## 3 Results and Discussion  
Two main morphologies were studied, as shown in Figure 2. Figure 2a shows long tapered rods that appeared to grow from a central ball. The rods had a hexagonal section ranging 1 to 2 \(\upmu\)m, tens of microns in length, and forming an angle of 90\({}^{\circ}\) to each other. The rods emerged from the vertices of a central, almost square-shaped ball. X-ray microanalysis and X-ray diffraction showed that these balls were formed of Li\({}_{2}\)SO\({}_{4}\), constituting the only regions in which residual S could be detected [19]. As shown in Figure 2b, the second morphology studied consisted of long tapered nails, with a hexagonal cross-section size between 1 and 2 \(\upmu\)m and lengths around 100 \(\upmu\)m. The heads of the nails were also hexagonal with varying cross-section sizes (2 to 5 \(\upmu\)m approximately) and around 1 \(\upmu\)m in height. Figure 2: SEM images of the structures with different morphologies: (**a**) long tapered rods growing from a central ball and (**b**) a long tapered nail. Both kinds of structures showed interesting behavior as resonant cavities, which were formed at the transversal section of the structure. Although the behaviors of both kinds of structures were different, some common features are worthy of highlighting prior to a more detailed analysis. Changes in the shape and size of the optical cavity produced a change in the position of the optical resonances; then, rod tapering had a visible effect on the resonant behavior. An increase in the diameter led to a shift of the resonant peak toward longer wavelengths and a decrease led to a shift toward shorter wavelengths. On the other hand, the smaller the cavity, the sharper and more separated the resonant modes. Let us begin the analysis of the rods. Figure 3a shows one of these rods in detail, where two regions with different cross-sections were clearly observed along the rod axis (Y-axis in the maps). The zero of the length scale was placed at the point at which the size of the cross-section began to change more rapidly to accommodate the second section of the rod (Figure 3a). Figure 3b-d shows how the resonant maxima varied along the length of the structure. The position on the structure is represented in the vertical axes of these graphs, following the scale indicated in Figure 3a. On the horizontal axis, the wavelength of the PL spectra is represented, whereas the intensity is the intensity associated with each wavelength for each point on the structure. These optical resonance maps were obtained for the total PL signal (b) and both TE and TM polarizations (c and d, respectively). The TE polarization was considered to be perpendicular to the c-axis of the structure, whereas the TM polarization was parallel to the c-axis (see Figure 3a for reference). When the maps for all polarization conditions were compared, it was inferred that the total PL signal could be decomposed into the two polarizations (TE and TM), and for both, optical resonant modes could be detected. That is, we could use the TE and TM polarized signals to discriminate the different resonant peaks and apply the formulas mentioned in the introduction. It was also seen that the evolution of the optical modes along the structure was the same for all the polarization conditions, although the positions of the peaks were slightly different for the TM and TE polarizations, as will be seen later. As it has been said before, the positions of the resonant maxima will change depending on the size of the optical cavity section. In all the polarization conditions, the maps show three different regions, labeled (i) to (iii) in Figure 3b-d. The first region (i) corresponds to the thickest part of the rod, close to the central ball. In this region, the resonant peaks shifted toward longer wavelengths (in the map, moving from \(-60\)\(\upmu\)m toward \(-30\)\(\upmu\)m), that is, this section of the structure increased smoothly in size.