# High Q-Factor Resonance in a Symmetric Array of All-Dielectric Bars
## 2 Simple Silicon Rod Arrays with High Q Resonance  
The structure of the all-dielectric metasurface is shown in Figure 1a, where a silicon rectangular rod array (\(n=3.45\)) is deposited on top of a semi-infinite quartz substrate (\(n=1.46\)). And it can be easily fabricated by plasma-enhanced chemical vapor deposition (PECVD), electron-beam lithography, residual resist etching and lift-off process [6; 35]. Unlike most previously reported rod-type all-dielectric metasurfaces, where normal incident light polarized along the rods is used to excite a broad ER [5; 6; 36; 37; 39], in this paper, the electric field of the incident wave is polarized perpendicular to the rods (i.e., in \(x\)-axis). Numerical simulations are conducted using the commercial CST software (CST Studio Suite 2014, CST company, Darmstadt, Germany) at frequency-domain, and periodic boundary conditions are utilized both in \(x\) and \(y\) directions and open boundary condition are used in the wave propagating direction of \(z\). The lattice periods in the x and y direction are fixed as \(Px=800\) nm and \(Py=900\) nm, respectively. Figure 1b shows the simulated transmission spectrum. Two strong and clear dips are observed in the wavelength range of 1100 nm to 1400 nm. To interpret the origin of these two resonance dips, the field distribution inside the silicon rod are calculated and illustrated in Figure 2. For the broad resonance at shorter wavelength of 1187 nm, the electric and magnetic field are illustrated in Figure 2a,b. The electric and magnetic fields are mainly localized inside the dielectric rods, and the electric field in the \(x\)-\(z\) plane is greatly enhanced (Figure 2a) showing a typical loop surrounding the rod. However, due to the existence of the quartz substrate, the electric field distribution is not uniform and exhibits strong directional emission into the substrate. Meanwhile, the azimuthal component of the  
Figure 1: (**a**) Schematic diagram of the unit cell for the all-dielectric metasurface. The length, width and height of the silicon rod are represented by \(a\), \(b\), and \(h\). The lattice constants of unit cell are \(Px\) (800 nm) \(\times\)\(Py\) (900 nm); (**b**) Transmission of the silicon rod arrays for the geometrical parameters of \(a=680\) nm, \(b=300\) nm, \(h=200\) nm. ER: electrical resonance; MR: magnetic response. displacement current inside each rod results that the magnetic field linearly polarizes along y direction in the center of the rod in the \(x\)-\(y\) plane at the same wavelength (Figure 2b). It mainly corresponds to MR and a typical fundamental mode TM\({}_{11\delta}\) of the dielectric rod resonator [40]. While for the narrow resonance at longer wavelength of 1357 nm, the strong electric field (Figure 2c) is polarized in the central region of the rod along \(x\) direction and formed ring-type at both side of dielectric rod. According to the [PERSON] electromagnetic theory, a strong magnetic field (Figure 2d) at the cross-section (\(y\)-\(z\) plane) is induced along the azimuth by the large displacement current, which corresponds to ER and a typical high order TE\({}_{12\delta}\) mode of the rod resonator [40], though it is usually hybridized due to the coupling between neighboring rods [41]. As [PERSON] et al. [39] indicated that both ER and MR contributed to the resonance in a long rod silicon metasurface when a normal incident light is polarized along the rods, to further confirm the distinct ER and MR behavior, we also adopted a standard S-parameter retrieval method [42] to compute the effective permittivity and permeability shown in Figure 3. At the resonance wavelength of \(\sim\)1187 nm, it shows negative permeability and positive permittivity which explain that this resonance is mainly attributed to the MR, but affected by the coupling between the MR and the ER. Whereas the ER dominates the resonance at the wavelength at 1360 nm in spite of very small coupling of the ER to the MR response.