A Metamaterial-Based Cross-Polarization Converter Characterized by Wideband and High Efficiency

Abstract

Metamaterial-based polarization converters, which have all kinds of polarizations realizable via adjusting metamaterial parameters, have been springing up at an increasing rate. However, the reported metamaterial-based polarization converters suffer from either limited bandwidth or low polarization conversion ratios. In this study, a metamaterial-based polarization converter consisting of multilayer copper split-ring resonators and a copper ground separated by dielectrics was demonstrated and was characterized by the cross-polarization with wideband and high-efficiency. For normal incidence, the simulated results illustrated that the expanded bandwidth benefited from the superposition of cross-polarization electromagnetic resonances around 2.78, 3.09, 3.68, and 4.54 GHz, and the polarization conversion ratio was higher than 99% in the frequency range of 2.73 and 4.63 GHz. For oblique incidence, the design can provide larger angle tolerance in the investigated band, except for a very narrow stopband. Moreover, the experimental results agreed well with the simulations, which verified the reliability of the performance.

1. Introduction

Polarization is an important concept in electromagnetic (EM) theory [1,2,3]. The polarization converter, which is an important class of EM device, manipulates the polarization state of EM waves and achieves significant progress [4,5,6,7,8,9,10,11]. In the past, polarization converters were achieved by using birefringent crystals based on Faraday effects, which were frequently bulky in size and resulted in much difficulty for miniaturization [12,13,14]. Recently, artificial metamaterials designed by subwavelength meta-atom structures provide an alternative to realize many special phenomena and functions, such as hyper lenses [15,16], negative refraction [17,18], invisibility cloaks [19,20], perfect absorption [21,22,23], and electromagnetic wave polarization manipulation [1,24].

In recent years, metamaterial-based reflective or transmissive polarization converters, with all kinds of polarizations realized via adjusting metamaterial parameters, have sprung up at an increasing rate. Zhang et al. reported a simple and broadband reflective polarization converter at gigahertz frequencies by breaking the symmetry of the cross-shaped resonator [25], and the experimental results demonstrated that the polarization conversion ratio (PCR) was over 80%, from 8.3 GHz to 14.3 GHz, with a relative bandwidth 53%. Regrettably, the dual band polarization conversion appeared as the PCR grew to 90%, which implied that the broadband property of polarization conversion disappeared. Peng et al. demonstrated a linear polarization converter based on 3D split-loop resonators arranged orthogonally [26]. Although the crossed polarization reflection coefficient was close to 1 and resulted in an approximately 100% PCR at 2.65 GHz, the polarization bandwidth was very narrow. Loncar et al. designed and fabricated a polarization converting metasurface composed of three metal pattern layers in the X-band [27]. The polarization conversion with a 99.4% PCR was accomplished by guiding and coupling electromagnetic energy between pairs of orthogonal slots in a ground plane, which were placed at the edges of each unit cell (UC). Unfortunately, the relative bandwidth of cross polarization was only 22%. It follows that the previously mentioned metamaterial-based polarization converters suffer from either limited bandwidth or low PCRs.

To address the above problems, this paper designs a reflection-type metamaterial polarization converter (MPC) based on multilayer split-ring resonators (SRRs), which is capable of converting the line polarization into its orthogonal one. Additionally, four electromagnetic resonances generated by the SRRs can significantly extend the reflection bandwidth of the cross-polarization. In addition, numerical simulations showed that the PCR was greater than 99% in the frequency range of 2.73–4.63 GHz, and the relative bandwidth achieved 52%, which basically coincided with the experiments.

2. Design of the Metamaterial Polarization Converter

2.1. Fundamental Theory

For simplicity, the normal incidence was considered. By starting from anticlockwise and rotating the x–y coordinate system for an angle of 45°, the u–v coordinate system was reached. Furthermore, the incident wave was supposed to be y polarization and vertically strike the surface of the metamaterial along the –z direction. Therefore, the y polarization wave can be decomposed into u and v orthogonal components, as shown in Figure 1a. Mathematically, the electric field of the incident wave is thus expressed as

$${\overrightarrow{\mathrm{E}}}_i={\overrightarrow{\mathrm{e}}}_y{\mathrm{E}}_i{\mathrm{e}}^{jkz}={\overrightarrow{\mathrm{e}}}_u\frac{{\mathrm{E}}_i}{\sqrt{2}}{\mathrm{e}}^{jkz}+{\overrightarrow{\mathrm{e}}}_v\frac{{\mathrm{E}}_i}{\sqrt{2}}{\mathrm{e}}^{jkz}={\overrightarrow{\mathrm{E}}}_{ui}+{\overrightarrow{\mathrm{E}}}_{vi}$$

