# A Transplantatable Frequency Selective Metasurface for High-Order Harmonic Suppression
## 2 Design of the Harmonic-Suppression Frequency Selective Metasurface Element (FSMSE)  
In general, a FSS with band-pass feature intrinsically has spurious transmission windows outside of the desired operational pass-band. For an example, a classic non-resonant FSS [7] which consists of square metallic patch with fishnet grids in multilayer structure is shown in Figure 1a. Full-wave analyses show that the pass-band characteristic of the FSS is operating at about 10 GHz, but with harmonic transmission bands around 25 GHz, as shown in Figure 2. When the plane wave is oblique incidence with Transverse Electric (TE) and Transverse Magnetic (TM) polarizations, the spurious transmission windows become much more. Similarly, a typical resonant type FSS which is composed of complementary loop structure [10] is shown in Figure 1b, which also operates at 10 GHz. Because the FSS is resonant structure, it has several harmonic pass bands at the higher frequency bands outside of the main pass-band, as shown in Figure 3. The geometry parameters of the two FSSs are shown in Table 1. Thus it can be seen that the harmonic suppression technique should be adopted. In this paper, a transplantable FSMSE is proposed that can be integrated with different types of band-pass FSS structures without deteriorating the operating frequency of the pass band. Figure 1: (**a**) Subwavelength multilayer patch and grid frequency selective surface (FSS), (**b**) resonant complementary loop FSS (The grey represents substrates, the yellow and orange parts represent metal). Figure 2: Transmission coefficient characteristics for oblique incidences on the non-resonant FSS for (**a**) Transverse Electric (TE) polarization and (**b**) Transverse Magnetic (TM) polarization (The red shadow represents harmonic transmission bands). The topology of the FSMSE for harmonic suppression is shown in Figure 4, which is composed of two-layer square loop elements that intrinsically own band-stop feature. It is known that the single-layer square loop FSMSE has a narrow stop band whose operating frequency could be adjusted by changing the length of square loop. As a result, when we want to obtain a relatively wide stop band, the multilayer square loop FSMSE with air spacing can be designed. At the same time, the pass band of 10 GHz has to be guaranteed. The equivalent circuit model is used to analyze the feature of the FSMSE for harmonic suppression, as shown in Figure 5.  
Here the square loop element can be equivalent to a band stop circuit. As a result, the equivalent circuit of the two-layer square loop FSMSE is a two-stage cascaded circuit which is connected by a uniform transmission line whose length depends on the electric size of the air spacing, as shown in Figure 5. The geometry parameters are shown in Table 2. The lumped elements in the equivalent circuit can be obtained using bisquare fitting algorithm [11]. According to the equivalent circuits of each layer of the square loop FSMSE, the lumped parameters are extracted as follows: \(L_{\text{1s}}=L_{\text{1s1}}=0.0834\) nH, \(L_{\text{2s}}=L_{\text{2s1}}=0.001\) nH, \(C_{\text{2s}}=0.6677\) pF, \(C_{\text{2s1}}=0.4462\) pF, \(L_{\text{3s}}=0.0762\) nH, \(L_{\text{3s1}}=0.0624\) nH, \(C_{\text{3s}}=0.1834\) pF and \(C_{\text{3s1}}=0.2167\) pF. With these lumped elements and the circuit prototype, the optimal air spacing h could be obtained using circuit optimization. It can be seen that when h equals to 2 mm, the maximum stop-band range can be obtained. Figure 6 depicts the comparison of transmission coefficient of the harmonic suppression FSMSE between the full-wave simulation and the equivalent circuit, which shows good agreement with each other. Furthermore, the oblique incidences of TE and TM polarizations with different incident angles on the harmonic suppression FSMSE are analyzed, respectively, as shown in Figure 7. It can be seen that the proposed FSMSE has good polarization and angle stability. And the \(-20\) dB suppression bandwidth is from 16.8 to 26.8 GHz.