# A Transplantatable Frequency Selective Metasurface for High-Order Harmonic Suppression
## 2 Design of the Harmonic-Suppression Frequency Selective Metasurface Element (FSMSE)
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameters** & **s** & **g** & **p1** & **r** & **d** & **p2** \\ \hline mm & 5.5 & 0.5 & 6.6 & 4.3 & 0.5 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the frequency selective surfaces (FSSs) shown in Figure 1.  
Figure 3: Transmission coefficient characteristics for oblique incidences on the resonant complementary loop FSS for (**a**) TE polarization and (**b**) TM polarization (The red shadow represents harmonic transmission bands). Figure 4: A 3D topology of harmonic suppression frequency selective metasurface element (FSMSE) (The blue part represents metal and the grey represents substrates). Figure 5: The equivalent circuit of harmonic suppression metasurface element. Figure 6: Comparison of transmission coefficients of the full-wave simulation and equivalent circuits of the harmonic suppression FSMSE. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameters** & **a** & **b** & **w** & **p** & **t** & **h** \\ \hline mm & 3 & 2.8 & 0.2 & 3.25 & 0.5 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the FSSs shown in Figure 4.  
Next, the designed harmonic suppression FSMSE can be integrated with the aforementioned non-resonant patch-grid FSS and the resonant complementary loop FSS, respectively, as shown in Figures 8 and 9. The air spacing h1 between the two original FSSs and the HS-FSMSE was also optimized using circuit analysis where the two types of FSSs are equivalent to band-pass circuits whose lumped elements can also be extracted by bisquare fitting algorithm. When h1 is 3 mm, the harmonic suppression feature can perfectly be achieved without deteriorating the operating frequency of the pass band. Figure 10 shows the transmission coefficient of non-resonant patch-grid FSS with HS-FSMSE for different incidence angles with TE and TM polarizations. It can be seen that the high-order harmonic waves can be suppressed below \(-40\) dB after integrating with HS-FSMSE structure. Similarly, Figure 11 depicts the transmission coefficient of the resonant complementary loop FSS with HS-FSMSE for different incidence angles with TE and TM polarizations. The results show that the high-order harmonic waves can also be well suppressed even with the strong resonant behavior. In the meantime, we can see that the two different types of FSSs with same HS-FSMSE own good polarization and angle stabilities. It can be seen that the FSS with narrower bandwidth will be less affected after HS-FSMSE is added. Hence, cascading HS-FSMSE layers to suppress spurious transmission of band pass FSS filters could be used for the applications which needs relatively narrow pass band. It is worth pointing out that the unit cell size of the patch-grid FSS and the complementary loop FSS are different. The patch-grid FSS is sub-wavelength structure whose period is only 6.6 mm, and the complementary loop is a conventional resonant structure whose period is 10 mm. For two different FSSs, the unit cell size of the harmonic suppression FSMSE is the same as 3.3 mm. As a result, when the HS-FSMSE is integrated with the patch-grid FSS, one unit corresponds to 2 \(\times\) 2 HS-FSMSEs. And for the resonant complementary loop FSS, one unit corresponds to 3 \(\times\) 3 HS-FSMSEs, as shown in Figures 8 and 10, respectively. In this case, the different implementations show the transplantability of the HS-FSMSE. Figure 7: Transmission coefficients for oblique incidences with different angles on the harmonic suppression (HS) FSMSE, (**a**) TE polarization and (**b**) TM polarization. Figure 8: Multilayer patch-grid FSS integrating with HS-FSMSE (The yellow and blue parts represent metal, the grey represents substrates). Figure 10: Transmission coefficient for oblique incidences with different angles on the multilayer patch-grid FSS with HF-FSMSE, (**a**) TE polarization and (**b**) TM polarization (The green shadow represents suppressed harmonic transmission bands).