Accurate compensation and prediction of the temperature cross-sensitivity of tilted FBG cladding mode resonances

The temperature dependence of core mode resonance has been thoroughly studied in fiber Bragg gratings (FBGs), but it is not the case for cladding mode resonances in multi-resonance gratings such as tilted FBGs (TFBGs). In this work, the temperature sensitivity of ultraviolet written TFBGs in SMF-28 fibers is assessed, demonstrating in the first, to the best of our knowledge, place that a single gauge factor K _T =6.25⋅10^-6±0.02⋅10^{-6 ∘} C ^-1 can be employed to characterize the response to temperature of the resonances over the full spectrum in the 10°-50°C range. Then, a simulation model is obtained, enabling to predict TFBG spectra in the 10°-50°C range with high accuracy. This requires a calibration of the core index and dispersion of the TFBG measured in air at 25°C, and determination of the glass refractive index thermo-optic coefficient (d n/d T=8.46⋅10^-6±0.1⋅10^{-6 ∘} C ^-1, common to both core and cladding glasses), leading to a mean error on the wavelength position of resonances between 1 and 3 pm. This mean error can be further reduced (less than 1 pm) by considering a linear dependence with temperature of d n/d T. Therefore, this model will enable to completely remove the temperature-induced shifts of all resonances in TFBG sensing applications and measure with great accuracy the variables of interest by using the scaled averages of groups of resonances instead of (less accurate) individual shifts.