# Corner Reflector Plasmonic Nanoantennas for Enhanced Single-Photon Emission
## 3 Results and Discussion
The irregularities in variations of directivity at smaller \(W\) values were less pronounced for gold mirrors compared to silver. Additionally, the positions of the maxima and minima shifted to larger values of \(S/\lambda_{M}\) as \(W\) increased. At the largest thickness of \(W=80\) nm, the directivity was null precisely at \(S=\lambda_{M}\). A better understanding of the variations observed in the curves of \(D\) can be achieved through a detailed analysis of the radiation patterns in each case. Such plots are presented for silver CRs with \(W=10\) nm, \(W=40\) nm, and \(W=80\) nm, respectively, in Figures 6-8. One of the main differences observed at small film thickness (\(W=10\) nm) was the presence of relevant amplitude side lobes at the lower values of \(S\). This phenomenon led to reduced directivity values, despite the main lobe exhibiting an narrower beamwidth at \(W=10\) nm. Conversely, the patterns seen at \(W=40\) nm and \(W=80\) nm were qualitatively similar, indicating a convergence as the thickness \(W\) increased. For thicker-sheet CRs, the gradual narrowing (or broadening) of the on-axis lobe contributed to regions of increasing (or decreasing) directivity values. The zero observed in the directivity curves arose from the splitting of the main lobe at \(S=\lambda_{M}\) that produced a radiation null along the \(Y\) axis. In contrast, for \(W=10\), the local minima in the directivity plots were correlated with the increasing relative weight of the side lobes in the radiation pattern. As \(S\) increased, separation of the main lobe was also noted; however, it occurred along the horizontal plane, unlike the vertical splitting seen at \(W=40\) nm and \(W=80\) nm. As \(S\) continued to grow, additional lobe bifurcations became apparent, leading to the emergence of a fractal structure in the radiation pattern for very large values of \(S\) in extensive CRs, as was analyzed in [18]. The sequences of radiation diagrams presented in Figures 6-8 ended up being very similar for the corresponding ones of gold CRs when the values of \(S\) were normalized by the respective operation wavelength \(\lambda_{M}\). We now examine the impact of the corner reflector on the losses and the emission rate of the dipole-NP system. Figure 9 displays the \(f_{R}\) and the normalized loss factor \(f_{L}\) of NAs incorporating silver CRs of four different thicknesses, \(W\), as a function of the normalized distance, \(S/\lambda_{Ag}\), between the silver NP and the corner apex. The corresponding results for the gold NAs are shown in Figure 10. In all the figures, the horizontal lines pinpoint the reference values for the NPs without the CRs. Figure 5: Values of the directivity as a function of the feeder position \(S\), normalized to the respective target wavelength, for four different reflector film thicknesses. (**a**) Results for the silver CR, with a target wavelength of \(\lambda_{Ag}=450\) nm. (**b**) Results for the gold CR, with a target wavelength of \(\lambda_{Au}=600\) nm. Figure 6: Radiation patterns of silver CR with \(W=10\) nm for values of \(S\) between \(S=0.2\) and \(S=0.75\). Figure 7: Radiation patterns of silver CR with \(W=40\) nm for values of \(S\) between \(S=0.2\) and \(S=0.75\). Figure 8: Radiation patterns of silver CR with \(W=80\) nm for values of \(S\) between \(S=0.2\) and \(S=0.75\). Figure 9: Purcell, \(f_{R}\), and normalized loss, \(f_{L}\), factors of silver CR as a function of the normalized feeder position \(S/\lambda_{M}\) for four different reflector film thicknesses: (**a**) \(W=10\) nm, (**b**) \(W=20\) nm, (**c**) \(W=40\) nm, and (**d**) \(W=80\) nm. The horizontal lines describe the corresponding reference levels without the CR. For silver CRs, the normalized loss factors displayed moderate deviations from the reference values except for very small values of \(S/\lambda_{Ag}\), where a steep increase in the losses occurred due to stronger interactions with the nearby CR metal films when the thickness, \(W\), was sufficiently large.