# A Multi-Coupling 3D Frequency-Selective Surface with High Selectivity and Wide Dual Passband
## 2 Design Principle
### Simulation and Analysis
As shown in Figure 3a,b, the current distribution at the transmission poles (fp1 at 10.6 GHz and fp5 at 15.1 GHz) reveals that the current flows through the S-gap and T-gap in different configurations, facilitating effective energy transfer. On the other hand, Figure 3c,d show the current distribution at the transmission zeros (fz2 at 16.17 GHz and fz3 at 17.57 GHz), where the surface current distribution changes significantly. At these transmission zeros, there is no effective coupling path, resulting in most of the incident wave energy being either reflected or absorbed. This illustrates the distinct behavior  
Figure 3: The coupled path of current transmission at the transmission pole. (**a**) fp1 = 10.6 GHz. (**b**) fp5 = 15.1 GHz and transmission zero. (**c**) fz2 = 16.17 GHz. (**d**) fz3 = 17.57 GHz. of the FSS at transmission poles and zeros, which is critical for achieving the desired filtering characteristics. Furthermore, the analysis of the surface current paths highlights the importance of coupling mechanisms in determining the frequency response of the FSS. The coupling between different gap structures creates multiple resonant modes, which directly influence the formation of transmission poles and zeros. By effectively managing these coupling paths, the FSS achieves a high level of selectivity and control over the transmission characteristics. The coupling behavior not only contributes to the desired dual-band performance but also ensures that the structure maintains a compact form factor without compromising functionality. The effectiveness of the coupling paths can also be observed in the differences between the transmission poles and zeros. While transmission poles are characterized by strong coupling that facilitates efficient energy transfer, transmission zeros represent frequencies where the coupling is insufficient, leading to energy reflection or absorption. The ability to accurately control these characteristics is key to designing an FSS with excellent frequency selectivity and stability, as demonstrated by the proposed 3D-DBFSS. The combination of different coupling paths, as shown in Figure 3, allows the FSS to maintain its performance across a wide range of frequencies, making it suitable for practical applications where dual-band frequency filtering is required. The transmission characteristics for incidence angles of up to 30\({}^{\circ}\) are illustrated in Figure 4. As depicted in Figure 3(a), the first passband exhibits insensitivity to variations in the incidence angle for TE polarization, showing consistent performance for angles from 0\({}^{\circ}\) to 30\({}^{\circ}\). However, the higher-frequency passband shows a slight ripple as the incidence angle increases, and frequency shifts of approximately 0.1% and 0.3% are observed in the two passbands, respectively. Similarly, Figure 3(b) presents the results for TM polarization, where the frequency shifts in the two passbands are less than 0.1% as the incidence angle varies up to 30\({}^{\circ}\). These findings demonstrate that the proposed 3D-DBFSS maintains good angular stability for both TE and TM polarizations under oblique incidence angles of up to 30\({}^{\circ}\). It is also noteworthy that, by coupling different types of gaps, the monolayer 3D-DBFSS achieves eight transmission poles within the two passbands, without the need for increasing the number of layers to enhance the transmission zero points. This innovative  
Figure 4: The variation of the transmission coefficient. (**a**) Transmission coefficient of TE wave varying from 0\({}^{\circ}\) to 30\({}^{\circ}\). (**b**) Transmission coefficient of TM wave varying from 0\({}^{\circ}\) to 30\({}^{\circ}\). design ensures that the proposed FSS is significantly thinner than most reported 3D-FSS structures, making it more efficient for practical implementation.