# Corner Reflector Plasmonic Nanoantennas for Enhanced Single-Photon Emission
## 3 Results and Discussion
In contrast, for gold CRs, Figure 10 indicates larger fluctuations in the loss factor around the reference levels. The calculated values of the Purcell factor, \(f_{R}\), also exhibited a pronounced effect due to the interaction with the corner sheets when \(W\) was sufficiently large. This interaction significantly impacted both silver and gold NAs, and the associated \(S/\lambda_{M}\) range was larger than that observed for \(f_{L}\) in silver NRs, increasing with \(W\). The variation in \(S/\lambda_{M}\) followed a distinct pattern: \(f_{R}\) reached a maximum near the first peak of directivity and then dropped to a minimum around the directivity null at \(S/\lambda_{M}=1\) before rising again near the second peak. Figure 11 displays the radiation efficiency \(\eta\) of the gold and silver CR NAs as a function of the feeder position \(S\). As discussed in Section 2, this parameter is a very good approximation regarding the quantum efficiency of the NA for a highly efficient fluorophore with a negligible non-radiative transition rate. For thin metal sheets, with \(W=10\) nm values, the fluctuations in \(\eta\) as a function of \(S\) were of small amplitudes. Larger efficiencies were observed for silver NAs, with values close to \(\eta=0.6\), compared to gold NAs, which reached values around \(\eta=0.4\). As the value of \(W\) increased, the amplitude of the fluctuations in \(\eta\) with \(S\) became larger. Once again, the peak value of \(\eta\) for silver, close to \(0.7\), was higher than that for gold, which approached \(0.6\). For silver CRs with \(W=80\) nm values, we found that near the first directivity maximum at \(S=0.30\)\(\upmu\)m (\(S/\lambda_{Ag}=0.67\)), the values were \(D=20.1\), \(f_{R}=14.5\), and \(f_{L}=6.7\). The second maximum yielded a significantly higher directivity of \(D=40.4\) at \(S=0.55\)\(\upmu\)m (\(S/\lambda_{Ag}=1.22\)), with \(f_{R}=6.0\) and \(f_{L}=5.9\). Thus, the CR provided very large improvements in the directivity value when compared to those of the electric dipole emitter, with \(D=1.5\). Figure 2:0 Radiative transition rate enhancement, \(f_{R}\), and normalized loss, \(f_{L}\), factors of gold 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. Considering the reference values for the NP emitter, \(f_{R}=8.3\) and \(f_{L}=5.4\), the first maximum offered a significant increase in both directivity and radiative emission rate enhancement factor, with only a modest rise in losses. At the second maximum, the directivity was much larger, though there was a slight reduction in \(f_{R}\) in relation to the reference. The loss factor, however, remained close to that of the emitter without the CR. The gain figure of merit values were \(G=13.8\) and \(G=20.4\) for the first and second maxima, respectively, largely exceeding the value of \(G=0.9\) obtained for the NA without the CR. For the gold NA, the reference values were \(f_{R}=4.9\) and \(f_{L}=6.1\). With a \(W=80\) nm thick CR NA, at the first maximum, located at \(S=0.35\) um (\(S/\lambda_{Au}=0.58\)), the directivity was \(D=18.0\), with \(f_{R}=8.2\) and \(f_{L}=7.0\). The second maximum occurred at \(S=0.75\) um (\(S/\lambda_{Au}=0.58\)), where \(D=29.0\), \(f_{R}=4.4\), and \(f_{L}=6.7\). For the gold CRs, the first maximum provided a high directivity and an improvement in the \(f_{R}\) value. At the second maximum, while the directivity was even greater, the \(f_{R}\) was close to the reference value. In both cases, the losses were similar to those of the gold NP without the CR. The gain figure of merit values were \(G=8.0\) and \(G=11.5\) for the first and second maxima, respectively, significantly exceeding the value of \(G=0.7\) obtained for the NA without the CR but significantly in value lower than the values obtained for silver CR NAs.