# Enhancement of Optical Chirality Using Metasurfaces for Enantiomer-Selective Molecular Sensing
## 2 Theory and Simulation Methods
**(b)** The profiles of the scattered electric and magnetic fields for the nanorod with the length of 600 nm under the incident light that is linearly polarized parallel to the x-axis. It supports the resonances with the magnetic dipole (MD) and the electric dipole (ED) at the target wavelengths of 475 nm and 750 nm, respectively. **(c)** Numerically simulated scattering efficiency (Q\({}_{\text{sca}}\)) of silicon (Si) nanostructures for the continuously tuned lengths of the nanostructure. Light is illuminated with the right-handed polarization. The condition of dipole resonances in **(b)** is indicated as red dots. **(d)** The calculated chiral enhancement (C enhancement, -C/C\({}_{0}\)) of Si nanorods is in **(c)**. On the other hand, the resonant wavelength for the ED mode varies significantly. The resonance of ED mode can be extensively adjusted over the broad spectral range of visible and near-infrared wavelength from 750 nm to 475 nm by tuning the length of the nanostructure from 600 nm to 125 nm. Ultimately, as the length reduces to approximately 125 nm, the ED and MD modes overlap spatially and spectrally, with the magnitude of resonance being twice the magnitude of individual resonance. The overlap of resonances in squared-silicon nanoblocks induces the [PERSON] effect [32; 33], which facilitates the effective enhancement of optical chirality. To verify this, the enhancement of optical chirality for the continuously tuned lengths of the nanostructure is analyzed as exhibited in Figure 1d, which features significant C enhancement when the ED and MD resonances overlap. Note that the trend of such overlap and the nanostructure's design for C enhancement is possible using various materials and a wide range of spectrums depending on target molecules. In addition, diverse shapes of nanostructures that feature rotation symmetry and induce the overlap of the resonances can effectively function for C enhancement, as studied in supplementary note 4. Note that the optical C enhancement is defined as the optical chiral density (C) divided by the chirality in free space (\(C_{0}\)), i.e., \(C_{0}\)\(=\pm\omega\epsilon_{0}\left|\mathbf{E}\right|^{2}/(2c)\), where c is the speed of light in a vacuum, and the plus or minus sign indicates right- or left-handedness, respectively, and \(\omega\), \(\epsilon_{0}\), and \(\mathbf{E}\) are the angular frequency of light, the permittivity of free space, and the complex electric field. The optical chiral density in a nanostructure is defined as [16; 34; 35]  
\[ \begin{array}{c}C=\frac{\epsilon_{0}}{2}E\cdot(\
abla\times E)+\frac{1}{2 \mu_{0}}B\cdot(\
abla\times B)\\ =-\frac{\omega\epsilon_{0}}{2}\text{Im}(\mathbf{E}^{*}\cdot\mathbf{B})=-\frac{ \omega}{2c^{2}}\left|\mathbf{E}\right|\left|\mathbf{H}\right|\cos(\beta_{i \mathbf{E},\mathbf{H}})\end{array}  \tag{1}\]  
where \(E\) (\(\mathbf{E}\)) and \(H\) (\(\mathbf{H}\)) represent the real (complex) electric and magnetic fields, and \(\mu_{0}\) and \(B\)(=\(\mu_{0}H\)) is the permeability of a vacuum and magnetic flux, respectively. Since the chiroptical reactivity of a chiral molecule is weak, distinguishing the enantiomer without signal amplification, i.e., without C enhancement, is more difficult, which typically requires significant molecular density. Thus, the enhancement of optical chirality in a devise amplifies and increases the circular dichroism (CD) signal, which allows the effective sensing of chiral molecules with less molecular density. The optical C enhancement (\(C/C_{0}\)) is calculated in the regions around the surface of a nanostructure with the thickness of 10 nm. Only a certain volume is included in the calculation area on surfaces, excluding the interior of the structure because molecules may exist through the surface, not inside the platform. The sensing of molecules on the surface of the platform requires amplification of the CD signal, which is enhanced by the C enhancement value.