## 3 Results and Discussion  
The variation in the scattering cross-section of SCS dimer antennas was monitored as a function of the wavelength at different values of \(g\) (\(=\)\(d-98\)), as depicted in Figure 2a. The gap \(g\) varied from 0.1 to 402 nm. Small values of \(g\) (0.1\(\sim\)2 nm) ensure strong near-field coupling. The number of plasmonic resonance peaks and their intensities were sensitive to inter-particle gap \(g\). The SCS dimer  
Figure 1: Silver-coated silica (SCS) dimer model. The brown sphere indicates the silica core and the light-blue semi-transparent circle around the silica core represents the silver shell; \(d=g+98\) is the separation distance between the centers of the nanoparticles. antennas exhibited a single major dipolar mode when 12 nm \(\leq g\leq\) 402 nm. A second dipolar mode appeared when the value of \(g\) was below 12 nm, and a third dipolar modes was generated when \(g\leq\) 2 nm, as shown in Figure 2b. The latter two dipolar modes we refer to here as high energy Multiple Dipolar Modes (HEMDMs). The corresponding resonance energies and wavelengths of all modes are tabulated in Table 1. In Figure 2a, the first resonance peak is represented by circles and has high intensity and broadness. This resonance peak is attributed to the major bonding dipolar mode and red-shifted as \(g\) decreased. Figure 2b shows the presence of HEMDM peaks in a more highlighted form in a \(g\) range from 0.1-12 nm. Only this range was selected for Figure 2b because HEMDM peaks above this range were not present. The major dipolar mode exhibits greater intensity and broadness than the HEMDM. All three resonance peaks corresponded to different dipolar modes with different resonance wavelengths and red-shifted with a decrease in \(g\) value. The most energetic HEMDM peak had resonance energy in a range from 2.434 to 2.805 eV and appeared when \(g\) was 0.1-1.1 nm, while the second HEMDM (1.990-2.794 eV) occurred when \(g\) was 0.1-12 nm. The peak corresponded to the major dipolar mode and shifted from higher (2.481 eV) to lower energy values (1.441 eV) as the \(g\) value decreased from 402 to 0.1 nm. In previous findings, the plasmonic behavior of major dipolar modes was investigated in a core-shell dimer system and was based only on the \(R_{1}/R_{2}\) ratio [22]. However, the findings of this article suggest that, by varying the inter-particle distance \(g\), the SCS dimer will possess high tunable plasmonic properties regarding the co-existence of different dipolar modes with different frequency and energy values. Figure 2: (**a**) Scattering cross-section of dimer as a function of wavelength at all calculated values of \(g\). The circles shows a main dipolar resonance peak, while the triangles indicate high energy multiple modes; (**b**) High-energy multiple resonance peaks where \(g\) is 0.1–12 nm. The origin for the presence of three resonance peaks can be better understood by considering the scattering and absorption cross-section as a function of wavelength in a more highlighted form, e.g., when \(g\) = 0.4 nm (Figure 3). Figure 3 shows that the scattering cross section for the major dipole resonance mode is high compared to the absorption cross section, while for the other two HEMDM peaks, both types of cross sections are comparable The position of the major dipolar mode is 740 nm\(\sim\)3\(\lambda_{o}\)/2, while the other two HEMDM peaks indicated by squares and triangles are located at 502 nm\(\sim\)\(\lambda_{o}\) and 438 nm\(\sim\)6\(\lambda_{o}\)/7, where \(\lambda_{o}\) = 504 nm is the reference wavelength and corresponds to the resonance wavelength of a single isolated SCS nanoparticle. These peak positions verify that all three peaks arise due to the co-existence of different dipoles. These dipoles are completely independent from each other, but their generation depends only on the inter-particle distance \(g\). Also the small \(g\) value causes the surface charges to reorient due to unbalanced Coulombic forces, resulting in a non-uniform charge distribution across the particles surfaces.