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Abstract
We report the design, fabrication, and measurement of an ultra-broadband wide-angle reflective cross-polarization convertor using the compact H-shaped metasurface. The significant bandwidth expansion is attributed to the four electromagnetic resonances generated in an H-shaped unit. The simulation results show that the polarization conversion ratio (PCR) of the proposed metasurface is above 90% in the frequency range from 7 to 19.5 GHz and the relative bandwidth reaches 94%. The proposed metasurface is valid for a wide range of incident angles, and the mean polarization conversion ratio remains 80% even though the incident angle reaches 41.5°. The experimental results are in good agreement with the simulation results. Compared with the previous designs, the proposed linear polarization converter has a simple geometry but an excellent performance and hence has potential applications in microwave communications, remote sensors, and imaging systems.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The polarization of electromagnetic (EM) waves refers to the oscillating direction of the electric field in a plane perpendicular to the propagation direction [1]. Effective controlling and manipulating the polarization state of EM waves is highly desirable because many fascinating phenomena are inherently sensitive to polarization [2,3]. Conventional polarization devices are achieved by using birefringent crystals based on Faraday effects [4], which are usually bulky in size and bring much difficulty in miniaturization [5–7]. Recently, metamaterial, artificially designed with subwavelength meta-atoms, has achieved many exotic phenomena and functionalities that cannot be found in conventional materials, such as negative refraction [8], superlens [9], invisibility cloak [10,11], perfect absorption [12] and so on. Thus, metamaterial also provides a potential way to manipulate the polarization state of EM waves [13–15].
On the basis of metamaterial technology, controlling the polarization state of EM waves has attracted great attention and achieved significant progress in recent years. In general, there are two metamaterials configuration for polarization manipulation, transmission mode and reflection mode. For the transmission mode, the polarization convertors can be divided into two categories, in which one is based on the birefringence effect of anisotropic MMs and the other is based on the optical activity of chiral MMs [16–22]. However, neither design can realize wide bandwidth and high efficiency simultaneously. For the reflection mode, there are three main approaches to realizing polarization conversion. One of these approaches is using single-layer metasurfaces, including dual-band [23], Multi-band [24], and broadband polarization converters [25–37]. To expand the bandwidth, many studies have been reported, such as ring/disk cavity structure [28], double V-shaped patches [32], double U-shaped MMs [34], and cut-wire structure [35]. However, most of them cannot realize the ultra-broadband, wide-angle, high-efficiency, and simple-geometry simultaneously. The topology design based on symmetry coding has been presented as another way to realize reflective polarization conversion [38,39]. However, the PCR is under 90% at several frequencies of operating bands. The third method to observe reflective polarization conversion is using multi-layer structures consisting of different metasurface layers [40]. However, the multi-layer structure is limited by complicated fabrication.
In this letter, we propose an ultra-broadband wide-angle linear polarization convertor that uses metasurfaces composed of H-shaped resonators. Compared with the first reflective cross-polarization convertor (which is also composed of H-shaped resonators) that only works in two narrow bands [23], the as-proposed polarization convertor shows much more advance in bandwidth. The broadband transform effect is attributed to the overlap of four polarization rotation resonances generated in an H-shaped unit. Both the numerical simulation and experimental results show that the PCR of the proposed polarization convertor is above 90% in the frequency range from 7 to 19.5 GHz. In addition, the proposed polarizer is valid to a wide range of incident angles, and the mean polarization conversion ratio remains 80% even though the incident angle reaches 41.5°. Since the proposed polarizer is extremely thin and robust to the angle, it is convenient for integration within other ultra-thin devices.
2. Modeling, simulation and experiment
Figure 1(a) schematically demonstrates the structure of the proposed polarization converter, which is composed of a top metasurface and a bottom continuous metallic layer separated by a dielectric layer. When a plane wave with a prescribed polarization illuminates the metasurfce, the reflected wave can be converted to its cross-polarization. Figure 1(b) shows the photograph of the fabricated polarization converter, which has an overall size of 291.2 × 291.2 mm2 and contains 32 × 32 unit cells. The dielectric layer is F4B-2 with relative permittivity of 2.65 and loss tangent of 0.002. The 17 μm thick copper film with an electric conductivity σ = 5.8 × 107 S/m is used as the metallic layer. The inset of Fig. 1(b) shows a unit cell of the design. The periodicity of the structure is p = 9.1 mm. The thickness of the dielectric is t = 3.5 mm. Other geometrical dimensions are presented in Fig. 1(b), in which a = 6.8 mm, b = 4.5 mm, w = 0.3 mm, and g = 1.0 mm.