(1)

where ${\overrightarrow{\mathrm{e}}}_y,{\overrightarrow{\mathrm{e}}}_u$, and ${\overrightarrow{\mathrm{e}}}_v$ are the unit vectors in different coordinate systems, and ${\mathrm{E}}_i$ is the amplitude of the electric field. For reflection-type anisotropic metamaterial, even if the incident wave possesses one (u or v) polarization, the reflection beam generally involves both u and v polarizations. The reflected wave of the electric field is then described as

$${\overrightarrow{\mathrm{E}}}_r=\frac{{\mathrm{r}}_{uu}{\mathrm{E}}_i{\mathrm{e}}^{j(-kz+{\varphi }_{uu})}+{\mathrm{r}}_{uv}{\mathrm{E}}_i{\mathrm{e}}^{j(-kz+{\varphi }_{uv})}}{\sqrt{2}}{\overrightarrow{\mathrm{e}}}_u+\frac{{\mathrm{r}}_{vu}{\mathrm{E}}_i{\mathrm{e}}^{j(-kz+{\varphi }_{vu})}+{\mathrm{r}}_{vv}{\mathrm{E}}_i{\mathrm{e}}^{j(-kz+{\varphi }_{vv})}}{\sqrt{2}}{\overrightarrow{\mathrm{e}}}_v$$

(2)

where r_uu and r_vv are the co-polarization reflection coefficient amplitudes; r_uv (v-polarized wave is incident and u-polarized wave is reflected) and r_vu represent the cross-reflection coefficient amplitudes; ϕ_uu, ϕ_vv, ϕ_uv, and ϕ_vu are the phases corresponding to the reflection coefficients. For given r_uv = r_vu = 0, r_vv = r_uu = r, and ∆ϕ = ϕ_vv − ϕ_uu = 2nπ ± π or r_uv = r_vu = r, r_vv = r_uu = 0, and ∆ϕ = ϕ_vu − ϕ_uv = 2nπ ± π (n is an integer), Equation (2) can be simply stated as

$${\overrightarrow{\mathrm{E}}}_r=\frac{\mathrm{r}{\mathrm{E}}_i{\mathrm{e}}^{-jkz}{\mathrm{e}}^{j{\varphi }_{uu}}}{\sqrt{2}}{\overrightarrow{\mathrm{e}}}_u+\frac{\mathrm{r}{\mathrm{E}}_i{\mathrm{e}}^{-jkz}{\mathrm{e}}^{j({\varphi }_{uu}+\Delta \varphi )}}{\sqrt{2}}{\overrightarrow{\mathrm{e}}}_v=\frac{\mathrm{r}{\mathrm{E}}_i{\mathrm{e}}^{-jkz}{\mathrm{e}}^{j{\varphi }_{uu}}}{\sqrt{2}}{\overrightarrow{\mathrm{e}}}_u-\frac{\mathrm{r}{\mathrm{E}}_i{\mathrm{e}}^{-jkz}{\mathrm{e}}^{j{\varphi }_{uu}}}{\sqrt{2}}{\overrightarrow{\mathrm{e}}}_v={\overrightarrow{\mathrm{e}}}_x\mathrm{r}{\mathrm{E}}_i{\mathrm{e}}^{j{\varphi }_{uu}}{\mathrm{e}}^{-jkz}$$

(3)

or

$${\overrightarrow{\mathrm{E}}}_r=\frac{\mathrm{r}{\mathrm{E}}_i{\mathrm{e}}^{-jkz}{\mathrm{e}}^{j{\varphi }_{uv}}}{\sqrt{2}}{\overrightarrow{\mathrm{e}}}_u+\frac{\mathrm{r}{\mathrm{E}}_i{\mathrm{e}}^{-jkz}{\mathrm{e}}^{j({\varphi }_{uv}+\Delta \varphi )}}{\sqrt{2}}{\overrightarrow{\mathrm{e}}}_v=\frac{\mathrm{r}{\mathrm{E}}_i{\mathrm{e}}^{-jkz}{\mathrm{e}}^{j{\varphi }_{uv}}}{\sqrt{2}}{\overrightarrow{\mathrm{e}}}_u-\frac{\mathrm{r}{\mathrm{E}}_i{\mathrm{e}}^{-jkz}{\mathrm{e}}^{j{\varphi }_{uv}}}{\sqrt{2}}{\overrightarrow{\mathrm{e}}}_v={\overrightarrow{\mathrm{e}}}_x\mathrm{r}{\mathrm{E}}_i{\mathrm{e}}^{j{\varphi }_{uv}}{\mathrm{e}}^{-jkz}$$

(4)

Equation (3) or (4) implies that the reflected wave is linearly polarized, and the polarization direction is perpendicular to that of the original wave. A complete cross-polarization conversion (CPC) is thus realized. And it draws a conclusion that the CPC strongly depends on the reflection coefficient, which relies on the metamaterial parameters. In other words, the limitation on the CPC performance is in the metamaterial parameters.

