## 3 Results and Discussion
### Photoluminescence Spectroscopy Analyses  
The photoluminescence spectroscopy (PL) analysis was performed by dispersing the nanoparticles in ethanol. The sample was excited with a xenon arc lamp laser emitting in the range from 250 to 850 nm. The response spectra of each sample were recorded from 300 to 650 nm. Figure 2 presents the PL analysis of the three samples S1, S2, and S3, in the form of their absorption intensity as functions of the wavelength of the incident light (electromagnetic, EM) wave. This figure demonstrates that each sample exhibited an optical response consisting of two higher order resonance modes at \(\lambda\)1 and \(\lambda\)2. The corresponding resonance wavelength of each sample falls in the wavelength ranges of \(\lambda\)1: 471-484 nm and \(\lambda\)2: 556-568 nm. The first PL intensity peak for S1 in Figure 2 is \(1.3\times 10^{2}\) at 483 nm, with the Ag shell thickness being 14 nm. The first PL intensity peak for S2 is \(1.7\times 10^{2}\) at 474.5 nm, with the Ag shell thickness being 18 nm. The first PL intensity peak for S3 is \(1.9\times 10^{2}\) at 471 nm, with the Ag shell thickness being 22 nm. It is clear that the first PL intensity peak increases and its position in wavelength moves to smaller values (high frequencies) as the Ag shell thickness increases from 14 to 22 nm. The increase in the intensity of the first peak is due to the decrease in concentration of charge trappers e.g., defects, vacancies, surface oxygen atoms, and dangling bonds, when the shell thickness is increased. This is true for all of the samples. This decrease subsequently leads to a high concentration of oscillating electrons; they are responsible for the observed first large intensity peak of the PL spectra. The corresponding simulations (see Section 3.3 below) incorporate these effects through a size-dependent collision frequency in a Drude model of the Ag shell. A collective blue or red shift occurs with any change in the shell thickness. In particular, the observed blue shift in the frequency response corresponds to an increase in the Ag shell thickness. Similarly, the second peak for S1 is \(0.8\times 10^{2}\) at 566 nm, the second peak for S2 is \(1.0\times 10^{2}\) at 567 nm, and the second peak for S3 is \(1.05\times 10^{2}\) at 559 nm. Again, this behavior shows a similar variance of the PL intensity peak and its wavelength position, i.e., the resonance frequency is blue shifted as the shell thickness increases. These results further confirm that one can indeed reasonably tune the resonance wavelength of a core-shell system by varying the thickness of the Ag shell [11; 12; 13]. From the experimental point of view, some factors are very important to consider when the particle size is reduced to the nano-scale. These factors significantly change the real and imaginary parts of the permittivity of the materials. For instance, the surface to volume ratio is very high in the nano-regime. However, most of the atoms lie on the surface of the core. Thus, the surface itself is a more defective region in comparison to the core of the nanoparticle. The atoms on the core have dangling bonds  
Figure 2: The plasmonic response of the three samples S1, S2, and S3, measured by photoluminescence (PL) spectroscopy and their corresponding resonance wavelengths. associated with them. In addition to these dangling bonds, the nanoparticle's surfaces are rich with various types of defects. These include lattice vacancies, extra oxygen atoms, and mismatches between the local lattices. Consequently, the crystallinity of the surface lattice is very weak. These surface lattice defects act as traps for charge carriers opposing the direction of the collective oscillation of the charges, i.e., the plasmons [16]. Because there is an additional interface defined by the boundary of the Ag and SiO\({}_{2}\) regions, these effects are stronger in core-shell nanoparticles than in pure metallic ones. Consequently, a depletion layer of charge carriers is formed in the vicinity of this interface [17; 18].