Fig. 1 (a) Scheme of the proposed polarization converter under the illumination of a linearly polarized wave. (b) Photograph of the fabricated sample. The inset shows a unit cell of the design. (c) Schematic demonstration of the measurement setup.
Figure 1(c) shows the schematic of the measurement setup, which is carried out in an anechoic chamber to avoid electromagnetic interference. The testing system contains a vector network analyzer (N5230A) and two standard gain horn antennas. One of the horn antennas is used to emit x- or y- polarized EM waves at nearly normal incidence (the oblique angle is less than 10°), and the other horn antenna is used to receive x- and y- polarized EM waves. The reflection coefficients are measured through the vector network analyzer. Since the unit cell of the design is symmetric along the diagonal direction, we only need to consider the situation that a y-polarized plane wave illuminates the structure. We define ryy = |Eyr|/|Eyi| as the reflection coefficient for co-polarization, where |Eyi| and |Eyr| correspond to the magnitude of incident and reflected electric fields in the y direction, respectively. In addition, we define rxy = |Exr|/|Eyi| as the reflection coefficient for cross-polarization, where |Exr| represents the magnitude of reflected electric field in the x direction.
Figure 2(a) shows the measured cross-polarized (rxy) and co-polarized (ryy) amplitude reflection spectra, which are in good agreement with the simulation results based on Finite-Difference Time-Domain (FDTD) method. It is observed that the co-polarization (ryy) is lower than −10 dB and the cross-polarization (rxy) is higher than −1 dB in the frequency range from 7 to 19.5 GHz, which means that the illuminated y-polarized wave has been efficiently converted to x-polarized wave after reflection. Furthermore, four resonant frequencies ( and ) can be found at 7.19 GHz, 9.10 GHz, 14.08 GHz, and 18.92 GHz, respectively, which means the conversion efficiency is extremely high at these four frequencies.
Fig. 2 The simulated and experimental results of the proposed polarization converter. (a) Cross-polarized (rxy) and co-polarized (ryy) amplitude reflection spectra. (b) Polarization conversion rate (PCR) spectra.
The polarization conversion rate (PCR) is often used to evaluate the efficiency of a polarization converter, which is defined as PCR = rxy2/(rxy2 + ryy2) [23]. Figure 2(b) shows the measured PCR of the proposed design, which is in good agreement with the simulated result. As expected, the PCR is above 90% in the frequency range from 7 to 19.5 GHz, and reaches near unity at the four resonance frequencies. The relative bandwidth is up to 94% (PCR>90%), which is broader than the previous designs [28–35]. A small discrepancy between the experiment and simulation can be found in Fig. 2, which is attributed to the following two reasons. First, an ideal normally incident plane wave is used in simulation, which cannot be achieved in experiment since the two antenna horns cannot be reunited. Second, the geometry of the proposed design is unlimited in simulation; however, the fabricated sample has a finite size.
Furthermore, compared with the other polarization converters, the proposed one demonstrates better performance with simple geometry. Table 1 presents a comparison between the proposed converter and other reported reflective linear polarization converters in microwave frequency ranges. From the comparison, it can be observed that the proposed converter has an ultra-wide frequency band in which the PCR is greater than 90%, indicating a better performance.
