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Abstract
We propose a bi-layer transmissive metasurface to obtain linear-to-circular polarization conversion in a wideband. The unit cell of each metasurface layer, which has identical configuration, consists of a Jerusalem-cross-like resonator and a metal strip. A universal equivalent circuit model is employed to guide the design of the polarizer. By analyzing the circuit parameters of the equivalent circuit, four metal strips are symmetrically inserted in each unit cell to broaden the bandwidth of linear-to-circular polarization conversion. Numerical and experimental results show that the polarizer can convert a linearly polarized wave into a circularly polarized wave in a wideband from 6.1 GHz to 12.6 GHz. Compared to the reported designs, the proposed polarization converter has advantages of ultrathin thickness and ultrawideband, and hence can be used in many applications, such as antennas and remote sensors.
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1. Introduction
Metasurfaces are planar periodic arrays of sub-wavelength elements. Compared to three-dimensional metamaterials, metasurfaces occupy advantages of ultrathin thickness, low loss, and easier to integrate with other devices. Also, metasurfaces are more freedom in manipulating electromagnetic (EM) waves by designing the geometry or arrangement of unit cells, addressing many applications from microwave to visible frequencies, such as absorbers, filters, imaging, and invisibility cloaks [1,2]. In recent years, metasurfaces have been employed to control the polarization state of EM waves, and many metasurface-based polarization converters including linear-to-linear, linear-to-circular (LTC), and circular-to-circular polarization conversions have been successfully developed [3–9]. In these devices, circular polarization converters operating in transmission mode are an important branch due to their extensive applications in wireless communication systems. For instance, a highly efficient LTC polarizer based on swastika-shaped metasurfaces was successfully developed for Cube Satellite application in S-band [10]. On the other hand, the LTC metasurfaces can also be used to realize circular polarization radiation when they are loaded to linearly polarized antennas [11,12]. However, these devices have disadvantage of a narrow band due to the limitation of physical mechanism. Many efforts have been made to enhance the operation bandwidth of transmissive polarizers [13–15]. Some researchers have verified that increasing the number of metasurface layer is an effective method to obtain high efficiency and broadband circular polarization conversion. Amin et al. proposed a multi-layer circular polarizer that is composed of capacitive patches and inductive wire grids separated by thin dielectric substrates [16]. This research shows that the device can maintain the 3-dB axial ratio (AR) bandwidth of 40% for incident angles within ±45°. Lin et al. presented a tri-layer metasurface that realized LTC polarization converter in the frequency range of 10.73 to 16.13 GHz [17]. These multi-layer structures can effectively enhance the bandwidth of circular polarization converters, but their thickness and bulk are also significantly increased [16–21]. Reducing the space between metasurfaces layer to subwavelength scale can effectively decrease the thickness of multi-layer structure. In this case, however, the near-field coupling becomes obvious and therefore deteriorates the device performance.
This paper presents an ultrathin bi-layer metasurface to obtain a broadband LTC polarization conversion. The bi-layer system is composed of two identical metasurface layers separated by a dielectric plate with sub-wavelength thickness. To consider the influence of the near-field coupling on polarization conversion, we employ the universal equivalent circuit model proposed in [22,23]. By transforming the universal equivalent circuit model into a π-typed circuit, we investigate the circuit parameters, such as surface impedance and coupling impedance, how to affect the performance of the proposed device. Then, a modified scheme for the bi-layer structure is proposed to enhance the bandwidth of LTC polarization conversion. The numerical simulations and experimental results reveal that the device can convert a linearly polarized wave to a circularly polarized wave in a wideband from 6.1 to 12.6 GHz. Moreover, the device has an ultra-thin thickness of $0.11{\lambda _0}$, where ${\lambda _0}$ is the central wavelength of operation bandwidth.
