Abstract

A method by detecting the ellipse fitting degree of the trajectory equation formed by two self-mixing (SM) signals in the multi-longitudinal mode laser SM system with a Wollaston prism is presented to test the free spectral range (FSR) of the laser. By utilizing the orthogonal vector and phase-shift characteristics between adjacent longitudinal modes, the fluctuations in multi-mode SM effects caused by changes in the external cavity length are transformed into alterations in the trajectory composed of two orthogonal SM signals. The FSR is calculated by detecting the difference in external cavity lengths between the two positions, where the trajectory of the two SM signals best fits an ellipse. To achieve an automatic FSR measurement, the ellipse fitting degree is proposed as the criterion for positioning the external cavity mode. Experimental results indicate that the FSR of the laser diode is measured to be 85.23 GHz with a resolution of 0.48 GHz, while the corresponding external cavity resolution is 10 µm, and the resolution of the ellipse fitting degree is less than 1. The compact and straightforward design, coupled with high sensitivity, automated measurements, and immunity to optical feedback, holds significant promise as a robust tool for measuring FSR and assessing laser performance.

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