## 3 Results and Discussion
Based on this analysis, it was found that the best dimensions are those in the inset of Figure 2e with: \(a=30\)\(\upmu\)m and \(g=7.5\)\(\upmu\)m. As observed in the curves of the reflection coefficient for different analyte thicknesses (Figure 2c), the frequency shift obtained is significantly larger than in the previous cases. Specifically, a maximum frequency shift of \(4.36\%\) is achieved for an analyte thickness of \(800\) nm (Figure 2f). This provides a mean sensitivity of \(6.4\times 10^{-5}\) nm\({}^{-1}\), giving rise to a \(172\%\) improvement regarding the hollow structure. In addition to being easy to design and manufacture, this structure is largely insensitive to the angle of polarization (as shown in the Supplementary Material), which is advantageous for sensing applications where it is vitally important to position the sample in the correct alignment. Once the optimal dimensions of the structure have been found, we continue this work by introducing changes in the design to improve the sensitivity and, therefore, the quality of the metasensor device. One way to enhance the electric field concentration is by adding arms to each of the three vertexes of the metallic pattern, as shown in the insets of Figure 3. In order to know the optimal length of these arms, we performed a parameter sweep of their length. The length of the arms (\(l_{arm}\)) varied from \(5\)\(\upmu\)m up to the maximum, limited by the size of the unit cell, see Figure 3. The best results were achieved for an arm's length equal to or less than \(10\)\(\upmu\)m, obtaining a higher quality factor resonance in the bare structure. Thus, due to the greater ease of manufacture, we have chosen an arm's length of \(10\)\(\upmu\)m.  
To compare the sensitivity achieved with the previous metastructures, we coated the new design with the same analyte thicknesses as before, obtaining the reflection coefficient results plotted in Figure 4a. When varying the analyte thickness between \(200\) and \(800\) nm, a maximum frequency shift of \(5.09\) GHz was obtained (see Figure 4c) with a mean sensitivity of \(7.32\times 10^{-5}\) nm\({}^{-1}\), leading to an improvement of \(196\%\) with respect to the hollow tripod. As can be observed in Figure 4a, this structure allows us to detect much thinner thicknesses than \(200\) nm, so we coated the structure with very thin films, with thicknesses ranging from \(5\) nm to \(25\) nm. The reflection coefficient and corresponding frequency shifts for these thicknesses can be seen in the inset of Figure 4a. With these results, we calculate a mean sensitivity of \(1.27\times 10^{-4}\) nm\({}^{-1}\) (improvement of \(341\%\) respect to the hollow tripod structure, which is not able to detect such ultrathin thicknesses, as shown in the supplementary material). As a final step, we rotate the metallic pattern of the metasurface unit cell \(30^{\circ}\) to perform the last comparison. The reflection coefficient and frequency shift achieved are shown in Figure 4b,d. Figure 3: Reflection coefficient for different arm lengths (linear sweep from \(0\) to \(95\)\(\upmu\)m) of the hollow tripod structure. Insets: schematic representation for arm lengths of \(0\)\(\upmu\)m (top) and \(95\)\(\upmu\)m (bottom). As observed, the performance of this design is similar to the previous one (without rotation), which agrees with the results found in [21] for single particles (non-periodic) plasmonic tripods with C\({}_{3}\) rotational symmetry. If we calculate the maximum frequency shift and the mean sensitivity again, the resulting values are 5.1 GHz, and \(7.35\times 10^{-5}\) nm\({}^{-1}\) for analyte thicknesses between 200 and 800 nm, respectively, which are approximately identical to the previous case. The mean sensitivity with very thin films (5 to 25 nm) was also calculated obtaining a mean value of \(1.42\times 10^{-4}\) nm\({}^{-1}\), leading to an improvement of 381% with respect to the hollow tripod, and thus becoming the best option for sensing applications.