## 3 Resonant Scattering of Nanocylinders  
### Scattering Characteristics of Single Nanocylinder  
The schematic of nanocylinder is shown in Figure 1. The light source is incident from the top of the nanocylinder particle. The displacement current can be formed in nanocylinder by the electric field of the incident light, resulting in the formation of the in-plane magnetic dipole [18; 19; 20]. Silicon material for nanocylinder is used because it is a high refractive index material with a relatively low absorption loss in the visible spectrum range, and it is compatible to nanophotonic devices and semiconductor components. In our simulation, the total field scattering field (TFSF) light source of finite-difference time-domain method (FDTD) was applied as the excitation source. The scattering cross-section and the electromagnetic field distribution of the nanocylinder or nanocylinder array were accurately calculated by FDTD method. Firstly, we study the scattering properties of single nanocylinder, as in Figure 2. \(Q_{scat}\) is defined as the scattering cross-section of a single silicon nanocylinder in air. The scattering cross section for a silicon nanocylinder with height and diameter of 100 nm is demonstrated. It can be seen that the scattering peaks are at 433 nm and 494 nm, respectively. We can use the field profiles inside the nanocylinder to identify the electromagnetic resonant modes and the corresponding current loops in Figure 3. Figure 3 shows the electric field vector distribution at the center of nanocylinder. It can be revealed that the resonant mode at \(\lambda=433\) nm corresponds to the electric dipole (ED) mode, and the  
Figure 1: **(a)** The schematic of nanocylinder, the direction of the red arrow indicates the direction of the displacement current, and the incident wave is normally incidence; and, **(b)** Interaction between nanocylinders with and without substrate. resonant mode at \(\lambda=494\) nm corresponds to the magnetic dipole (MD) mode based on the field lines loop induced by the driving field. In order to further reveal electromagnetic field characteristics of nanocylinder, the electromagnetic field distribution in Figure 4 is plotted at \(\lambda=433\) nm and \(\lambda=494\) nm, respectively. From the electric field distribution in Figure 4a, a linear electric field distribution in the center of nanocylinder at \(\lambda=433\) nm is shown, and there is a displacement current loop with the circulating electric field at \(\lambda=494\) nm in Figure 4c. From the magnetic field distribution, there is a node at the center at \(\lambda=433\) nm in Figure 4b, which indicates the presence of electric dipole. There is an antinode at the center at \(\lambda=494\) nm in Figure 4d, which is consistent with a magnetic dipole. By the vector field lines and the electromagnetic field distributions, it can be revealed that the scattering resonant mode at \(\lambda=433\) nm can be attributed to the electric resonance, and the scattering resonant mode at \(\lambda=494\) nm originates from magnetic resonance. Figure 3: The electric field vector distribution of the XOZ cross-section at the center of nanocylinder. (**a**) at \(\lambda=433\) nm; (**b**) at \(\lambda=494\) nm. Figure 2: Scattering cross-section of a single silicon nanocylinder. Figure 5a shows the scattering spectra for particle radius from 50 nm to 70 nm, with the height of 100 nm. It can be seen that the scattering resonant modes, ED and MD, show a clear red-shift and an increase in \(Q_{scat}\) for increasing nanocylinder diameter. For the diameter of 140 nm, the higher order mode of electric duadrupole occurs at visible spectrum. In Figure 5b, the influence of particle height with diameter of 100 nm to scattering resonance is shown. With the increase of height, the two maxima of the scattering cross-section show a clear redshift, and the amplitude increases. For the nanocylinder with a height of 50 nm, it is not sufficient to support the MD mode, so the amplitude of MD resonance is smaller.