## 2 Materials and Methods
The monitor collects the electromagnetic near-fields and decomposes them into a set of plane waves which propagate to the far-field. The near-to-far field projection results in a complex electromagnetic field which reaches the far-field hemisphere at a point defined by spherical coordinated \(\theta_{\text{em}}\) and \(\Psi_{\text{em}}\); there, it is decomposed into the LCP and RCP components by a Jones transfer matrix formalism. In this way, one can obtain I\({}_{\text{LCP}}\) and I\({}_{\text{RCP}}\), as well as the total intensity I\({}_{\text{tot}}\) at each point on the hemisphere, which models the extrinsic chirality experiments where a quarter-wave plate and a linear polarizer were placed in the far-field [35; 36]. The intensities from 3 \(\times\) 85 simulations for all positions and orientations are then summed with weights \(\eta\) which account for the dipoles, which are shared between two- or four-unit cells, depending on their position [32]:  
\[\overline{I}_{i}=\sum_{k=1}^{k=85}\eta_{k}\Big{(}I_{i,k,x}+I_{i,k,y}+I_{i,k,z} \Big{)}; \tag{2}\]here, the subscript \(i\) denotes the LCP or RCP field, or their sum (\(\overline{I}_{LCP}\), \(\overline{I}_{RCP}\), and \(\overline{I}_{tot}\), respectively). The final result of these simulations is the circular dichroism in the emission CD\({}_{\rm em}\):  
\[CD_{em}[\%]=100\frac{\overline{I}_{LCP}-\overline{I}_{RCP}}{\overline{I}_{LCP }+\overline{I}_{RCP}}. \tag{3}\]  
We performed convergence testing to ensure that simulation results did not depend on the FDTD volume [37]. As the simulation of single wavelength emission collects total, LCP and RCP far-fields after 3 \(\times\) 83 single simulations, we saved time-cost of our simulations by means of the far-field filter. This Lumerical property is a parameter of near-to-far field transformation, set between 0 (which turns the filter off) and 1 [33]; it ensures that the electromagnetic fields at the very edges of the near-field monitor in the xy-plane went to zero, which translates to higher numerical stability and faster convergence. For all the following simulations, we opted for an FDTD domain of 36 um\({}^{2}\) in the xy-plane, and a far-field filter of 0.1. As a final step, we combined the two simulation approaches to investigate the influence of the electromagnetic field at the excitation wavelength. Emission enhancement in plasmonic nanostructures is governed by both enhancement at the emission wavelength, and by the near-field confinement at the excitation wavelength [38]. The previous active simulations of 85 random dipoles account for the weights of dipoles at different positions in the xy-plane by considering the homogeneous medium and dipole sharing between the neighboring unit cells; in Figure 1b, \(\eta=1\) for the dipoles inside the hexagon, \(\eta=1/2\) for the dipoles on the hexagon margins, and \(\eta=1/4\) for the two dipoles at the top and at the bottom. However, if the excitation laser leads to the enhancement and the inhomogeneous distribution of the electric field at the position of the dipoles, this can be approximated by a new weight factor, which now depends on both the position and the electric field confinement at excitation wavelength \(\lambda_{exc}\). We extracted this factor by performing passive single-wavelength simulation at \(\lambda_{exc}\), and by collecting the electric field intensity at the points of the dipole positions at z = 120 nm. Finally, we normalized the emission of the dipoles as:  
\[\overline{I}_{i}=\sum_{k=1}^{k=85}\eta(|\overset{\rightarrow}{E}(k,\lambda_{exc })|^{2})_{k}\Big{(}I_{i,k,x}+I_{i,k,y}+I_{i,k,z}\Big{)}. \tag{4}\]