# A Quad-Band Highly Selective Frequency Selective Surface with Ultra-Wideband Rejection
## 2 FSS Description and Simulation Results
### Performance Simulation and Analysis  
HFSS and ADS were used to simulate the transmission characteristics of the proposed FSS structure. Figure 4a shows the transmission coefficient curves in TE and TM modes. It can be observed that the proposed structure provides a quad-band FSS. The transmission poles are \(f_{p1}\) = 6.54 GHz, \(f_{p2}\) = 8.41 GHz, \(f_{p3}\) = 10.80 GHz, and \(f_{p4}\) = 13.06 GHz, respectively. The \(-3\) dB bandwidths of the passbands are 6.42-6.63, 8.23-8.62, 10.75-10.95, and 12.97-13.26 GHz, respectively. The insertion losses of the four passbands are 0.77, 0.45, 0.71, and 1.11 dB, respectively. In addition, the transmission coefficient between the operating bands is below \(-10\) dB, in the ranges of 1 to 5.5 GHz and 14 to 40 GHz, and the transmission coefficient is below \(-20\) dB. Here, we define the frequency difference as the bandwidth of the transition band for judging the roll-off performance when the transmission coefficient drops sharply from \(-3\) dB to \(-20\) dB. The bandwidths of the transition band located on both sides of the passbands are 0.69 GHz and 0.57 GHz, respectively. The narrow transition bandwidths provide the FSS with a highly selective response. Figure 4a also shows that this structure has good polarization stability; the transmission coefficient curve fitting of the structure is consistent in the TE and TM modes. In comparison, the transmission coefficients obtained using the software HFSS 2019 and ADS 2019 are shown in Figure 4b. Although there are some subtle differences, it can be seen that the simulation results of HFSS and ECM are in good agreement, and the suppression effect of both is the same.  
For further verification of the working principle of the multilayer structure, the surface current and electric field distributions at a resonant frequency were determined, and they are shown in Figure 5. Because the surface currents of each laye  
Figure 4: Comparison of the proposed FSS transmission coefficient. (**a**) TE and TM. (**b**) HFSS and ECM.  
the same region at the four resonant frequencies, we provide the surface current and electric field distributions at 6.54 GHz. In the winded cross-slot region, the surface current is weak and the electric field is strong. The electric field is mainly concentrated in the bending gap, which can be modeled as a series \(LC\) resonator. It can be seen that there is almost no attenuation of the electrical intensity of the incident wave after passing through the winded cross-slot region. The surface current at the square ring region is distributed along both sides of the loop. At the square patch region, the current flows mainly predominantly throughout the area.  
The transmission coefficient curves of the proposed FSS under different incident angles for both polarizations are depicted in Figure 6. It is observed that the frequency response of the proposed FSS is basically stable for TE and TM polarization with an incidence angle up to 30\({}^{\circ}\). However, as incidence angle increases, the latter two passbands tend towards high frequency. This is because the grating lobe is delayed until higher frequencies appear [1]. For TE polarization, the transmission coefficient remains below \(-20\) dB within the 37 GHz frequency band. For TM polarization, the transmission coefficient shifts slightly upward at 30-34 GHz when the incidence angle reaches 30\({}^{\circ}\). However, the proposed FSS still maintains stable transmission performance. As the incidence angle of TM polarization increases, a ripple resonance occurs between the second and third passbands. The ripple resonance has a negligible effect on the passband.