Cascaded Fabry-Perot interferometer with thin film based on Vernier effect

The Vernier effect is often utilized to boost the sensing ability of optical fiber sensors. In this paper, theoretical model of cascaded Fabry-Perot interferometer (FPI) with thin film based on Vernier effect is established. The sensitivities of the envelope spectra, thin film cavity and mixed cavity of air-thin film are analyzed qualitatively. According to the theoretical analysis, although sensitivity from mixed cavity of air-thin film is amplified, the value is equal to the sensitivity of sing thin film cavity. Experimental verification is carried out by an example of thin film named polydimethylsiloxane (PDMS) polymer. Herein, a new FPI constructed by air cavity from a hollow-core fiber, PDMS cavity, and air-PDMS mixed cavity is proposed and demonstrated. In order to facilitate the generation of the Vernier effect, the length of the PDMS cavity is intentionally designed shorter than the air cavity, making the free spectral range of the air-PDMS cavity and air cavity is approximately equal. The temperature change makes the refractive index and thermal expansion of PDMS change, while gas pressure change results in elastic deformation of PDMS. The Vernier envelope wavelength shifts with the temperature and gas pressure change. The proposed FPI features high temperature and gas pressure sensitivities of 3.07 nm/℃, and 23.07 nm/MPa, and a high magnification factor of 17 when the lengths of HCF and PDMS are 82.5 and 3.7 μm, respectively. The experimental results show that the temperature and pressure sensitivities of the cascaded FPI's envelope spectra are equal to the sensitivity of a single thin film microcavity, and the theoretical calculation is in good agreement with the experimental verification. The theoretical model is also applicable to thin film prepared by other polymer materials. Additionally, the proposed FPI has good stability, reversibility, and repeatability, which is a good choice in the field of optical fiber sensing.