Table 1. Comparison with other wideband polarization converters
3. Discussion
Figure 3 schematically shows the working principle of the proposed polarization converter. The normally incident y-polarized EM wave, can be decomposed into two perpendicular components as , and accordingly the reflected wave can be expressed as . Here, and indicate two directions that are rotated 45° in the counterclockwise direction from the x-axis and y-axis, respectively. ru and rv mean the reflected coefficients along the u-axis and v-axis, respectively. The proposed polarization converter can be treated as an anisotropic material with dispersive relative permittivity and permeability due to the asymmetric of the structure, thus leading to a phase difference (Δφ = |φu−φr|) between ru and rv. If ru≈rv and Δφ = 180°, either Eru or Erv will be opposite to their incident direction, then the synthetic field Er will be along the x-direction, as shown in Fig. 3(a). In other words, the oscillation direction of electric field is rotated 90° after reflection by the structure. Figure 3(b) gives the reflection amplitudes and phase difference (Δφ), when the incident plane EM wave is polarized along the u- and v-axis, respectively. It can be seen that the reflection amplitudes are nearly equal to one and the phase difference is roughly 180° from 7 to 19.5 GHz, which leads to an ultra-broadband and high-efficiency polarization conversion. In particular, at the resonance frequencies of 7.19 GHz, 9.10 GHz, 14.08 GHz and 18.92 GHz, the phase difference is close to 180°.
Fig. 3 (a) The working principle of the polarization converter. (b) The reflected amplitudes and phase difference, when the electric field of incident waves along u-axis and v-axis, respectively.
To understand the physical mechanism of the proposed polarization converter, we then simulated the surface current distributions on the top metasurface and bottom layer at resonant frequencies of 7.19 GHz, 9.10 GHz, 14.08 GHz, and 18.92 GHz, respectively, as shown in Fig. 4. We can see that the surface currents along the H-shaped resonator are antiparallel to those on the background sheet at 7.19 GHz and 9.10 GHz. It means that they are forming current loops in the intermediate dielectric layer, which is known as magnetic resonance. In contrast, the surface currents along the H-shaped resonator are parallel to those on the background sheet at 14.08 GHz and 18.92 GHz, which corresponds to electric resonance. These four resonances are vital to realize high-efficiency and wide-bandwidth. Actually, the broad bandwidth enhancement operation results from the superposition of multiple PCR peaks around resonance frequencies.
Fig. 4 Distributions of the surface current on the metallic parts of the metasurface unit cell and metallic ground sheet at four resonant frequencies: (a) 7.10 GHz, (b) 9.10 GHz, (c) 14.08 GHz, and (d) 18.92 GHz.
It is important to investigate the angular dependence of the proposed H-shaped polarization converter. Figures 5(a) and 5(b) show the simulated reflection map of ryy and rxy as a function of the frequency and of the incident angle. We can see that the bandwidth of the proposed polarization converter is slightly reduced with the increase of the incident angle, which is attributed to the destructive interference at the surface of the metasurface under oblique incidence. At higher frequencies, the destructive interference affects more drastically when incident angle is increased. In addition, from Figs. 5(a) and 5(b) we find that a dip simultaneously appears at around 12.7 GHz, which implies a strong absorption. In order to quantify the conversion efficiency of the proposed polarization converter under oblique incidence, Fig. 5(c) shows the mean value of the reflectivity PCR in the frequency range from 7 to 19.5 GHz. It is clear that the mean PCR remains as high as 96% when the incident angle changes from 0 to 12.5°. Even though the incident angle reaches 41.5°, the mean PCR is still above 80%. Therefore, the proposed polarization converter has a good performance for oblique incidence.
Fig. 5 Reflection map for (a) co-polarization (ryy) and (b) cross-polarization (rxy) as a function of the frequency and the angle of incidence. (c) Polar plot of simulated values of mean PCR in the frequency range from 7 to 19.5 GHz.
4. Summary
In conclusion, we have presented both theoretically and experimentally that array of H-shaped metasurface can convert the linear polarization of light with ultra-broadband and high-performance. The significant bandwidth expansion is attributed to the four electromagnetic resonances generated in an H-shaped unit. Both the numerical simulation and measurement results show that the PCR of the proposed metasurface is above 90% in the frequency range from 7 to 19.5 GHz and the relative bandwidth reaches 94%. We also investigated the performance of the proposed converter for oblique incidence, and found that the mean PCR remains above 80%, even though the incident angle reaches 41.5°. The proposed linear polarization converter has a simple geometry but an excellent performance and hence has many potential applications in the microwave, terahertz, and even optical frequencies.
Funding
National Natural Science Foundation of China (NSFC) (11304253); Fundamental Research Funds for the Central Universities (XDJK2016A019); Undergraduate Science and Technology Innovation Fund (201810635040, 20171802001).
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