## 3 Results and Discussion
This dependence allows to define the sensitivity, \(S_{B}\), and the figure of merit (FOM) of this sensor [31; 32]:  
\[S_{B}=\frac{\partial}{\partial n_{a}}(\Delta R), \tag{6}\]  
\[\text{FOM}=\frac{S_{B}}{\Delta R}. \tag{7}\]  
These expressions have been adapted from previously reported contributions where the change in the refractive index is caused by other parameters than wavelength (spectral interrogation) or angle (angular interrogation) [33; 34; 35; 36]. For comparison, we model a [PERSON]'s design that uses a glass prism of refractive index 1.447 working at \(\lambda=1.351\) nm with a metallic gold layer 35 nm thick. Figure 4: **(a)** Variation of the resistance of the structure as a function of wavelength. (**b**) Variation of the resistance with the index of refraction of the analyte when the structure is illuminated on resonance (\(\lambda=1.351\)\(\upmu\)m). The linear fitting in the interval \(n_{a}\in[1.331,1.336]\) defines a value of sensitivity, \(S_{B}=10.45\)\(\Omega\)/RIU (where RIU means refractive index units). (**b**) Variation of the sensitivity, \(S_{B}\), as a function of the index of refraction of the analyte, \(n_{a}\). (**d**) Dependence of the FOM in terms of \(n_{a}\). The open circles in (**b–d**) denote the evaluated values, and the solid lines represent an interpolation of these dependences. The vertical dotted lines in (**b–d**) show the range in the index of refraction, \(n_{a}\), where the system is linear. This system provides an angular shift of \(0.6^{\circ}\): when the refractive index of the analyte changes from 1.331 to 1.336. In reflectance, the full width at half maximum of the spectral line shape is 0.68 nm. This results in a sensitivity of \(S_{B}=120\) deg/RIU and a FOM=176 RIU\({}^{-1}\) (RIU means refractive index units). When necessary, full optimized results of angular interrogated devices are reported by [PERSON] et al. [37]. Figure 4c,d show the sensitivity and FOM defined in Equations (6) and (7). We can see how \(S_{B}\) reaches a maximum value of \(S_{B,\max}=12.4\)\(\Omega/\text{RIU}\) at \(n_{a}=1.3335\), and \(\text{FOM}_{\max}=398.2\) at \(n_{a}=1.3360\). So, this would be best for aqueous samples. All these values are competitive with recently reported devices [24], plus it is based in a simpler physical mechanism [38]. Also, from Figure 4b we can make a linear fit of \(\Delta R\) within a given range in the index of refraction. This fit reveals an almost linear dependence when \(n_{a}\in[1.331,1.336]\) and sensitivity \(S_{B}=10.45\)\(\Omega/\text{RIU}\). This range in the index of refraction of the analyte (marked between vertical dotted lines in Figure 4a-c) corresponds with a variation around \(n_{a}=1.333\), which is the index of refraction of water in the visible. Actually, this index slightly decrease when moving towards longer wavelengths. Therefore, this system seems appropriate to monitor parameters of substances in aqueous media. If necessary, the design can be tuned to perform at other ranges in the index of refraction by slightly modifying the geometry of the arrangement, for example, by changing the periodicity of the subwavelength grating, \(P\)[3]. In fact, a potential application of this design is the sensing of human tear with a refractive index \(n_{\text{tear}}=1.33698\pm 0.001\) at \(\lambda=589\) nm [39, 40], or the salinity of water with an index of refraction ranging from 1.33 till 1.35 [41, 42].