A Simple Equation to Describe Cross-Sensitivity Between Temperature and Refractive Index in Fiber Bragg Gratings Refractometers

In this paper, we propose a simple nonlinear equation to describe the cross-sensitivity between temperature and refractive index in fiber Bragg grating refractometers. A numerical analysis using Comsol Multiphysics software was performed to understand how the effective index changes with the temperature and refractive index. The sensor response to refractive index (from 1.33 to 1.45) and temperature (from 15 °C to 45 °C) was fitted using a surface equation. Even though the refractive index range considered being significantly large, and the sensor response being nonlinear, proper concordance between computer simulations and experiments point out that this multivariable equation is suitable to describe the Bragg wavelengths as a function of temperature and refractive index. When applied to multimode fiber Bragg gratings, the proposed equation can be used to construct a system of equations to calculate temperature and refractive index from the measured Bragg wavelengths.