# Corner Reflector Plasmonic Nanoantennas for Enhanced Single-Photon Emission
## 3 Results and Discussion
The local field enhancement factor can be evaluated as the ratio  
Figure 2:2  
between the field strength at the dipole source position \(|\mathbf{E}|\) and the incident field strength \(|\mathbf{E}_{0}|\), which is the field strength that would be found at that position in the absence of the NA. Figure 2:3 Directivity of silver (**a**) and gold (**b**) CR antennas with and without NP coupled to the dipole emitter. Purcell (\(f_{R}\)) and loss (\(f_{L}\)) factors for silver (**c**) and gold (**d**) CRs with a single dipole emitter feeder. Figure 14a displays the calculated electric field strength \(|\mathbf{E}|\) over the \(XZ\) plane scattered from a gold nanosphere when illuminated by a unit amplitude E-field plane wave. For the transmitting mode of the NA, the dipole source was positioned at \(x=0\), \(z=50\) nm. Figure 14b shows the corresponding electric field amplitude for the CR NA at the first directivity maximum. The results reveal a significant LFE for the isolated NP and a strong enhancement of this effect by the CR at the selected feeder position \(S=0.35\)\(\upmu\)m in agreement with the values obtained for \(f_{R}\). The calculated LFE factor for the previously optimized geometries yielded, for silver NAs, \(f_{E}=13.8\) at \(S=0.3\)\(\upmu\)m and \(f_{E}=12.8\) at \(S=0.55\)\(\upmu\)m. For gold NAs, the values were \(f_{E}=9.9\) at \(S=0.35\)\(\upmu\)m and \(f_{E}=9.1\) at \(S=0.75\)\(\upmu\)m. For the isolated NPs, the calculated LFE factors were \(f_{E}=2.8\) for silver and \(f_{E}=2.2\) for gold nanospheres. The properties of plasmonic NAs are largely influenced by interactions with nearby metal nanostructures. These can be leveraged in designing more efficient emitting structures, such as nanoparticle dimers [8; 9] or optimized NP arrays [13; 14], and are also relevant in the development of substrates for surface-enhanced fluorescence spectroscopy [39] and surface-enhanced Raman scattering (SERS) applications [40]. We now examine the potential effects on the emission properties of the CR NA due to a nearby metal NP. To this end, we considered the presence of a \(d=70\) nm NP at a distance \(\rho=1.5\)\(\upmu\)m from the feeder NP at the origin, which was positioned at various angles \(\alpha\) from the \(Y\) axis. The position vector of the NP is given by \(\mathbf{r}_{n}=(\rho\sin(\alpha_{n}),\rho\cos(\alpha_{n}),0)\), where the values of \(\alpha\) considered were \(\alpha_{n}=n\cdot 30^{\circ}\) for \(n=0\dots 6\). Figure 2:4 Field strength \(|\mathbf{E}|\) across the \(XZ\) plane in the environment of a \(d=70\) nm gold NP at the origin illuminated by an unit magnitude \(Z\)-polarized E-field plane wave. The plot (**a**) displays the results for the isolated NP and (**b**) when the NP was within the CR at \(S=0.35\)\(\upmu\)m.  
Figure 2:5 Calculated resonance wavelengths of silver (**a**) and gold (**b**) NPs as a function of the absolute feeder position \(S\) for four different reflector film thicknesses: \(W=10\) nm, \(W=20\) nm, \(W=40\) nm, and \(W=80\) nm. Figure 15 shows the results calculated for a silver CR NA with \(W=80\) nm in thickness and a feeder position of \(S=0.55\) um in the presence of an interfering NP. The results indicate a very small deviation in the values of \(f_{R}\) and \(f_{L}\) compared to those determined without the interfering NP, as shown in Figure 9d, regardless of the position angle \(\alpha\). The directivity values in Figure 15b also exhibit minimal deviations from those obtained without the interfering NP, shown in Figure 5a, especially when the interfering NP was positioned behind the CR. These calculations demonstrate a certain degree of robustness in the CR NA's response to plasmonic NP contamination in the NA surroundings, at least outside the region defined by a circle centered at the feeder NP with a radius equal to the mirror length \(L\) of the CR. Figure 16 shows the directivities calculated for the silver and gold CR NAs when the corner length was increased to \(L=3\) um for three values of \(W\) (10 nm, 40 nm, and 80 nm).