A Miniaturized Frequency Selective Surface Based on Square Loop Aperture Element

We propose a miniaturized band-pass frequency selective surface (FSS) with periodic unit cell structure. The proposed FSS is realized by symmetrically bending the edges of the square loop aperture element, by which our proposed FSS increases the resonant length, and, hence, reduces its size. In this FSS, each unit cell has a dimension of 0.0538λ× 0.0538λ, where λ represents the wavelength of the corresponding resonant frequency. Both the theoretical analysis and simulation results demonstrate that our proposed FSS, having high polarization stability and angle stability, can achieve smaller size in comparison with the previously proposed structures.


Introduction
Frequency selective surfaces (FSSs) are two-dimensional planar periodic structures which are realized by using patch or aperture elements to provide frequency filtering characteristic to incoming wave [1].FSS has attracted a great amount of attention and has been widely studied for microwave and light-wave applications owing to its frequency selective properties [1][2][3][4][5][6][7].Recently, FSS has been adopted in subreflector of Cassegrain antenna system to achieve frequency reuse, used to design band-pass radomes on the aircraft to reduce the outof-band radar cross section (RCS) of antennas, and used in circuit analog absorber to expand its bandwidth [2].
FSS is an infinite periodic array, which is difficult to design.In fact, it can be implemented by using finite elements to make it suitable for practical engineering applications.This is because the finite FSS structure has no infinite expansibility and results in end current and scattering at the edges of the finite array, which seriously affect the performance of the FSS [3].Therefore, it is necessary to use sufficient elements to approximate the characteristics of infinite FSS.Generally, the number of unit cells should not be less than 20 × 20 [4].However, the size of a unit cell is so large that it is difficult to design a finite FSS array with sufficient number of elements in a finite space when the FSS is operating in a low frequency such as L-band.As a result, minimization of FSS becomes one of the attractive and hot topics.Furthermore, the FSS should have good resonance stability performance with respect to various polarizations and incidence angles to achieve stable filter property in operating band [5].
Recently, a great number of FSSs have been developed to reduce their sizes.Chiu and Chang proposed a novel FSS structure which is realized by using two metal patch layers and a dielectric layer.The two metal patch layers coupled together via the dielectric layer.The size of each element is 0.104 × 0.104 [5].Then, Li et al. developed an octagon FSS using fractal theory and reduced the final FSS element size to 0.0814 × 0.0814 [6].After that, Yang et al. reported an improved FSS by bending the edges of cross aperture element into the external space [7] and the size of each element was 0.061 × 0.061.All these unit cells are symmetrical in order to ensure the stability of the corresponding FSSs.However, the size of the FSS is still large for practical applications in very low frequency.
In this paper, we propose a miniaturized band-pass FSS with periodic unit cell structure.The proposed FSS is realized by symmetrically bending the edges of the square loop aperture element to the inner space.In this FSS, each unit cell has a dimension of 0.0538 × 0.0538.The simulation results demonstrate that our proposed FSS, having high polarization stability and angle stability, can achieve smaller size in comparison with the previously proposed structures.

Fundamental of Miniaturized FSS
On the basis of the electromagnetic theory, when a plane wave is incident on a patch array, there exists induced current.Examples are shown in Figure 1.In Figure 1(a), we choose the vertical direction as reference direction of electric field in the two-dimensional plane.When a plane wave is incident on a patch array, the electric field creates positive and negative charges on the edges of the two adjacent patches, which is a gap capacitor.Similarly, in a wire grid shown in Figure 1(b), parallel wires can also generate induced current, resulting in a magnetic field, which acts as inductors.The first-order approximation of the capacitance of the patch array and the inductance of a wire gird are determined by ( 1) and (2), respectively [8]: where  0 is the permittivity constant of the air,  eff is the effective dielectric constant of the substrate,  is the side length of the patches,  is the distance between the two patches,  0 is the permeability of air,  is the length of the wire, and  is the width of the wire.
From (1), we find that  is proportional to  and is inversely proportional to  when  > .In a word, only the narrow apertures in the horizontal direction act as big equivalent capacitance, which is shown in Figure 1(a).In (2), we observe that  is proportional to  and is inversely proportional to  with  > .Thus, the equivalent inductance effects are mainly dependent on the vertical direction of these long wires.
Based on the theoretical analysis and discussions above, we can choose appropriate dimensions of the FSS elements to obtain required resonant frequency.In addition, we know that different FSS structures may have different equivalent circuits.For square loop aperture element illustrated in Figure 2, the narrow aperture in horizontal direction plays an important role in forming the big equivalent capacitance, the long wire in vertical direction plays an important role in forming the big equivalent inductance [2], and the equivalent circuit model of such element is shown in Figure 3, in which  is large equivalent capacitance and  is large equivalent inductance.
From the previous knowledge on the circuit analysis, the resonant frequency of the equivalent model described in Figure 3 can be expressed as where   = 0.5 and   = 0.5.From (1), (2), and (3), we find that the resonant frequency of the square loop aperture element mainly relies on the equivalent capacitance  and the equivalent inductance .As for the square loop aperture FSS, we should increase the International Journal of Antennas and Propagation  length of the narrow aperture of the element structure to obtain large equivalent capacitance so as to reduce the size of the FSS structure.Inspired by the analysis given above, we propose an improved unit cell structure named four sides loading aperture (FSLA) element, and it is shown in Figure 4.In this structure, the apertures implied by the yellow dotted line can act as large capacitors.The corresponding equivalent circuit model is shown in Figure 5, where  is the large equivalent capacitance and  is the large equivalent inductance.
To further reduce the resonant frequency of the above structure, we bend the FSLA element into the inner side of the square loop.The new structure of the highly improved FSS unit cell is described in Figure 6 and its equivalent model can also be illustrated by using the model shown in Figure 5.However, the values of the two capacitances in Figure 5 increase.

