## 3 Results and Discussion
This charge distribution gradient leads to the generation of two additional dipolar modes with high energy and resonance frequency. The expected electric field distribution and its directivity at all three resonance wavelengths are shown in Figure 4a-f. Significant enhancement was predicted in the local field inside or in close proximity to the dimer. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**S. No.**} & \multirow{2}{*}{**\(g\) (nm)**} & \multirow{2}{*}{**No. Peaks**} & \multicolumn{3}{c}{**Energy (eV)**} & \multicolumn{3}{c}{**Wavelength (nm)**} \\ \cline{3-6}  & & & **Main Dipolar Peak** & **HEMDEM Peaks** & **MAIN Dipolar Peak** & **HEMDM Peaks** \\ \hline \multirow{2}{*}{1} & \multirow{2}{*}{0.1} & \multirow{2}{*}{3} & \multirow{2}{*}{i. 1.441} & ii. 1.990 & ii. 481.1 \\  & & & & iii. 2.434 & i. 348.4 & iii. 588.5 \\ \hline \multirow{2}{*}{2} & \multirow{2}{*}{0.4} & \multirow{2}{*}{3} & \multirow{2}{*}{i. 1.660} & ii. 2.406 & ii. 581.7 \\  & & & & iii. 2.805 & i. 401.3 & iii. 678.2 \\ \hline \multirow{2}{*}{3} & \multirow{2}{*}{02} & \multirow{2}{*}{2} & \multirow{2}{*}{i. 1.89} & ii. 2.78 & i. 654.1 & ii. 445.9 \\ \hline \multirow{2}{*}{4} & \multirow{2}{*}{07} & \multirow{2}{*}{2} & \multirow{2}{*}{i. 2.10} & ii. 2.86 & i. 589.4 & ii. 432.5 \\ \hline \multirow{2}{*}{5} & \multirow{2}{*}{12} & \multirow{2}{*}{2} & \multirow{2}{*}{i. 2.16} & ii. 2.88 & i. 572.5 & ii. 430.0 \\ \hline \multirow{2}{*}{6} & \multirow{2}{*}{17} & \multirow{2}{*}{1} & \multirow{2}{*}{i. 2.27} & – & i. 556.7 & – \\ \hline \end{tabular}
\end{table} 
Table 1: Peaks positions at small value of \(g\). Figure 3: Scattering cross-section of the silver-coated silica nanoparticles as a function of wavelength at \(g\) = 0.4 nm. In Figure 4a,c,e, the field vectors pronounce the density and direction of the current, which correspond to the major bonding dipole and HEMDM, respectively, in the SCS dimer at their resonance frequency/wavelength. There is a uniform electric field distribution inside and nearby the SCS dimer during the major dipolar mode where resonance wavelength \(\lambda\) = 740 nm. However, the local field in the vicinity of the dimer is stronger than the field of the incident electromagnetic planewave. In the case of HEMDM (\(\lambda\) = 502 nm, 438 nm), the local field enhancement becomes more significant with a slight phase change. This phase change is more apparent in the directivity plot of the nanoantenna. Interesting directivity of the electric field was observed for all three resonance peaks, as shown in Figure 4b,d,f. It should be noted that the planewave is directed along the \(Z\)-axis. The inside and outside fields during the major dipolar mode is uniform and is propagating along the positive and negative \(X\)-axes equally. The scattered electric field during the HEMDM exhibits different behavior. In the HEMDM, a unidirectional scattered field along the \(Y\)-axis was predicted. There is a small back lobe of the scattered electric field for the HEMDM resonance at \(\lambda\) = 438 nm (Figure 4f). This means that the major dipolar and HEMDM corresponds to longitudinal and transverse dipolar modes, respectively. In recent literature, these modes have been predicted to have a gap narrower than 1 nm and have been attributed to morphology and quantum charge transfer (QCT) [20]. However, our work suggests the existence of such longitudinal and transverse dipolar modes for spherical shell surfaces with a gap \(\leq\)2 nm. Hence, it is suggested that QCT may affect the strength or intensity of these HEMDMs. Moreover, in our case, such high energy dipolar modes occur at \(g\) values of 12 nm, which is high compared to the previously reported value (\(g\) = 1-2 nm). The generation of these modes is explainable using a classical Drude model modified by including the size of effects of plasmonic nanostructures. The far-field characteristics of all three dipolar modes have been depicted independently in Figure 5a-c.