Disappearance of fringes in the self-mixing interferometry sensing scheme: impact of the initial laser mode solution.

We report here the first-ever, to the best of our knowledge, observation of an inconsistency in the fringe disappearance that occurs in self-mixing interferometers. The disappearance of fringes has been observed in vibration and absolute distance sensing schemes under moderate/strong feedback regimes, and it has a major impact on the design of self-mixing sensors. The number of missing fringes that mostly depends on the feedback strength is also linked to the establishment of the initial stable solution, and, as a consequence, the first modulation period will result in more fringes than expected in the case of an already permanent modulation. We demonstrate that this phenomenon is entirely predicted by the well-admitted dynamic rate equation model of the laser under optical feedback followed by the perfect agreement with experimental results.