# Angle-Resolved Fluorescence of a Dye Coupled to a Plasmonic Nanohole Array
## 4 Discussion  
In consideration of the aforementioned optical behavior, a possible coupling between the GNA plasmonic modes and the organic dye features was analyzed. Recalling Figure 3, it is then clear that two different behaviors for the spectral evolution can be defined with respect to the collection and pumping angle. To better understand the dependence on the collection angle, the ratio of the fluorescence spectra at the different angles with respect to the one at normal incidence (collected at 0\({}^{\circ}\)) was considered, and their plots are gathered in a map reported in Figure 6, panel (a). For the sake of comparison, a subset of the second derivative of the TE component of the T map measured impinging from the front side (see Appendix A.2, Figure A2) is reported in panel (b) of Figure 6.  
The dispersion of the spectral features can be identified in either the fluorescence or T maps, highlighting the interplay between the GNA plasmonic modes and the fluorescence emission. This agrees with the literature where the explanation of the coupling mechanism is proposed in terms of excitation transfer between plasmonic resonances and dyes. According to [PERSON] [7], emission efficiency is critically related to a direct interaction between the plasmonic modes with the far-field radiation, either in absorption or in emission [8; 9; 10]. In our case, the structure periodicity guarantees the optical coupling of the LSPR and SPP plasmonic resonances. Figure 5: Second derivative of variable-incidence-angle R spectra for both TE and TM polarization. Panels (**a,b**) display the curves resulting from the spectra measured by impinging from the front side, while panels (**c,d**) display the curves from the back side, respectively. The dashed red line indicates He-Ne pumping at 632 nm. The black curves in panel (**d**) are the SPP dispersion branches calculated with the model in Appendix A.2 at the back side. Specifically, [PERSON] et al. in [26] give an interpretation of the complexity of such an interplay, going beyond the pure Purcell effect due to field enhancement. They also report the collection of fluorescence emission spectra showing the clear signature of a single plasmonic mode overlapped with the dye emission spectral range. Consistently, as in our case, several different plasmonic modes contribute to reshaping the fluorescence signal. Instead, the influence of the pumping angle can be understood by focusing on the absorbance (A), defined as A = 1\(-\)R-T, evaluated at the pumping laser wavelength of 632 nm. In Figure 7, A is presented for both front and back configurations as a function of the incident angle. For the sake of completeness, the variable-incidence-angle A maps are reported in Appendix A.2, Figure A3. Regarding the front configuration, a tiny variation in A intensity is observed with a maximum in the range of (15\(\div\)20)\({}^{\circ}\). On the contrary, a relatively large variation occurs for the back configuration with a monotonic growth until 20\({}^{\circ}\) and a subsequent slowdown in growth for higher angles. This is perfectly in line with the fluorescence results when considered together with the increase in absorbance at 632 nm This can also be easily correlated to the crossing highlighted in Figure 5 between the laser excitation wavelength, with the GNA plasmonic modes around (15\(\div\)20)\({}^{\circ}\). This represents the fraction of energy that is stored in the plasmonic modes excited with a specific wavelength but at different angles. In addition, when focusing on the pumping mechanism, the plasmonic contribution to fluorescence is crucial. Remarkably, it can be noticed that the absorbance in the front configuration is roughly twice the intensity of the back configuration. Therefore, it is not surprising that, as observed above, the largest fluorescence intensities are measured when pumping from the front side.