2.2. Polarization Converter Model

After optimizing the metamaterial parameters, the polarization converter model was proposed. Figure 1b–d depict a UC of the MPC, which consists of three copper split-ring resonators (SRRs) (labeled as SRR1, SRR2, and SRR3 as shown in Figure 1c) and a metal ground separated by four dielectric spacers. The upmost dielectric layer is the PTFE (ε_r = 2.2) with the thickness h₁, and the others FR4 (ε_r = 4.4) with the thicknesses h₂, h₃, and h₄, respectively. And in Figure 1d, the widths of SRR1, SRR2, and SRR3 are respectively $w_1={r^{\prime }}_1-r_1$, $w_2={r^{\prime }}_2-r_2$, and $w_3={r^{\prime }}_3-r_3$. The parameters relating to the UC are listed in

Table 1. Structural Parameters of Converter. (Unit: mm).

Parameter	Value	Parameter	Value
r1	4	g2	1.2
r2	6	g3	2
r3	7.7	h1	2.4
r1′	4.8	h2	3
r2′	6.8	h3	2.4
r3′	8.8	h4	5
g1	1.2	p	22

.

3. Simulations and Discussions

In this paper, CST Microwave Studio was used to simulate the performance parameters of the design. Again, the normal incidence electromagnetic wave possessing y polarization propagated along the -z direction.

The simulation results in the u–v coordinate system are presented in Figure 2a, in which r_vu and r_uv were equal to 0, r_uu was consistent with r_vv, and the phase difference was approximately −180° or 180° in the 2.73–4.63 GHz band. It showed that the reflected electric field agreed with that in Equation (3), and the proposed polarization converter effectively converted y-polarized incident waves into cross-polarized reflected waves in the mentioned broadband range. To estimate the polarization conversion performance, the cross-polarization reflection coefficient amplitude $r_{xy}=\left|E_{xr}/E_{yi}\right|$, the co-polarization reflection coefficient amplitude $r_{yy}=\left|E_{yr}/E_{yi}\right|$, and the cross-polarization conversion rate $PCR=r_{xy}{}^2/(r_{xy}{}^2+r_{yy}{}^2)$ were obtained. Obviously, it can be seen from Figure 2b,c that r_xy (green) is far greater than r_yy (blue), and the PCR was above 99% in the range of 2.73–4.63 GHz, which was superior to the ones found in [28,29,30,31,32] (in which, the reported optimal converters could only operate with a PCR ≥ 99% at certain frequencies, and operated with a PCR < 99% and even at 90% in most of frequency bands) and indicated that the proposed polarization converter was characterized by high efficiency and a wide band, with a relative bandwidth of 52%. Moreover, Figure 2b shows that four resonances, such as 2.78, 3.09, 3.68, and 4.54 GHz, contributed to the perfecter cross-polarization conversion. In other words, four resonant frequencies were brought closer to result in the broadband cross-polarization conversion [33].

To reveal the physical mechanism of the proposed MPC, the co-polarization reflection coefficient magnitudes and the surface current distributions for normal incidence at resonant frequencies of 2.78, 3.09, 3.68, and 4.54 GHz were plotted, with the results shown in Figure 3. In Figure 3a, the black stars and solid lines (red, green, blue, pink, and brown) express the y–y polarized reflection coefficient magnitudes for models with SRR1, SRR2, SRR3, then with SRR1 and SRR2, next with SRR1and SRR3, and finally with SRR2 and SRR3, respectively. The comparison of results (green, pink, and brown solid lines) implied that the SRR1 made no impression on the resonance at 2.78 GHz when depending on SRR2 & SRR3, which is clear in Figure 3b. Furthermore, it is observed from Figure 3b,f that the strong surface current induced on the SRR2 metal was antiparallel to that on the ground sheet at 2.78 GHz, which was equivalent to loop currents and resulted in the magnetic dipole moments m₁ exciting the magnetic field H₁. In addition, H₁ decomposed into H_1y and H_1x components, which were parallel and perpendicular to E_y, respectively. Obviously, H_1y resulted in a x-direction reflected electric field, which indicated that the structure was capable of achieving y to x cross-polarized conversion. In contrast to other designs of polarization manipulating devices in which the coupling between different resonators is exploited [34], in the proposed design, the coupling between corresponding SRRs and the ground plane was dominant.

