Estimation Models for the Refractive Index Response Curve of EFBGs

Estimation models for the surrounding refractive index response of EFBGs were developed from computer simulations and tested on experimental data. Numerical simulations were used to investigate the fundamental core mode's effective refractive index dependence with the fiber radius and the surrounding refractive index. An empirical mathematical model was developed upon the simulation results, and it was used to derive the estimation models. The response curve is estimated from a reference calibration curve using two different approaches: interpolation and extrapolation. The interpolation is performed using the wavelength response of the EFBGs at two different surrounding refractive index values. Then, the response curve is obtained solving a simple pair of linear equations. The extrapolation is performed using the wavelength shift observed during the etching process, which is used to derive a multiplicative factor for the calibration curve. The response curves estimated by the model were compared with the experimental results, showing good agreement within the experimental uncertainties. Considering the surrounding refractive index ranging from 1.333RIU to 1.458RIU, with the sensors' response ranging from 1544.84nm to 1552.70nm, the maximum deviation between the estimation and the experimental results were 0.26nm and 0.41nm, and the maximum standard deviation were 0.03nm and 0.05nm, respectively for interpolation and extrapolation.