2. Initial unit-cell design and simulation
The initial schematic of the proposed LTC polarizer is shown in Fig. 1(a), which is a bi-layer metasurface spaced by a subwavelength dielectric plate. The unit cell of the two identical metasurfaces layers is composed of a Jerusalem-cross-like resonator and a metal strip along the x-direction. The dielectric plate is F4B with a dielectric constant of 2.65 and tangent loss of 0.001. Figure 1(b) presents the unit cell of the proposed device, and Fig. 1(c) presents the front view of the unit cell. Their initial geometric parameters are set as t = 3.5 mm, Px = Py = 9.5 mm, gx = 1 mm, gy = 1.25 mm, wx1 = 0.4 mm, wx2 = 0.35 mm, wy1 = 0.3 mm, wy2 = 0.4 mm, wy3 = 0.8 mm, lx = 4.4 mm, ly = 3.2 mm, and w = 0.25 mm, respectively.
Fig. 1. (a) Schematic configuration of the proposed LTC polarizer. (b) Unit cell. (c) Front view of the unit cell. (LP: linearly polarized wave, CP: circularly polarized wave.)
When a linearly polarized wave with the electric field vector oriented at 45° relative to x- direction [see Fig. 1(a)] perpendicularly illuminates the device, it can be decomposed into two orthogonal linear polarization components [horizontal (x) and vertical (y) components],
3. Equivalent circuit model and modified polarizer
3.1. Equivalent circuit model
Attributing to the subwavelength thickness of the device, the near-field coupling effect between the two metasurface layers is nonnegligible. As described in the following content, we will find that the near field coupling can significantly improve or deteriorate the device performance. Here, we employ the universal equivalent circuit model proposed in [23] to analyze the near-field coupling mechanism and the polarization conversion performance of the device.
As described in [23], the universal equivalent circuit model of two-layer metasurface is presented in Fig. 3. In this circuit model, Z11 and Z22 are self-impedances of individual metasurface, Z12 and Z21 are mutual-impedances of the bi-layer system, i1 and i2 represent the currents flowing through the two metasurfaces, and V1 and V2 are equivalent voltages on each metasurface layer. Under these assumptions, the near-field relationship between the equivalent voltages Vn and in (i = 1 and 2) is denoted by the impedance matrix [Z] as follows.
To achieve the [Z] matrix, the bi-layer metasurface is needed to be decomposed into a four-layer system, in which each metasurface layer only includes a simple structure. The detailed process is outlined in Appendix.
After introducing the self- and mutual-impedance to equivalent circuit model, the dielectric layer in the bi-layer metasurface can be simply treated as a transmission line. In this case, the relationship between the equivalent currents and voltages is written as
Finally, the scattering matrix of the bi-layer coupling system is obtained from the total admittance matrix. According to Eq. (4), the transmission coefficient (S21) of the bi-layer coupling system is given by
Figure 4 presents the calculated S21 parameters from the equivalent circuit model and from simulations. For comparison, we also give the S21 parameter without considering near-field coupling, namely Z12 = 0. It is observed that the results from equivalent circuit (${\textrm{Z}_{12}} \ne 0$) show excellent agreement with simulations, demonstrating the accuracy of our proposed equivalent circuit model. However, the calculated results from the equivalent circuit with Z12 = 0 [see the blue dashed lines] are obviously different with the case of ${\textrm{Z}_{12}} \ne 0$ and simulations. It is concluded that the coupling impedance Z12 significantly affects the transmission performance of the bi-layer system. Hence it is essential to consider the near-field coupling effect in equivalent circuit model. As described in Appendix, the parameter Z12 is determined by the harmonics around the metasurfaces. When the thickness of the dielectric layer is reduced, the computational precision of S parameters can be kept by increasing the number of higher harmonics. More fortunately, when the equivalent circuit is transformed into a $\pi \textrm{ - }typed$ circuit [see Fig. 5], it can guide us how to modify the bi-layer structure for achieving high-efficiency polarization conversion.
Fig. 4. Comparison of transmission coefficients and phase obtained from equivalent circuit and full wave simulations. (a) x-polarization, and (b) y-polarization. It is noted that Z12 = 0 corresponds to the results without considering near-field coupling.
