# Enhancement of Optical Chirality Using Metasurfaces for Enantiomer-Selective Molecular Sensing
## 2 Theory and Simulation Methods  
We carry out a numerical analysis based on the finite-difference time-domain (FDTD) method. The nanostructured crystal silicon (Si) is placed in the three-dimensional simulated space with the boundaries in all directions set as a perfectly matched layer (PML). The total-field scatter-field (TFSF) light source with specific polarization is normally incident to the nanostructure, and the condition for optimal C enhancement is derived by rigorously analyzing the simulated parameters. To demonstrate the impact of geometric features in the metasurface on C enhancement, we investigate the resonances in various nanostructures induced by the oscillations of electric and magnetic dipoles. Figure 1a shows a schematic of a Si nanorod with a constant cross-sectional area under incident light directed to z-direction. The refractive index of crystal Si in the simulation is plotted in the inset of Figure 1a based on the value from palik [30]. By the repeated simulations, the origin of chirality is analyzed based on the resonances of a nanostructure to find the general trend that the squared nanoblock with an aspect ratio of similar width and length shows superior performance to the nanorods with a high aspect ratio. To prove this, we set the simulation to observe the relationship of resonances and chirality as the length of a nanostructure changes, and the height and width fixed to be 60 nm and 125 nm, respectively. The chirality for the tuning height or width of a nanostructure is additionally presented in supplementary note 1 and 2. Figure 1c demonstrates a numerically simulated map of the scattering efficiency (Q\({}_{\text{sca}}\)) of Si nanostructures under the incident light of right-handed circular polarization. The scattering efficiency is defined as the ratio of scattered cross-section to the geometrical cross-section of the nanostructure. As shown in the figure, there are two resonance modes induced by the oscillations of the electric dipole (ED) and the magnetic dipole (MD), which are highlighted as the bands of enhanced Q\({}_{\text{sca}}\). To confirm these dipole resonances, the profiles of electric and magnetic fields for each resonant wavelength are visualized in Figure 1b for the representative geometric structure. The length of the nanorod is fixed to be 600 nm as indicated by the condition of the black dotted line in Figure 1c, and the field profiles for the resonances of the ED and the MD are monitored at the wavelength of 475 nm and 750 nm, respectively. To confirm the resonance mode of the dipoles, light is illuminated with the polarization parallel to the x-axis. The electric and magnetic fields at the cross-sectional area of the nanorod, i.e., viewed from the direction of the x-axis, show the maximum value at the center of the area by the strong dipole resonances. We also theoretically conducted an analysis to verify that the overlap of the ED and the MD occurs, which can be confirmed in supplementary note 3. The wavelength of the resonances is effectively tuned as the length of the nanorod changes, which is illustrated in Figure 1c, and interestingly, the tuning trend of such dipole resonances significantly differs from each other. The resonant wavelength of MD mode is rarely shifted and remains as a constant value (\(\lambda_{0}=475\) nm), even when the length of the nanorod varies significantly. It is also noteworthy that the spectral linewidth is narrower than the linewidth of ED mode. Additionally, the slight undulation of the magnitude of Q\({}_{\text{sca}}\) along the vertical region can be explained by the 0-order longitudinal Fabry-Perot (FP) resonance supported by the two reflective-end faces of the nanorod [31]. Figure 1: **(a)** Schematic of the resonant dielectric nanostructure as a unit cell. The nanostructure is designed with a constant cross-sectional area (60 nm by 125 nm) and various lengths.