# Refractive Index Sensing through Surface Plasmon Resonance in Light-Diffusing Fibers
## 3 Results and Discussion
Instead, for the scrambled, non-Lambertian case, power is equally distributed among the various angles; therefore, the relative weight of rays escaping away due to loss of TIR is lower. After this preliminary study, we have used the SPR-based LDF sensor configuration. Figure 4a shows the experimental spectral transmission of our sensor, normalized to the spectrum recorded with air as the surrounding medium, for different water-glycerol solutions. A clear red-shift of the resonance wavelength (SPR dip) is observed when increasing the RI of the sensing medium. For comparison purposes, in Figure 4b we show the corresponding spectra obtained by using the same  
Figure 3: (**a**) Variation of the transmitted power through the LDF as a function of the external medium’s RI. The continuous lines are the simulation results. (**b**) Angular distribution of optical power. model previously described (Equation (1) with \(P_{0}(\theta_{i})=const\)), with the only difference that reflectance coefficients are now calculated taking into account the metal film. In order to examine the obtained results, we recall some parameters, such as sensitivity and signal-to-noise ratio (SNR). The sensitivity (S) can be defined as the shift in resonance wavelength per unit change in refractive index [12; 19; 20; 21; 22]. It is usually reported in nanometers of peak shift per RI Unit (nm/RIU):  
\[S=\frac{\delta\lambda_{\text{SPR}}}{\delta n_{sm}}\Big{[}\frac{\text{nm}}{ \text{RIU}}\Big{]} \tag{3}\]  
where \(\delta\lambda_{\text{SPR}}\) is the SPR wavelength shift, and \(\delta n_{sm}\) is the variation of refractive index of the sensing medium. Analogously, the SNR of an SPR sensor with spectral interrogation is a dimensionless parameter defined as [19]:  
\[\text{SNR}=\frac{\Delta\lambda_{\text{SPR}}}{\Delta\lambda} \tag{4}\]  
where \(\Delta\lambda_{\text{SPR}}\) is the SPR wavelength shift induced by a prescribed RI change, and \(\Delta\lambda\) is the spectral width of the SPR response curve corresponding to some reference level of the transmitted power [19]. From Figure 4 we see that, differently from the previous results, the agreement between experimental and numerical data is not excellent: in particular, the experimental spectra exhibit a deeper and wider resonance. Furthermore, the RI-induced SPR dip shift is larger in the experiments (173 nm in the analyzed range against a shift of 128 nm derived from simulations). In other words, the experimental sensitivity (S) is better than numerical sensitivity; vice versa, the SNR is worse. This discrepancy may be attributed to several reasons: first, some nonuniformity of the gold film thickness may exist along the length and/or circumference of the fiber; second, our model only takes into account meridional rays, while some skew rays may exist, especially if considering the influence of the scattering centers; third, the scattering of light due to the helicoid voids has been taken into account only partly in our model, in particular setting a uniform angular power distribution. However, the presence of the scattering centers could also affect the distribution of energy among p-polarization and s-polarization. Unfortunately, an accurate description of light scattering within the fiber core may be performed only if a statistical distribution of the helical voids were available, which was not our case. It is worth noting that, for \(n_{sm}=1.332\), the experimental response indicates a resonance wavelength of \(\approx\)630 nm and a minimum transmittivity of \(\approx\)52%, while the corresponding numerical values are \(\approx\)650 nm and \(\approx\)75%, respectively. As discussed in Reference [23], the propagation of skew rays leads to a downward, as well as a backward, shift in the SPR curve, which is consistent with our observations and suggests a major influence of skew rays, compared to a conventional multimode fiber. Figure 4: Experimental (**a**) and numerical (**b**) SPR spectra obtained after normalization to the transmission spectrum in air.