3.2. Modified polarizer
The aforementioned equivalent circuit is a general model for bi-layer metasurface, which can help us to understand the coupling mechanism between metasurface layers. However, this circuit model cannot provide us a guiding scheme how to modify the polarizer for obtaining the optimum device performance. To solve this issue, we further transform the above equivalent circuit into a $\pi \textrm{ - }typed$ circuit. Due to the anisotropy of the metasurface, there are two $\pi \textrm{ - }typed$ circuits corresponding to x- and y-polarizations, but they have similar circuit topology. Hence, we only present the $\pi \textrm{ - }typed$ circuit for x-polarization, as presented in Fig. 5. In this circuit, Ztl and ZS,tl comprise the $\pi \textrm{ - }typed$ circuit of dielectric layer, and Zx and ZS,x form the $\pi \textrm{ - }typed$ circuit of bi-layer metasurface excluding the dielectric layer. These parameters of $\pi \textrm{ - }typed$ circuit are determined by the elements of [Z] and [Ytl] presented in Eqs. (2) and (3),
For y-polarization, the $\pi \textrm{ - }typed$ circuit can be achieved by replacing the components Zx and ZS,x [see Fig. 5] with Zy and ZS,y, and the parameters Zy and ZS,y are still calculated from Eqs. (6–9). In this case the Z11 and Z12 should correspond to the elements of the impedance matrix [Z] for y-polarization.
Figure 6 presents the circuit elements varying as a function of frequency. We observe that in the frequency range of 3 to 16 GHz, the imaginary part of Zx is greater than zero while the imaginary part of Zy is less than zero. Therefore, the metasurface is inductive for x-polarization and capacitive for y-polarization. From Fig. 6, we also find that the value of Zs,x is much higher than that of Zs,tl, implying that the currents almost flow along the branch of Zs,tl. Hence the influence of Zs,x on the circuit can be ignored. Similarly, the ZS,y in $\pi \textrm{ - }typed$ circuit for y-polarization can also be ignored. Since the parameters Ztl and Zs,tl are invariant for dielectric layer with constant thickness, the amplitudes and phases of txx and tyy are simplified as a function of Zx and Zy. Based on these analyses, we can analyze the influence of Zx and Zy on the transmission coefficients txx and tyy. We first let Zy be fixed, and calculate the txx and the phase difference $\Delta \varphi \textrm{ = arg(}{\textrm{t}_{yy}}\textrm{) - arg(}{\textrm{t}_{xx}}\textrm{)}$ for different Zx, as presented in Fig. 7(a). It is observed that the parameter Zx slightly affects the amplitude of txx but significantly impacts the phase difference $\Delta \varphi$. Then we make the parameter Zx be constant, and further investigate the influence of Zy on tyy and $\Delta \varphi$, as presented in Fig. 7(b). We see that the parameter Zy not only effectively affects the amplitude of tyy but also significantly influences the phase difference $\Delta \varphi$. Especially for ${Z_y} - 5\Delta {Z_y}$, the phase difference $\Delta \varphi$ is reduced to around 90° in a wideband from 6 to 13 GHz, as the area marked by grey color. Fortunately, the amplitudes of txx and tyy are approximately equivalent in this frequency range. It implies that the bi-layer structure can be developed into a broadband circular polarization converter by adaptively altering the surface impedance of each metasurface layer along x- or y-direction.
Fig. 7. (a) The effect of ZL,x on transmission coefficient and phase difference. (b) The effect of ZL,y on transmission coefficient and phase difference. Here, $\Delta {Z_x} = 0.1Z$, and $\Delta {Z_y} = 0.1Z$.