Furthermore, Figure 3a,c–e demonstrate that SRR2 and SRR3, SRR2 and SRR1, and SRR2 determined the resonances at 3.09, 3.68, and 4.54 GHz respectively, at which a similar physical mechanism occurred as depicted in Figure 3g–i. In brief, the x components (H_1x, H_2x, H_3x and H_4x) of the induced magnetic field were perpendicular to E_y, which signified that the induced electric field was parallel to E_y and could not excite the cross-polarization. Furthermore, the y components (H_1y, H_2y, H_3y and H_4y) of the induced magnetic field were parallel to E_y and induced an electronic field (E_x) perpendicular to E_y, which resulted in the cross-polarization conversion. It can be seen from the simulations that the wideband operation resulted from the superposition of four cross-polarization peaks around 2.78, 3.09, 3.68, and 4.54 GHz.

Next, the polarization converter performance for oblique incidence was considered. For incidence angles θ = 0°, 15°, 30°, 40°, 55°, 70°, and 80°, the cross-polarization reflection coefficient amplitudes are shown in Figure 4. Obviously, the cross-polarization performance could be sustained for θ ≤ 15° when varying from 2.73 to 4.63 GHz. For 30° ≤ θ ≤ 55°, the design presented a narrow stopband near 3.45 GHz, as shown in the inset, which resulted in a dual-band cross polarization conversion. For θ > 55°, the converter performance sharply declined. Clearly, the incidence angle had a great influence on the cross-polarization conversion. The main reason can be seen in Figure 5. For the normal incidence, as shown in Figure 5a, the phase difference ($∆\phi =2\beta ∆z$) of directly reflected wave and emergent wave satisfied the ideal destructive interference condition. Nevertheless, for the oblique incidence, as shown in Figure 5b, $∆{\phi }^{\prime }=2\beta ∆z^{\prime }=2\beta ∆z/\cos \theta$ increased with the increase in incidence angle, which broke the ideal destructive interference condition [28]. Finally, the polarization conversion performance degradation occurred, which resulted in some dips. In spite of this, the results show that the proposed design can provide a larger tolerance of oblique incidence in the investigated band, except for a very narrow stopband.

4. Experimental Validations

Based on the proposed design, a sample with an array of 20 × 20 units, was fabricated and measured. As shown in Figure 6a,b, the measurement for normal incidence exploited the free space method, which was performed in an anechoic chamber using a vector network analyzer. Concretely speaking, the experimental configurations were as follows:

• Two ridge horns operating at 1–6 GHz were connected to a vector network analyzer, and were respectively utilized to generate the y-polarized plane wave at nearly normal incidence (the oblique angle was less than 10°) and received both the co-polarization and cross-polarization reflective waves;
• The fabricated sample was placed in front of the horn antennas, and they were surrounded by absorbing materials. Then, original co-polarized reflection wave amplitude r_yy and cross-polarized reflection wave amplitude r_xy were recorded by the network analyzer respectively, as detailed in Figure 6c.
• As plotted in Figure 6c, the reflective wave amplitude r of a same-sized metal plate was also measured for the calibration. Consequently, r_yy_Exp = r_yy – r and r_xy_Exp = r_xy – r were the available reflection coefficient amplitudes in dB, as shown in Figure 2b.

Furthermore, the experimental PCR could be obtained, as plotted in Figure 2c. When compared with the simulation results, the measured ones suffered from a slight tolerance, which was probably due to the unavoidable manufacturing error in the sample and the difference in incident waves (i.e., the incident waves used in the simulation and the measurement were the ideal plane wave and the quasi-plane wave respectively). Basically, the measured results were consistent with the simulation results, which verifies the polarization conversion performance of the design.

5. Conclusions

In this paper, we proposed a multilayer broadband and high-performance reflective polarization converter based on metamaterial. The significant bandwidth expansion was attributed to the four electromagnetic resonances generated in multilayer SRRs. The nature of the polarization conversion was elucidated by the reflection amplitude decompositions and surface current distributions at four resonant frequencies. Furthermore, the measurement results were consistent with the numerical simulation, which validates the excellent performance of the proposed polarization converter. The design can be used in antenna radiation, target stealth, and electromagnetic measurement, etc.