## 3 Numerical and Experimental Results  
As a first step, we numerically evaluated the mutual coupling between the two concentric spirals constituting the single unit-cell. Indeed, in order to have the metasurface working simultaneously at both the desired frequencies (17 and 64 MHz), it is particularly important that the two concentric spirals of a single unit-cell are sufficiently decoupled at the respective operating frequencies. The results, shown in Figure 6, demonstrated that the two concentric spirals present a low coupling level, although larger at 64 MHz. While this value is acceptable in terms of performance, room for improvement is still available in this parameter. We therefore proceeded with the unit-cell's currents homogenization procedure. By following the calculations performed in the previous section, we loaded each element of the metasurface with the appropriate capacitor in order to avoid truncation effects. In Figure 7a,b, the maps of the capacitive loads at 17 MHz and 64 MHz are reported. As apparent from Figure 7b, the capacitance values at 64 MHz do not depend in essence on the unit-cell position within the metasurface. This is due to the larger periodicity for the unit-cells internal spirals, which results in a lower reciprocal mutual coupling (and, thus, less correction required for homogenization). Once the loads are applied, the currents flowing in the unit-cells are homogenized for both the operative frequencies, as is evident in the numerical results reported in Figure 8a,b. Due to the not completely negligible mutual coupling between the single unit-cell external and internal spirals at 64 MHz, a minor deviation (not affecting in practical aspects) from  
Figure 6: Mutual coupling between the two concentric spirals constituting a single unit-cell, respectively, tuned at 17 and 64 MHz. The level of coupling is higher at 64 MHz but still limited. Figure 7: Currents homogenization procedure: calculated capacitances (pF) maps at 17 MHz (**a**) and 64 MHz (**b**). perfect homogenization can be spotted at the four metasurface corners. Notably, when the metasurface is working at a specific frequency (e.g., 17 MHz), the current does not flow in the coils tuned at the other frequency (e.g., 64 MHz), as expected. Another important metric, as explained before, relies on the transmission efficiency evaluation. In Figure 9, we reported the numerical transmission efficiency increase achievable thanks to the metasurface adoption, respectively, without (Figure 9a,b) and with (Figure 9c,d) the presence of a biological phantom, at 17 MHz and 64 MHz. As is evident, in the absence of the biological phantom, the transmission efficiency increases by a factor 4.5 (at 17 MHz) and 5.5 (at 64 MHz). Instead, in the presence of the phantom, we obtain an increase in a factor 3.5 and 5 at 17 MHz and 64 MHz, respectively. Since the same RF coil and metasurface are used to receive the signal, the \(B_{1}^{-}\) also increases by the same factor of the \(B_{1}^{+}\) by the principle of reciprocity [36]. Therefore, in the reasonable hypothesis that the biological load losses are dominant, the SNR percentage enhancement obtained with the metasurface is also represented by the map reported in Figure 9c,d. In addition, we also investigated the effect that capacitor's tolerances, which are unavoidable in practical scenarios, can have on the field map produced by the metasurface. Therefore, we randomly assigned a \(\pm 1\%\) tolerance (a typical commercial value) to the capacitances determined in Figure 7. After that, we evaluated the H-field map on a plane parallel to the metasurface and 40 mm distant from it. By comparing the map obtained with the ideal capacitor's values of Figure 7 and the one with tolerances, we found that the maximum percentage deviation happens for the 64 MHz Larmor frequency. As can be observed from Figure 10, the maximum field deviation due to the tolerances remains under 9%, thus proving the robustness of the proposed solution.