, ϕ₀) 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.

Dynamic stability analysis for a self-mixing interferometry system