Dynamic stability analysis for a self-mixing interferometry system

Abstract

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. Abstract: 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 ( 0 L ) 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 LangKobayashi model. The stability boundary of such system is presented in the plane of ( C , 0  ), from which a critical C (denoted as critical C ) is derived. Both simulations and experiments show that the stability can be enhanced by increasing either 0 L 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 semistable region has potential applications on sensing and measurement but needs re-modeling the system by considering the bandwidth of the detection components. Disciplines Engineering | Science and Technology Studies

Modeling for optical feedback laser diode operating in period-one oscillation and its application

“…In stable region, for a stationary target, the laser intensity will be constant after the transient state, whereas in semi-stable and unstable region, relaxation oscillation will be undamped and the laser may enter period-one, quasiperiodic or chaotic oscillation under different feedback strength. The work [21,22] discovers that an OFLD can easily and sometimes inevitably enter the period-one oscillation, e.g. for the case when the feedback level factor C is around 2.5, which is quite commonly reported for the moderate feedback regime in the literature.…”

“…However, many works [18][19][20] have demonstrated that an OFLD system with a stationary external target may be unstable under some certain operation conditions, such as in periodic, quasi-periodic or chaotic oscillation state. We studied OFLD signals with a moving target in different conditions and our recent works [21,22] shows that such sensing system may produce different types of OFLD signals which are classified into three regions defined in [21], i.e. stable, semi-stable and unstable region under different feedback level factors C. C is defined as:…”

“…Usually, the PD packaged inside an LD is used to detect the laser intensity, but it has limited bandwidth less than 1GHz. However, the frequency components contained in an OFLD-POO signal can even higher than several GHz [21,22]. Hence, using existing OFI configuration for detection of OFLD-POO signal, many frequency components are missing.…”

Influence of system bandwidth on self-mixing signal

“…It was found that damped oscillation appears on the discontinuous point of the SMI signal when the SMLD system operates in moderate feedback regime and this kind of damped oscillation corresponds to the external cavity mode, which contains information on the target distance and reflectivity. Additionally, our recent work [17,18] shows another kind of oscillation, i.e. undamped relaxation oscillation (RO), may occur when the SMLD operates in moderate or strong feedback regime.…”

Self-mixing interferometry and its applications

“…In this A B case, ( ) E t and ( ) N t exhibit complicated oscillations rather than a constant level. Depending on the value of C , a recent work in 43 shows that three operational regions (referred to as stable, semi-stable and unstable which are shown in Fig. 9(a)) can be used to describe the behaviour of an SMI.…”