# A Multi-Coupling 3D Frequency-Selective Surface with High Selectivity and Wide Dual Passband
## 2 Design Principle  
### Design Configuration  
This study introduces a novel single-layer, dual-bandpass, electromagnetic 3D frequency-selective surface (FSS) designed to regulate the transmission of incident electromagnetic waves across two passbands. By employing an orthogonal arrangement of metal patches with distinct slit structures, a 3D unit capable of bandpass filtering is achieved, as reported in [21]. The proposed FSS consists of a unit cell supported by a dielectric substrate with a relative permittivity of 4.3 and a loss tangent of 0.02. The structure is formed by two identical surface waveguides oriented perpendicularly to each other. Figure 1 presents the configuration of the 3D FSS unit cell, while Table 1 summarizes the final dimensions of the unit cell.  
In the design of the planar unit cell, the S-gap, T-gap, and R-gap are incorporated into the unit cell of the 3D FSS, as shown in Figure 1a. The S-gap primarily influences the lower-frequency band by extending the current path, while the T-gap and R-gap are tailored to adjust the higher-frequency band, providing multiple resonances that contribute to the dual-band response. This strategic combination allows for a compact unit cell design with efficient use of space and material, maintaining a thin profile of approximately one-third of the free-space wavelength.  
When designing the 3D unit cell, the planar unit cells are orthogonally configured. The use of two perpendicular surface waveguides further enhances the filtering capability, enabling the unit cell to support dual-band functionality without significant performance degradation. The orthogonal configuration of the metal patches, along with the introduction of multiple gap structures, allows the FSS to achieve selective transmission characteristics at multiple resonant frequencies. The combination of different gap structures provides multiple degrees of freedom in designing the resonant characteristics, enhancing both the selectivity and the miniaturization of the FSS. This design can be effectively utilized in applications where compact, multi-band electromagnetic filters are required. The chosen substrate, with a relative permittivity of 4.3, ensures adequate support for the surface waveguides while maintaining low loss characteristics.  
Furthermore, the flexibility of the design allows for easy adaptation to different frequency ranges by scaling the dimensions of the unit cell and the gap structures. This  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Parameter** & **h** & **d** & **L1** & **L2** & **L3** & **w1** & **w2** & **w3** \\ \hline
**Value (mm)** & 10.8 & 4 & 1.4 & 3.6 & 1.2 & 0.2 & 2 & 1.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Dimensions of the proposed FSS unit cell.  
Figure 1: The 3D-FSS unit cell model. (**a**) Three kinds of gaps. (**b**) Perspective view of full structure and unit cell.  
scalability makes the 3D-FSS a versatile solution for a wide range of electromagnetic filtering applications, where space constraints and multi-band functionality are critical requirements. The innovative use of gap structures, combined with the orthogonal waveguide configuration, represents a significant advancement in the development of compact and efficient frequency-selective surfaces