Results and Discussions
On the basis of the analysis, we propose a miniaturized FSS, which operates at 1.647 GHz.The FSS element is shown in Figure 6 while the related parameters are shown in Table 1.
The simulation results are obtained by using the computer simulation technology (CST).The simulated model is shown in Figure 7 and the transmission coefficients with normal incidence of the designed FSS are shown in Figure 8.We can see from Figure 8 that the resonant frequency of our designed FSS is 1.647 GHz for normal incidence.When   is 2.65, the resonant frequency is 1.995 GHz; when   is 4.4, the resonant frequency is 1.713 GHz.
According to the results shown in Figure 8 and ( 4), the size of the FSS element can be obtained with size of 0.0538 × 0.0538, where  0 is the speed of light in air,  represents the resonant frequency of the FSS and  is the corresponding wavelength,  is the size of FSS element, and  represents the length of the element.Moreover, the element size is different as the dielectric is different.It is found that  is inversely proportional to   .The proposed FSS is compared with the previously proposed studies in [5][6][7] and the comparisons are shown in Table 2.It can be seen from Table 2 that the designed FSS can achieve smaller size.This means that our proposed design is smaller in size at the same resonant frequency.In order to further discuss the bandwidth performance of our proposed FSS, the S-parameter characteristics, including the reflection coefficient (S 11 ) and transmission coefficient (S 21 ), are obtained by using CST and the simulation results with TE-polarized incidence are shown in Figure 9.It can be seen from Figure 9 that the proposed FSS has a −10 dB impedance bandwidth of 5.34% with respect to the center frequency of 1.647 GHz.

Stability Analysis of the Proposed Miniaturized FSS
As a FSS, it should be stable for different applications.Therefore, we investigate the stability of the proposed miniaturized FSS for different situations, such as different polarizations or different incident angles.The simulation transmission coefficients are shown in Figure 10.As shown in Figure 10, our designed miniaturization FSS has stable resonance properties under different situations, and the resonant frequency  deviations of the deigned miniaturization FSS are illustrated in Tables 3 and 4. We can see from Tables 3 and 4 that the resonant frequency deviations for TE-polarized and TM-polarized International Journal of Antennas and Propagation both have a little shift at different incident angles.These deviations are within the scope of the allowed operation bandwidth of the FSS.Thereby, the proposed miniaturization FSS can achieve excellent polarization stability and angle stability.

Conclusion
In this paper, we proposed a miniaturization FSS with unit cell size of 0.0538×0.0538.The proposed FSS was designed by setting the bent FSLA element in the inner sides of the square loop.The designed FSS was analyzed step by step by using the equivalent circuit model.The simulation results obtained from CST demonstrated that our proposed FSS had excellent polarization stability and angle stability, which render it suitable for practical engineering applications.

Figure 3 :
Figure 3: Equivalent model of square loop aperture element.

Figure 6 :Figure 7 :
Figure 6: Structure of the proposed FSS element.
Figure 9: S-parameter characteristics of the designed FSS.

Table 1 :
Parameters of the designed FSS element.

Table 3 :
The resonant frequency deviation of proposed FSS at TEpolarized.

Table 4 :
The resonant frequency deviation of proposed FSS at TMpolarized.