## 3 Experimental Results
### Polarization Analysis  
As previously outlined in [22], the MgO-NP fiber induces a beat length of polarization that has a higher frequency than a standard SMF, with polarization switching every few centimeters. This effect is common with the other methods proposed for enhancing the Rayleigh backscattering of the fiber [13; 14; 15]. Thus, in this section we investigate the polarization-sensitive behavior of the FBG, by separating the S/P polarizations into the analysis.  
The polarization effects are shown in Figure 6, which reports the FBG spectra for S and P polarizations. At first, we observe a different amplitude between the two spectra, with the S polarization having a higher value, but also fluctuating as the temperature increases. The spectra for the polarization P appear narrower in bandwidth, and as temperature increases we observe that the spectra at the P polarization take a different wavelength shift than the spectra for the polarization S.  
We can analyse independently the two polarizations, and determine the sensitivity to temperature at each wavelength; this analysis is shown in Figure 7. We observe a linear pattern for both polarizations, with thermal sensitivity of 11.53 pm/\({}^{\circ}\)C for the polarization S (R\({}^{2}\) = 0.997) and 11.08 pm/\({}^{\circ}\)C for the polarization P (R\({}^{2}\) = 0.995). The analysis shows a significant deviation between the two polarizations, as the sensitivity for the S polarization (the dominant one, given its higher amplitude) is 4.0% higher than for the P polarization; this is a reliable measurement given the fidelity of the linear fit, as the R\({}^{2}\) term is higher than 0.99 for both estimates. At room temperature, the Bragg wavelength is higher for the polarization P and lower for the S; as temperature increases however we see a progressive divergence between the Bragg wavelengths for both polarization states.  
A polarization analysis is carried out in Figure 8, reporting the FBG bandwidth (estimated as the full-width half-maximum, FWHM) and the maximum spectral amplitude for each polarization. At first, we observe an interesting pattern for the FWHM, which at room temperature is wider for the P polarization (as shown in Figure 6) where the minimum amplitude is recorded; as the temperature increases, the FWHM assumes different values for the 2 polarization, and is equal to 0.33-0.35 nm for the S polarization and to 0.27-0.28 nm for the P polarization, showing a significant deviation which is also clear as the spectra are plotted in Figure 6.  
Figure 5: Bragg wavelength of the MgO-NP FBG as a function of the temperature variation. The chart shows the measured data and the linear fit (11.45 pm/\({}^{\circ}\)C, R\({}^{2}\) = 0.997).  
The amplitude of the spectral response also shows a temperature-dependent pattern, as the light appears to transfer from the S to P polarization as the temperature increases. At room temperature, the polarization difference is over 12 dB, but reaches a minimum of 0.6 dB at \(\Delta\)T = 75 \({}^{\circ}\)C, where the two polarizations have similar amplitude; at higher temperature, the process reverses and S polarization appears to have higher amplitude.  
Figure 6: Reflection spectra of the FBG on MgO-NP fiber, evaluated for S (**upper**) and P (**lower**) polarizations.  
Figure 7: Bragg wavelength for each polarization as a function of the temperature variation.