# A Multi-Coupling 3D Frequency-Selective Surface with High Selectivity and Wide Dual Passband
## 2 Design Principle
### Simulation and Analysis  
To elucidate the underlying physical mechanisms responsible for the bandpass behavior, the differences between wave transmission in the passband and stopband were analyzed. The simulation was conducted using the numerical simulation software, with periodic boundary conditions along the x and y directions and open conditions along the z direction. The simulations were performed using the Finite Element Method (FEM) algorithm, providing a comprehensive understanding of the electromagnetic behavior of the designed 3D-FSS. Figure 2 presents the simulated S-parameter results of the proposed frequency-selective surface (FSS). The first passband is located between 10 GHz and 14 GHz, containing five transmission poles at 10.6 GHz, 11.27 GHz, 13.7 GHz, 14.83 GHz, and 15.1 GHz. The second passband lies between 22 GHz and 25.7 GHz, with three transmission poles at 23.2 GHz, 25.13 GHz, and 25.35 GHz. As illustrated in Figure 2, the designed FSS features four transmission zeros: three are located between the two passbands at 15.45 GHz, 16.17 GHz, and 17.571 GHz, while the fourth is at 26.1 GHz, beyond the upper passband. The transmission zeros near the passbands enhance the selectivity of the FSS. The passband of the proposed 3D-DBFSS exhibits very low insertion loss, with variations of less than 0.8 dB, ensuring a flat frequency response. From Figure 2, it can also be observed that the designed FSS demonstrates distinct transmission characteristics for both TE and TM polarizations. The S-parameters ( 1S111 and 1S211) for TE and TM polarizations are plotted, showing consistent performance across the frequency bands. For TE polarization, the reflection coefficient (S11) maintains a high level of rejection in the stopbands, while the transmission coefficient (S21) shows sharp peaks at the transmission poles (fp1 to fp8). For TM polarization, a similar behavior is observed, with distinct transmission poles and transmission zeros (fz1 to fz4) that contribute to the overall selectivity. The presence of multiple transmission poles and zeros enhances the ability of the FSS to filter out unwanted frequencies effectively, thereby improving the performance of the proposed structure. Figure 2: The S-parameters of proposed 3D-DBFSS. To evaluate the frequency selectivity of the FSS, a technical index (K) is defined. This index quantifies the sharpness of the frequency response at the cutoff frequencies, indicating the filter's ability to suppress unwanted signals outside the passband. The index \(K\) is defined as the ratio of the \(-3\) dB bandwidth to the \(-20\) dB bandwidth. \[K=BW_{\rm 3 dB}/BW_{\rm 20 dB} \tag{1}\]  
For the first passband, the \(-3\) dB bandwidth ranges from the lower cutoff frequency of 9.9 GHz to the upper cutoff frequency of 15.2 GHz, yielding a bandwidth (BWL3 dB) of 5.3 GHz. The \(-20\) dB bandwidth (BWL20 dB) for the same passband is 6.4 GHz. Thus, the sharpness index (KL), defined as the ratio of BWL3 dB to BWL20 dB, is 82.8%. For the second passband, the \(-3\) dB bandwidth extends from 22 GHz to 26 GHz, providing a bandwidth (BWU3 dB) of 4 GHz. The sharpness index for the second passband (KU) is calculated as 80.2%. It is well understood that increasing the number of transmission poles enhances the passband characteristics by reducing insertion loss and widening the bandwidth. In this design, the five transmission poles (fp1-fp5) within the first passband facilitate a broad passband between approximately 10.6 GHz and 15.1 GHz. A detailed examination of the current transmission paths at frequencies of 10.6 GHz and 15.1 GHz, as shown in Figure 3, reveals significant differences in the current loops. Through specific structural combinations, the three gap structures depicted in Figure 1 form multiple coupling paths to direct incident waves through the FSS. Figure 3 illustrates the coupled path of current transmission at the transmission poles and zeros.