Features of a Self-Mixing Laser Diode Operating Near Relaxation Oscillation

Abstract

When a fraction of the light reflected by an external cavity re-enters the laser cavity, both the amplitude and the frequency of the lasing field can be modulated. This phenomenon is called the self-mixing effect (SME). A self-mixing laser diode (SM-LD) is a sensor using the SME. Usually, such LDs operate below the stability boundary where no relaxation oscillation happens. The boundary is determined by the operation condition including the injection current, optical feedback strength and external cavity length. This paper discovers the features of an SM-LD where the LD operates beyond the stability boundary, that is, near the relaxation oscillation (RO) status. We call the signals from such a SM-LD as RO-SM signals to differentiate them from the conventional SM signals reported in the literature. Firstly, simulations are made based on the well-known Lang and Kobayashi (L-K) equations. Then the experiments are conducted on different LDs to verify the simulation results. It shows that a RO-SM signal exhibits high frequency oscillation with its amplitude modulated by a slow time varying envelop which corresponds to the movement of the external target. The envelope has same fringe structure (half-wavelength displacement resolution) with the conventional SM signals. However, the amplitudes of the RO-SM signals are much higher compared to conventional SM signals. The results presented reveal that an SM-LD operating near the RO has potential for achieving sensing with improved sensitivity.

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.…”

“…Hence, using existing OFI configuration for detection of OFLD-POO signal, many frequency components are missing. The work in [22] has experimentally revealed the features of such signals and indicated the possible sensing application but it did not make analytic expression on the signal waveform. As an OFLD-POO signal contains rich information associated with the laser and its external target, it is of great interest and significance to investigate the signal features by modelling the signal waveform, from which we can develop a suitable signal processing algorithm to retrieve the useful information contained in the signals.…”

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.…”