## 3 Results  
The SPR condition occurs when the phase of the fundamental fiber mode matched the phase of the surface plasmon at the metamaterial interface. At this coupling, the modal confinement losses reached a peak, as exemplified in Figure 2 for a metamaterial layer with filling fraction \(f=0.5\) and refractive index of the analyte \(Ri_{analyte}=1.33\). The confinement losses of the sensor could be calculated by [23]:  
\[\alpha=8686\times 2\pi/\lambda\times Im_{neff}\times 10^{4}\left(\frac{\text{dB}}{ \text{cm}}\right), \tag{4}\]  
where \(\lambda\) represents the wavelength and \(Im_{neff}\) is the imaginary part of the effective modal index. The effective constitutive optical relations that characterize the wire metamaterial resulted from the coupling between surface plasmons excited by the electric field with polarization parallel to the optical axis. Therefore, only the electric field oriented perpendicularly to the metamaterial interface (\(y\) axis direction in Figure 1a) allows for the excitation of plasmonic modes, even though the fundamental mode of the PCF is degenerate for two orthogonal polarizations. The variation of the refractive index of the analyte changed the SPR wavelength as well as the magnitude of the confinement losses. Figure 3 shows the confinement loss spectra presented by the D-shaped PCF with a metamaterial layer regarding a filling fraction \(f=0.3\) and refractive indexes of the analyte in the range of 1.30-1.39. Figure 3: Confinement loss spectra for different analyte refractive indexes for the D-shaped fiber with a metamaterial with filling factor \(f=0.3\). Figure 2: Dispersion curve of the fundamental fiber mode and SPP modes for a refractive index \(Ri_{analyte}=1.33\). Y-pol is the perpendicular polarization to the metamaterial film. The insets show the intersections between the dispersion curve of the fundamental Y-pol fiber mode and the plasmonic mode at the metamaterial interface. The tunable spectral sensing response of the D-shaped PCF with the metamaterial was accounted by the sensitivity \(S\) estimated as the average change in the SPR wavelength with the change in the refractive index of the analyte [24]:  
\[S=\Delta\lambda_{peak}/\Delta n_{analyte}\ (\mathrm{nm}/\mathrm{RIU}) \tag{5}\]  
where \(\Delta\lambda_{peak}\) is the wavelength resonance displacement and \(\Delta n_{analyte}\) is defined as the changes in the analyte refractive index. Correspondingly, regarding an optical spectrum analyzer of minimal detectable change \(\Delta\lambda_{min}=0.1\)nm in the SPR loss spectra [25; 26; 27], the resolution associated to S could be expressed by:  
\[R=\Delta n_{analyte}\times\left(\Delta\lambda_{min}/\Delta\lambda_{peak}\right) \ (\mathrm{RIU}) \tag{6}\]  
From the spectra shown in Figure 3, the obtained sensitivity and resolution were 532 nm/RIU and 1.8789 \(\times\) 10\({}^{-4}\) RIU, respectively. The fractional volume of constituents modified the conductive character of the metamaterial. Figure 4 displays the distribution of electric field intensity at the SPR wavelength for three different volume fractions of silver in the metamaterial layer. In all cases, surface plasmon resonance was achieved at the optimal coupling between the Y-polarized fundamental fiber mode and the surface mode at the metamaterial interface; however, the field enhancement at the resonance wavelength benefited from a major amount of metallic inclusions. The net consequence was a shifting of the SPR spectra according to different filling fractions of silver in the metamaterial layer. Therefore, the spectral range for the sensor operation and even the sensitivity levels can be tuned by modifying the volume fraction of silver embedded in alumina. Figure 5 depicts the influence of the metamaterial filling fraction on the amplitude and spectral location of the confinement loss peak regarding a constant refractive index of the analyte, \(Ri_{analyte}=1.33\).