## 3 Resonant Scattering of Nanocylinders
### Scattering Characteristics of Double-Nanocylinders-Combination  
Next, we study the interaction between two identical silicon nanocylinders by changing the spacing \(g\) between two particles in Figure 6. When the gap \(g\) is comparable to the diameter 100 nm of nanocylinder, the scattering performance is similar to that of a single nanocylinder, except for the enhancement of scattering amplitude. The amplitude of electric dipole resonance is lower than that of magnetic dipole resonance, and both resonant modes are separated completely. As the spacing becomes smaller, the interaction between two nanocylinders becomes stronger, and a broadband scattering characteristic occurs. In order to intuitively understand the effect of strong interaction of nanocylinders in close proximity on broadband scattering properties at the gap \(g\) = 10 nm, we study the electric and magnetic field distributions at the XOZ plane (y = 0). From the scattering cross-section curve, we select two positions: at \(\lambda\) = 444 nm and at \(\lambda\) = 499 nm, which have deviated from the electrical resonance at \(\lambda\) = 433 nm and the magnetic resonance at \(\lambda\) = 494 nm of a single nanocylinder. From the electromagnetic field distribution in Figure 7, it can be seen that the strong electric field is concentrated on the gap between nanocylinders. In Figure 7a,b, at the electric field distribution indicates a roughly linear distribution, while the magnetic field shows an approximate node, implying the electric dipole resonant mode. It is obvious that the field distribution in dimeric nanocylinders demonstrates asymmetric features, which is attributed to the strong interaction between dimer. From Figure 7c,d, at the electric field, introduces a displacement current loop and the magnetic field indicates an antinode in each nanocylinder. These characteristics exhibit magnetic dipole resonance. It is interesting that by the enhancement of interaction with a decre  
Figure 5: Scattering spectra of a single silicon nanocylinder with (a) various radius \(R\) and (b) various height of nanocylinder in air. Figure 6: Scattering spectra of double-nanocylinders-combination with the decreasing spacing from 100 nm in air. \(g\) represents the spacing between two nanocylinders. The diameter and height are 100 nm. resonant bandwidth, including ED and MD, is broadened. The ED and MD resonances nearly merge with each other and form hybrid broadband resonant mode. Next, the interaction of two different nanocylinders dimer is illustrated in detail by calculated scattering spectra in Figure 8. The scattering spectra were calculated with the two different nanocylinders at the unchanged gap width of 100 nm from Figure 8a-d. The diameter of one nanocylinder is 100 nm, and the diameter of the other nanocylinder is varying from 100 nm to 130 nm. In the case of Figure 8a, the scattering spectrum is similar to that of a single silicon nanocylinder, which indicates that the interaction between two nanocylinders is weak. As the diameter of the right nanocylinder in the double-nanocylinders-combination increases, the scattering amplitude of the electric resonance is decreased, and it shifts slightly closer to the mainly magnetic dipole resonance. When the diameter of the right nanocylinder is increased to 110 nm in Figure 8b, a newly emergent mode occurs. After carefully analysis, it results from the interaction of two nanocylinders. This new mode introduces a splitting phenomenon of magnetic dipole resonance. This mode can be named as \"MD2\", and the original magnetic dipole resonance can be called as \"MD1\". The splitting of \"MD1\" and \"MD2\" results from the magnetic-magnetic interaction in both of the nanocylinders. With the increase of diameter, the newly magnetic mode of \"MD2\" is redshift, but the resonant frequency of \"MD1\" is unchanged. Because of this splitting performance of magnetic resonance, the dimeric silicon nanocylinders shows a clear broadband scattering effect.