# Design and Experiment of Wideband Filters Based on Double-Layered Square-Loop Arrays in the F-Band
## 2 Design and Simulation  
The unit cell of the proposed MDM structure is presented in Figure 1. The structure is composed of a dielectric layer and two metallic layers, which are deposited on both surfaces of the dielectric. The metallic layers are patterned with the same periodic subwavelength air square-loops. The specific parameters of the model are as follows: The lattice period L is 900 \(\upmu\)m, internal square length A is 470 \(\upmu\)m, loop width W is 40 \(\upmu\)m, dielectric thickness D is 350 \(\upmu\)m and metal thickness H is 1.5 \(\upmu\)m. The electromagnetic performance of these structures has been analyzed and optimized using numerical finite-difference time-domain (FDTD) simulations while considering a conductivity of \(\sigma\) = 5.8 \(\times\) 10\({}^{7}\) S/m for copper. The substrates are formed on a 350 \(\upmu\)m thick quartz plate with a relative dielectric constant and loss tangent of \(\varepsilon_{\text{QL}}\) = 3.78 and tan\(\delta_{\text{QL}}\) = 0.002, respectively. A plane wave linearly polarized along the y-axis is normally incident on the structures and propagates along the negative z-axis direction. To better illustrate the performance, a metal-dielectric (MD) structure with only one metallic layer was also considered.  
Figure 1 shows the transmittance spectra through the two proposed structures. For the MD structure, a maximum transmittance of 0.825 was obtained when an electromagnetic wave linearly polarized along the y-axis interacts with the structure. The phase changes on transmission of MDM structures also were shown in Figure 1. It is widely accepted that surface plasmons (SP) play crucial roles in the transmission of resonant electromagnetic waves [27]. The SP resonance originates from the excitation of collective oscillations of free electrons at the metal/dielectric interface termed as propagating surface plasmon (PSP) and localized surface plasmon (LSP). In the F-band, metals are regarded as almost perfect conductors and most energy of the SPs is owing to the electromagnetic wave localized at the air side. Thus, we call them surface waves (SWs) in this paper. For an array with a relatively thin metallic layer, SWs reside on both sides of the metal layer, which then couple via evanescent waves, thus leading to the formation of a transmission mode. For the MDM structure, when two metal interfaces are brought together (\(D<2\delta\), where \(\delta\) is the attenuation length of the SW), SWs around each interface couple together to produce two resonant peaks at \(f_{1}\) = 103.8 GHz and \(f_{2}\) = 127.45 GHz. It is evident that adding another metallic layer makes both resonant peaks more pronounced. The maximum in transmission is observed at the resonant frequencies for the MDM  
structure is formed by two complementary metasurfaces. The 3-dB bandwidth of proposed structure is 33.6 GHz in the 99.28-132.88 GHz frequency range, and both resonance peaks have maximum transmittance of approximately 0.945. Such a high transmittance indicates that the proposed structures possess potential in millimeter wave communication.