## 2 Design and Analysis
According to the transmission line theory, to obtain the minimum reflection coefficient, the input impedance should match that of the free space, as mathematically expressed in Equation (4). The input impedance of the plasmonic metasurface is composed of those of the dielectric layer and the split circular structure. These split rings were positioned very close to one another, resulting in coupling effects between them. This caused the plasmonic metasurface to function similarly to a multilayer frequency-selective surface [30]. The final outcome was the existence of a broad frequency band where the plasmonic metasurface exhibited a low reflection coefficient and high absorption. To further clarify the absorption characteristics of the plasmonic metasurface, we examined the response of the split-ring components within the structure. Figure 3a illustrates the absorption characteristics of the structure formed by pairs of adjacent split rings in the following order: Rings 1-2, 3-4, 5-6, 7-8, and 9-10, as depicted in Figure 1a. These paired split rings present the absorption spectra with two resonance peaks in a range of 12.30 to 14.80 GHz. At both end frequencies, a high absorption of over 95% is shown. The results indicate that, for the rings with smaller radii, the absorption peaks shift slightly toward higher frequencies, which can be explained by the fact that the total length of the split ring is shorter when the ring radius is smaller. It is noteworthy that the split-ring pairs can be formed not only by adjacent rings but also by any arbitrary pairing of rings. Consequently, a large number of coupled ring pairs can be generated. These coupled rings are capable of strongly absorbing EM waves across different frequency ranges. As a result, the plasmonic metasurface exhibits an overlap of multiple absorption peaks from various coupled ring pairs, leading to a broadband absorption spectrum. Figure 3b presents the surface current distribution on a coupled ring at the resonance frequency. It can be observed that strong currents flow on its surface, and notably, the current directions on the two branches of the adjacent rings are opposite. This phenomenon can be explained by the presence of a connected bar linking the two sections. To ensure a continuous current flow within the structure, the current directions on the two branches should be opposite. These results highlight the critical role of the connecting bars in this structure. Without them, the split-ring branches in the two rings would act independently,  
Figure 3: (**a**) Comparison of the absorption of coupled rings, and (**b**) surface current distribution on the adjacent coupled ring. not allowing the existence of multiple interconnected resonance peaks. This interconnection is essential in forming a broadband absorption. Two parameters, the strip width of ring (\(W\)) and the spacing between adjacent rings (\(S\)), are critical factors in the design of the plasmonic metasurface structure. These parameters influenced the coupling between neighboring rings as well as the overall length of split rings, thereby determining both the resonance frequency and the absorption efficiency of the structure. Therefore, we conducted an investigation on various values of \(W\) and \(S\) to identify the optimal dimensions. Figure 4a illustrates the simulated absorption performance of the plasmonic metasurface by varying the \(W\) value from 0.05 mm to 0.3 mm while keeping all the other parameters constant. The results indicate that, at \(W\) = 0.1 mm, the plasmonic metasurface shows an absorption exceeding 90% with the broadest frequency bandwidth. Similarly, Figure 4b presents the corresponding results by varying the \(S\) value from 0.05 to 0.3 mm while keeping the other parameters fixed. The results reveal that the optimal absorption performance, exceeding 90% over a wide frequency range from 12.30 GHz to 14.80 GHz, is obtained when \(W\) = 0.1 and \(S\) = 0.1 mm. Therefore, we selected \(W\) = 0.1 and \(S\) = 0.1 mm as the optimal dimensions for further studies.