## 2 Materials and Methods  
We investigated absorption and emission chirality by using two distinct simulation approaches in the commercially available finite difference time domain (FDTD) solver by Lumerical [33]. The first part of the work involved \"passive\" simulations of the chiro-optical response of the ENHA previously optimized in [26]. The second part involved \"active\" simulations of distribution of dipoles within the dielectric layer above the ENHA. Finally, we combined the two approaches to account for the excitation influence on the emission chirality. Below, we present the two main simulation methods of this work. Firstly, we simulated the broadband optical response of the ENHA in the range of 400-1000 nm using plane-wave excitation. In Figure 1a, we show the geometry of the ENHA, which is defined by the lattice parameter \(a\), while \(\rm D_{x}\) and \(\rm D_{y}\) represent the short and the long nanohole diameters, respectively. Here, the FDTD domain is defined by periodic Bloch boundary conditions (BBC) in the xy-plane, while in the z-plane we define perfectly matched layers (PML). We take t = 100 nm as the thickness of the plasmonic (Auor Ag) layer. This plasmonic layer lies on the semi-infinite dielectric substrate, and it is embedded in 300 nm of additional refractive index matching medium; in this way, the ENHA is surrounded by a dielectric medium with a refractive index of 1.45. The unit cell of the array is defined by the surface of \(a\) and \(a\)/3, as NHAs with such hexagonal symmetry can be fabricated using the low-cost NSL technique (as in our previous experimental works). The nanohole has elliptical geometry, and the long ellipse axis is \(15^{\circ}\) shifted with respect to the hexagonal symmetry, as has been previously optimized in [26]. For the Au-ENHA, we used the Au complex refractive index from the Lumerical material database; for the Ag-ENHA, we used experimental data from the ellipsometric measurements performed in our previous work [27]. In order to simulate circularly polarized plane-wave excitation, we combined two x- and y-polarized broadband plane-wave sources with the same properties, except for the phase difference. The phase differences of \(90^{\circ}\) and \(-90^{\circ}\) correspond to LCP and RCP polarizations, respectively. The ENHA is excited under normal incidence from the top. Power monitors below the plasmonic layer and behind the source, detect transmission and reflection, respectively. Absorption is then calculated as \(\text{A}_{\text{i}}=1-\text{R}_{\text{i}}-\text{T}_{\text{i}}\), where \(\text{i}=\text{LCP}\) or \(\text{i}=\text{RCP}\), and the final result of these passive simulations is the normalized circular dichroism in the absorption \(CD_{A}\):  
\[CD_{A}[\%]=100\frac{A_{LCP}-A_{RCP}}{A_{LCP}+A_{RCP}}. \tag{1}\]  
While the passive properties of nanohole-based chiral materials have been previously studied, here we investigate the chiral properties of ENHAs coupled with the emitting layer. In the following, we will consider the light emission possibility of the ENHA coupled with dipole sources to be active. In this approach, a large FDTD domain surrounds more than 100 unit cells in the xy-plane, and it is defined by the PML boundaries in all six directions. A larger, non-periodic, FDTD volume is necessary in order to account for the periodic nature of the ENHA without introducing unnatural coherence [34]. An electric dipole oscillates as a point source, exciting the ENHA at 20 nm above the plasmonic layer. We show the schematic of such simulation in Figure 1b. The dipole emits at the single emission wavelength \(\lambda_{em}\), and it is defined by its orientation (x-, y-, or z-orientation), and position in the embedding layer. While we keep z position at 120 nm above the substrate, in the xy-plane we considered a homogeneous dipole distribution, which properly models  
Figure 1: **(a)** xy- and xz-plane views of the ENHA, with geometric parameters. The dashed region in the top schematic shows the unit cell used in the “passive” simulations.