## 2 Materials and Methods
(**b**) Simulation set-up for the “active” simulations; the randomly oriented dipole is positioned inside the embedding medium, 20 nm above the ENHA, and at a distance from the center which corresponds to one of the points in the inset. The dipole emits at a single wavelength \(\lambda_{em}\). The electromagnetic field at the excitation wavelength \(\lambda_{exc}\) is further introduced as an additional tuning and optimization possibility. dielectric layers doped with emitting materials. Next, we explain the novelty of the active simulation set-up for chiral emission, compared to previous, achiral nanostructures. It must be noted that all the chiral phenomena presented, arose from the coupling of an achiral dipole with a chiral nanostructure, as the dipole sources do not represent molecules which possess their own intrinsic chirality. In the past, electromagnetic modelling followed experimental studies of fluorescence from emitting layers coupled to achiral NHA. The authors in [30; 31] reported on SPP-mediated red light emission from circularly shaped nanoholes organized in a 2D periodic array with quadratic symmetry. The authors in [32] investigated low-cost achiral NHAs with hexagonal symmetry, coupled with Er\({}^{3+}\) emitters. In these cases, the averaging of different dipole positions across the unit cell was simplified due to the in-plane symmetry of the achiral structures, allowing for the simulation of one quarter of the unit cell. Here, instead, the ENHA in-plane symmetry is broken by both the elliptical shape and the 15\({}^{\circ}\) offset from the hexagonal symmetry lines. Therefore, the emitted characteristics need to be averaged over the complete distribution of the dipoles across the unit cell, which is done by properly modelling the homogeneous dipole distribution in the cell with hexagonal symmetry, as shown below. The position of a dipole for a single simulation is defined by its \(\Delta\)x and \(\Delta\)y offset from the center of the FDTD domain; this domain, now defined by PML layers, has equal dimensions in the x- and y-directions, thus preventing any additional asymmetry in the chirality calculations. Next, we focus on modelling suitable for real applications, where light emitters are homogeneously immersed in the host matrix in the vicinity of the nanostructures. In this case we consider emitters homogeneously distributed across the hexagon of the side \(a/2\), as shown in the inset of Figure 1b. The surface density of the dipoles across this hexagon is constant, while the hexagon itself encompasses one chiral object (i.e., an elliptical nanohole tilted from the symmetry of the hexagon). Therefore, the final averaging of the emitted field and its chirality will take into account both the dipoles close to the nanohole center and those close to the rims of the nanohole. After convergence testing, we chose the ensemble consisting of dipoles on the points defining the hexagon (shared between 3 hexagons), and two or three additional dipoles between these points, on the hexagon rims (shared between 2 hexagons). Considering the constant surface density, the total number of dipole positions equal 85, while the distance between two neighboring positions was held constant and equal to \((1/5)^{*}(a/2)\); the specific positions are marked as dots in the inset of Figure 1b. In this way, the homogeneity of the emitting material is ensured, while the polarization analysis of the simulation results reveals the overall chiral properties, which stem only from the chiral effects of the underlying nanostructure. For each of the 85 possible positions, three simulations were run for each dipole orientation. The result of a single simulation was dipole radiation to the far-field, which was detected by a frequency-domain field-profile monitor. This near-field monitor was positioned in the air, 10 nm above the embedding medium, i.e., at 310 nm (dashed lines in Figure 1b); it encompasses the whole xy-plane of the FDTD region.