The Echo-Induced Influence on the Frequency-Modulating Calibration of the 3×3 Coupler-Based Michelson Interferometer and Its Suppression

A low-distortion 3×3 interrogation algorithm requires the accurate parameters calibration of the 3×3 coupler-based Michelson interferometer. The ellipse fitting method with a frequency modulation conducted on the laser is one way that contributes to the implementation of the calibration. However, the unused dangling tail fiber of the 3×3 coupler-based Michelson interferometer generates a harmful echo and leads to an unexpected triple-beam interference. Consequently, it gives rise to a drastic fluctuation on the desired elliptical Lissajous figure, which damages the accuracy and stability of the calibration greatly. In this paper, the echo influence on the calibration is studied theoretically and experimentally. A theoretical model is built based on the coupled mode theory and the interference theory, which is verified by the experiment. According to the model, the echo coefficient, the input state of polarization and the length of the unused dangling tail fiber are three factors that affect the intensity of the fluctuation. Two practical methods of angle cleaving and pulse delay are adopted to suppress the echo influence and restore the accuracy of the calibration in the paper, which are both demonstrated to be feasible and stable. In the end, the suitable applications of the two methods are discussed, which are different for them due to their characteristics. This research has laid the foundation for the practical application of the frequency-modulation-based calibration to the 3×3 coupler-based Michelson interferometric probe.