## 3 Results and Discussion
At the beginning of this head, the optical resonances were hardly defined, although the spectra recorded at this initial point showed  
Figure 6: Analysis of the whispering gallery modes in region (iii). The measured length side “a” measured in the (**a**) SEM images was 0.72 \(\upmu\)m. (**b**) \(\upmu\)-PL spectra for all the polarization conditions, (**c**) interference order \(N\) of the peaks observed in the spectra, and (**d**) estimation of the refractive index from the wavelength that virtually overlapped for both polarizations. some modulation of the signal that could be related to the Fabry-Perot modes established along the length of the structure. The blurred resonance map was the result of the superposition of the different resonant modes established in this cavity. It was only when the spectra were recorded at the end part of the head when the whispering gallery modes associated with a hexagonal section could be observed (Figure 8b). However, the resonant peaks were broader than at other regions of the nail (see the map in Figure 7b). A similar situation was seen in the last region considered, corresponding to the tip of the nail (Figure 8c,d). In region (iv), the size of the cross-section decreased rapidly toward the tip; therefore, the resonance peaks were less sharp and defined. Figure 8: SEM micrograph and \(\upmu\)-PL spectra for all polarization modes for the hexagonal head in region (i) (**a,b**) and the tip of the nail in region (iv) (**c,d**). The resonance modes were broader than other regions due to the rapid changes in the cross-section length, blurring the peaks. Figure 2:0 (**a**) SEM image of a long nail ending in a hexagonal head with the Y-axis scale used to record the \(\upmu\)-PL map in (**b**). The \(\upmu\)-PL map shows the variation along the stem of the nail in terms of the intensity and wavelength shifts. Region (ii) had an almost constant hexagonal cross-section, although the initial part had a slight increase in the size of the cross-section, as can be seen in the map of Figure 7b. Figure 9a shows the detail of this region, where the hexagonal faceting is visible. Correspondingly, the resonances were extremely well defined, as shown in the spectra in Figure 9b, especially at the last part of this region where the section was almost constant and at the point that is located at Y = \(-20\) um in the map of Figure 7b. This point had the highest intensity in the map and corresponded to the nicest resonances observed all along the structure (Figure 9b). As has already been described, the order \(N\) (Figure 9c) was determined using Equations (1) and (2), while using Equation (6) to find the starting values for the refractive index. The final estimated values for the refractive index are shown in Figure 9d. The values were quite similar to those reported for the previous rod (Figures 4 and 6), although the shape of the curve of the dispersion relation was a little bit different. The refractive indexes of the TE and TM modes virtually overlapped. The absent change in the section size seemed to favor the resonance conditions. Toward the center (Figure 10a) in region (iii), the size of the cross-section was again practically constant and the resonances were very well defined (Figure 10b), but the intensity was lower than in the case shown in Figure 9b. This section of the nail was thicker, allowing us to appreciate a second set of resonant peaks, shown in Figure 10c, that would correspond to the Fabry-Perot modes established along the length of the structure. However, we expected less accuracy than in the calculation of Figure 9d, as the peaks were slightly broader and there was the contribution of a second set of Fabry-Perot resonances. Then, by performing the optical resonances maps and by selecting and studying the \(\upmu\)-PL spectra at the good points, we were able to identify the best resonant cavities that were present for both structures.