Modeling of spectral reflectance characteristics in a semi-distributed interferometer sensor as a randomly segmented structure

In this work, a refractive-index fiber-optic sensor, referred to as a semi-distributed interferometer (SDI), was modeled to estimate spectral reflectance. The SDI originates from a Fabry–Pérot (FP) structure formed between a cleaved fiber tip and the reflective interface between a single-mode fiber and a high-scattering fiber with a core doped with magnesium silicate nanoparticles. We modeled the SDI as a multilayer system of randomly distributed FP interferometers, each characterized by a different refractive index and length. The reflectance and transmittance of the multilayer structure were numerically calculated using Fresnel reflection and the standard two-mirror FP transmission formula. This approach enables the calculation of the spectral characteristics of the interferometer under the assumption of single reflections at each layer surface. For simplicity, all layer boundaries were assumed to be flat and orthogonal to the beam propagation axis, aligning with the typical configuration of real systems. A superposition of all possible multiply reflected beams was analyzed using a general theory for multi-mirror interferometers. Specifically, the m-th backscattered wave, which passes through m dielectric layers, reflects, and propagates in the opposite direction, was examined. The spectral and sensitivity analyses were performed for several refractive index values. The results demonstrated excellent agreement with previously reported experimental findings.