## 3 Results and Discussion
### Numerical Analysis
Figure 3 indicates that the first ACS peak increases in amplitude as the Ag shell thickness increases from 14 to 22 nm and its position moves to lower wavelengths (i.e., to higher frequencies), which is in agreement with the experimental results in Figure 2. Similarly, the second ACS peak position also moves to higher frequencies as the Ag shell thickness increases, again in agreement with the experimental results in Figure 2. On the other hand, the ACS peak values decrease as the Ag shell thickness increases, in contrast to their measured behavior shown in Figure 2.  
Due to large size of the Ag shells, the higher order resonance peaks are quite broad [20]. It is also clear that all of the resonance frequencies are blue shifted as the Ag shell thickness increases. In particular, a direct comparison of the theoretical, simulated and measured resonance frequencies is given in Table 1. The analytical Mie theory, CST numerical and experimental results are in favorable agreement. There are two well-defined peaks in the ACS values within the wavelength range from 450 to 650 nm. The simulation peaks all move to a higher frequency when the silver thickness increases, which is in agreement with the measured outcomes: 14, 18, and 22 nm for S1, S2, and S3, respectively. Figure 3: The simulated absorption intensity of the core–shell samples S1, S2, and S3, and their corresponding resonance wavelengths. In addition to CST simulation based on size-dependent Drude modal, we also compare the experimental results with CST and Mie theory simulation results based on Johnson & Christy (JC) and size-dependent Drude (SDD) model data shown in Figure 4. In both CST and Mie simulations we used the JC and SDD dielectric data for Silver. It is should be noticed that unlike to the size-dependent Drude model, the Johnson data does not incorporate the additional size effects at nanoscale [19]. A comparison of the normalized, measured CST (JC and SDD) numerical and Mie analytical (JC and SDD) results for Sample S2 is given in \[\varepsilon_{\mathbf{Draude}}(\mathbf{R},\mathbf{\omega})=1-\frac{\omega_{p}^{2}}{ \Gamma(\mathbf{R})^{2}+\ \mathbf{\omega}^{2}}+j\frac{\Gamma(\mathbf{R})\ \omega_{p}^{2}}{\mathbf{\omega}[\ \Gamma(\mathbf{R})^{2}+\ \mathbf{\omega}^{2}\ ]} \tag{2}\]0 It was found that both CST and Mie are coincident, providing sufficient evidence about the reliability of CST to simulate the optical response of core-shell nanoparticles. The resonance frequency points in the CST and Mie simulation are in reasonably close agreement; however, a notable difference with experimental data was predicted using the JC data in both CST and Mie simulation. Obviously this difference is due to the fact that unlike to the Drude model, Johnson model does not include the size effects. However, the simulated results using the SDD data in both cases are reasonably close to the experiment. This further provides evidences for the existence of the NSD and MQB losses and their corresponding blue shift. Confidence in the remaining CST results arises from this comparison and previous applications of it to model nanoparticle phenomena [21] and validation studies with analytical and other numerical approaches [22]. The values of resonance wavelength corresponding to the experiment, CST (JC and SDD), and Mie theory (JC and SDD) are given in \[\varepsilon_{\mathbf{Draude}}(\mathbf{R},\mathbf{\omega})=1-\frac{\omega_{p}^{2}}{ \Gamma(\mathbf{R})^{2}+\ \mathbf{\omega}^{2}}+j\frac{\Gamma(\mathbf{R})\ \omega_{p}^{2}}{\mathbf{\omega}[\ \Gamma(\mathbf{R})^{2}+\ \mathbf{\omega}^{2}\ ]} \tag{2}\]1 One can observe from the Table 1 that CST (SDD) and Mie (SDD) simulated results are closer to the experiment as compared to the CST (JC) and Mie theory (JC).