Self Interferometry

Self-mixing Interferometry has been studied extensively in the last five decades in various sensing applications. Sensors under the SMI technique have the laser diode as the light source, the interferometer, and the detector. The light from the laser diode propagates towards a distant target where it is partially reflected or back-scattered before being re-injected into the active cavity of the laser. When the laser diode experiences the external optical feedback, the reflected light imprinted with information from the distant target or from the external cavity medium induces perturbation to the operating parameters of the laser. For SMI measurement sensors such as harmonic motion and absolute distance applications, the fringe counting method is basically used to determine the target's displacement and distance respectively. Two different approaches to modelling the SMI phenomenon have been developed: the three-mirror cavity and the perturbation of the rate equation. The single equation that describes the phase condition imposed by the optical feedback is usually referred to as the excess phase equation. One of the most important and most useful parameters in the excess phase equation is the feedback parameter C as it can be used to qualitatively categorize the regime of the laser under optical feedback. When the feedback level C 1, the laser behaviour is stable. On the other hand, when the feedback level C 1, more complex phenomena are observed such as hysteresis effect, presence of multiple emission frequencies (including the unstable frequencies), apparent splitting of the emission line due to mode hopping and fringe disappearance phenomenon. The fringes disappearance phenomenon in the self-mixing interferometry occurs whenever the external round-trip phase at free-running state is modulated by either external modulation such as external cavity length changes or internal modulation when the laser injection current is modulated with a high back-scattered light power. This phenomenon has been observed by many authors for harmonic motion or vibration application and more recently in the case of the absolute distance measurement scheme when the laser injection current is modulated in the triangle waveform. This phenomenon is highly dependent on the feedback parameter C and it is described in detail based on the coupled cavity model. The primary cause for fringes disappearance is demonstrated to be the expansion of the excess phase equation stable solutions range with the increment of the parameter C, thus reducing the number of stable solutions for a given phase stimulus. This new approach in the modelling of the fringe disappearance phenomenon allows determination of the C values for which a pair of fringes are expected to disappear and as a consequence correlates the number of missing fringes to the value of C. This approach is validated both by a behavioural model of the laser under optical feedback and by a series of measurements in the SMI absolute distance configuration.