The aforementioned $\pi \textrm{ - }typed$ circuit enables us how to modify the bi-layer metasurface to obtain broadband LTC polarization conversion. That is to say, increasing the capacitance along the y-direction or decreasing the inductance along the x-direction can improve the phase condition for generating circular polarization conversion, resulting in the bandwidth extension of the device. Among them, increasing the capacitance along the y-direction is a better way to broaden the bandwidth of the proposed device. According to [19], inserting a metal strip along the y-direction can effectively increase the capacitance along the y-direction and not affects the impedance along the x-direction. Thus, we symmetrically insert four metal strips along the y-direction in each unit cell, as presented in Fig. 8. Here the parameters of the four metal strips are wx3 = 0.32 mm, la = 1.69 mm and lb = 3.2 mm, and the other parameters are identical to those in Fig. 1.
For the modified structure, we calculate the AR of transmission waves and compare it with that of the initial structure. According to [6], the calculated AR is presented in Fig. 9(a). It is observed that, for the initial structure, there are only two narrow bands (relative bandwidth: 25.6% and 7.7%) to realize LTC polarization conversion. In contrast, the relative bandwidth of the modified device is significantly expanded to 69.5%, verifying the validity of our method.
Fig. 9. (a) Comparison of the AR between the initial structure and the modified polarization converter. (b) AR of the optimal polarizer for various angles of incidence.
We also investigate the AR of the modified polarizer for different incident angles (θinc), as presented in Fig. 9(b). We see that the AR bandwidth is relatively stable when θinc is changed from 0° to 30°.
4. Experimental verification
To demonstrate the performance of the modified polarizer, a sample was fabricated using the standard printed circuit board (PCB) technique, which contains 33×33 cells with an area of 400 mm × 400 mm. Figure 10(a) presents the photo of the fabricated sample. The experiment was carried out in an anechoic chamber. As presented in Fig. 10(b), two horns (6–18 GHz) were respectively connected to an Agilent vector network analyzer (N5230C), and the sample was positioned between the two horn antennas. In this measurement, one horn was used to emit the vertically polarized (y-polarized) incident waves, and the other horn was employed to receive the vertically polarized transmission waves to obtain the transmission coefficient tyy. Then, we fix the two horns and rotated the sample by 90° to test the transmission coefficient txx.
Figure 11 presents the comparison of experimental results with simulations, which shows good consistency. Based on these measured transmission coefficients, we further obtain the AR, as illustrated in Fig. 11(b). It is observed that the measured 3 dB AR bandwidth is approximately equal to 69%, which is in good agreement with the simulation results, verifying the performance of the proposed device. The difference between simulations and experimental results may be caused by the fabrication and measurement tolerance.
Fig. 11. The simulated and measured transmission coefficients (txx and tyy) and axial ratio. (a) Transmission coefficients. (b) The phase difference and Axial ratio.
Table 1 compares the proposed LTC polarizer and other reported transmissive LTC polarizers. The comparison shows that our converter has an excellent overall performance, including broadband, ultrathin thickness, and comprehensive incident angle.
Table 1. Comparison with other transmissive circular polarization converters
5. Conclusions
We have presented a LTC converter composed of a bi-layer metasurface separated by a subwavelength dielectric plate. A general circuit model is employed to analyze the near-field coupling effects. Then the general equivalent circuit is further transformed into a $\pi \textrm{ - }typed$ circuit to investigate the influences of surface impedances (Zx and Zy) on transmission coefficients of two orthogonally polarized waves (x- and y-polarization). Under the guidance of the $\pi \textrm{ - }typed$ circuit, a modified polarizer is proposed to broaden the bandwidth of LTC polarization conversion. Simulated results show that the modified polarizer is able to convert a linearly polarized wave into a circularly polarized wave in the frequency range of 6.1 to 12.6 GHz. Furthermore, the broadband performance can maintain for the incident angle up to 30°. We also fabricate a sample to verify the performance of the proposed device experimentally. The experimental results are in good agreement with simulations.
Funding
Natural Science Foundation of Guangxi Province (2021GXNSFDA220003, 2020GXNSFAA297018, 2019GXNSFDA245011); National Key Research and Development Program of China (2021YFA0715404); National Natural Science Foundation of China (62071133, 62161002).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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