## 2 Design and Analysis
When observing the results in Figure 4a,b, it can be seen that, as the values of \(S\) and \(W\) increase, the broadband absorption region of the plasmonic metasurface becomes narrower. This phenomenon can be explained by the fact that the broadband absorption region of the plasmonic metasurface is formed, based on the overlap of the resonance regions of the split rings. When the spacing between the split rings increases, this overlap is reduced, thereby narrowing the broadband absorption frequency range as well as the absorption itself. To better understand the underlying mechanisms responsible for the broadband absorption of the plasmonic metasurface, it is critical to examine the distributions of the E-field and surface current within the structure. Figure 5a-c provide a detailed visualization of the E-field distributions across the plasmonic metasurface at three representative frequencies: 12.5, 13.5, and 14.5 GHz. The components of this field represent the absolute value of the E-field on plane \(z\) = 0. The directions of the field are not considered here. Instead, we focus on observing the direction of the surface current flow within the structure later. It should be noted that, at all three frequencies, the metasurface showed an absorption exceeding 90%, as in Figure 4, highlighting its efficiency in capturing EM energy. However, the spatial distribution of the E-field reveals significant variation depending on the frequency,  
Figure 4: Comparison of the absorption of plasmonic metasurfaces with structural parameters \(L\) = 18.7, \(R_{out}\) = 7, and FR-4 thickness \(t_{\text{subl}}\) = 3.2 mm. (**a**) \(S\) = 0.1 and \(W\) = 0.05–0.3 mm. (**b**) \(W\) = 0.1 and \(S\) = 0.05–0.3 mm. indicating that different regions of the metasurface contribute dominantly to the absorption at different frequencies. At a frequency of 12.5 GHz, which corresponds to a wavelength of approximately 24 mm, the strongest E-field concentration is observed at the outermost cut circular segments of the plasmonic metasurface structure. These regions, located at the periphery of design, act as hotspots for field enhancement and play a critical role in the absorption process at lower frequencies. As the frequency increases to 13.5 GHz (wavelength \(\sim\) 22.2 mm) and further to 14.5 GHz (wavelength \(\sim\) 20.6 mm), the regions of maximum E-field intensity progressively shift inward, focusing on the smaller-diameter split rings closer to the center of the structure. This inward movement of the E-field intensity with an increasing frequency suggests a frequency-selective interaction between the EM wave and structural elements of the plasmonic metasurface, highlighting the role of geometric scaling in determining the resonant behavior of different regions. The results of the field distribution, which depend on the positions of the split rings within the unit cell, can be explained by the fact that each split ring with a different length resonates at a different frequency of the incident EM wave. The relationship between the length of the split ring and its resonance frequency can be expressed by the following formula [37]:  
\[f_{ij}=\frac{c\sqrt{i^{2}+j^{2}}}{2L\sqrt{e_{\textit{eff}}}} \tag{5}\]  
where \(i\) and \(j\) are integers (0, 1, 2\(\ldots\)), \(i^{2}+j^{2}\
eq 0\), and \(e_{\textit{eff}}\) is the effective dielectric constant. Based on Equation (5), the operating frequency of the structure is inversely proportional to the length of the split ring. Therefore, the split rings located on the inner side respond to higher frequencies of the EM waves, and vice versa. Figure 2.0 (**a–c**) E-field intensity distributions in the plasmonic metasurface at various frequencies. (**d–f**) Analysis on the surface current distribution of the plasmonic metasurface at the specific frequencies corresponding to the investigated E-field distributions. In addition to the E-field distributions, Figure 5e,f present the surface current distributions within the plasmonic metasurface at the same frequencies.