# Corner Reflector Plasmonic Nanoantennas for Enhanced Single-Photon Emission
## 2 Materials and Methods  
The numerical calculations were conducted using ANSYS Lumerical FDTD Solutions, release 2024 R2.1, on a HP Z6 G4 Workstation with two Intel Xeon 6226R processors and 512 GB of RAM. For the FDTD simulations, a variable-size discretization was employed, with a finer grid in the dipole-nanoparticle region. The discretization parameters were adjusted based on a series of convergence analyses, setting the maximum grid step to \(\Delta l=1\) nm within this region. To reduce computational costs, the symmetry planes \(XZ\) and \(YZ\) were utilized for the feeder system, and \(YZ\) symmetry was exploited in simulations, including the CR. In principle, exploiting the symmetry of the problem when specifying the boundary conditions should not affect the accuracy of the obtained solutions, which should remain consistent with the symmetry considerations, regardless of the boundary conditions used. Nevertheless, several test computations were carried out without the symmetry boundary conditions, and no significant differences were observed in the results. The dipole source emitted a short pulse covering the spectral region between 300 and 800 nm. The total duration of the simulations was set to \(T=150\) fs. The analyses focused on a target wavelength \(\lambda_{Ag}=450\) nm for silver and \(\lambda_{Au}=600\) nm for gold. The wavelength of interest in any application will depend on the specific fluorophore being used. To ensure a fair comparison between the two metals, which have different plasmonic resonance wavelengths, the target wavelengths for the silver and gold NAs were arbitrarily selected to be redshifted from their respective resonances by similar spectral separations, typical of those found in applications. In spite of the intrinsically quantum nature of the fluorescence effect, the enhancement factor of the radiative decay rate, \(f_{R}\), due to the Purcell effect [22] of a nanoantenna in an homogeneous dielectric environment can be calculated using a fully classical model [21; 23] as the ratio between the total power collected in the far-field region when the noble metal antenna is present, \(P_{rad}\), and the power that would be radiated from a point dipole source in free space, \(P_{0}\):  
\[f_{R}=\frac{\gamma_{r}}{\gamma_{r,0}}=\frac{P_{rad}}{P_{0}}, \tag{1}\]  
where \(\gamma_{r}\) (\(\gamma_{r,0}\)) is the radiative emission rate in the presence (absence) of the plasmonic structure. \(P_{rad}\) and the radiative emission rate enhancement factor, or Purcell factor, are readily obtained from FDTD computations [9; 24]. For this purpose, the atom-like emitter was modeled using a time-windowed dipole soft source. Instead of setting a given value of the electromagnetic field at a point in space, the field from this type of source adds to the existing electromagnetic fields without causing scattering, therefore permitting the modeling of fluorescence. The value of \(P_{0}\) can be computed from its analytical expression [25], but it is also provided by Lumerical via the sourcepower script command. On the other hand, complex non-exponential or non-Markovian emission processes cannot be accounted for by the model. Similarly, the impact of the losses in the antenna structure, which affect the overall quantum efficiency, can be evaluated from the normalized loss rate factor  
\[f_{L}=\frac{\gamma_{l}}{\gamma_{r,0}}=\frac{P_{loss}}{P_{0}}. \tag{2}\]  
\(P_{loss}\) is computed as \(P_{loss}=P-P_{rad}\), where \(P\) is the power radiated by the dipole in the NA environment used to modify its radiation in a vacuum--\(P_{0}\). The total photon emission rate is influenced by radiative and non-radiative transitions and losses in the noble metal structures.