A novel Vernier effect fiber optic sensor with tunable M-factor via effective refractive index adjustment

Abstract

In this paper, we present the design and fabrication of a Vernier effect sensor with a tunable magnification factor (M-factor). We define a set of limiting conditions to specify the applicable range of the sensing and reference extrinsic Fabry-Perot interferometer (EFPI) cavity lengths (L_s and L_r) and their effective refractive indices (n_s and n_r), which ensure the stability of the Vernier effect and reliable signal demodulation. Simulations are conducted to validate the proposed limiting conditions by analyzing spectral characteristics under varying relative length differences. The simulation results confirm the effectiveness of the proposed framework. To make the M-factor tunable and extend the feasible range for length design, we propose a method to adjust the M-factor by tuning the effective refractive index (RI) of the EFPI. This adjustment of RI affects the detuning factor, which in turn allows precise control of the M-factor. Various combinations of L_s, n_s and n_r are simulated to assess their impact on the Vernier effect and to investigate the applicable range of these parameters. Finally, we fabricate the proposed M-factor tunable Vernier effect sensor and verify the theoretical predictions through experiments. The experimental results show that by using the fabricated EFPI and the RI range provided by saline solutions, an M-factor tuning range of 6.5 to 9.5 is achieved. These results closely match the simulations, confirming the feasibility and reliability of the proposed framework for practical sensor applications. Building on these findings, the sensor could broaden its applicable range through targeted design, offering greater flexibility for various applications.