1. IntroductionPolarization is an important characteristic of electromagnetic (EM) wave, and fully manipulating the polarization state is highly desirable in several electromagnetic applications.[1,2] Metamaterials, which have extraordinary electromagnetic properties that natural materials do not have,[3,4] provide a very effective way to manipulate several basic properties of the EM wave and can be applied to polarizers,[5–7] lenses,[8,9] high gain antennas,[10,11] and invisible cloaks.[12,13] Compared with the conventional polarizers using the Faraday effect[14] and twisted nematic liquid crystal, the polarization converters based on the metamaterials are relatively thin (subwavelength thickness) and light. On the basis of metamaterial technology, many studies have been devoted to controlling the polarization state of EM waves recently. Many polarization converters based on anisotropic and chiral metamaterials have been proposed.[15–17] However, these polarizers suffer from narrow bandwidth, which extremely limits their practical applications. To expand the bandwidth, stacked multilayer structures,[18–24] gold helix structures,[25] and anisotropic high-impedance surfaces[26] can be utilized. However, these polarizers are hard to fabricate and integrate into the existing systems due to their complex structures or unacceptable thickness. Planar polarizers based on metasurfaces that are ultra-thin layered two-dimension metamaterials[27–35] were designed to achieve both wideband bandwidth and higher conversion efficiency. Nevertheless, these proposed polarization devices may not keep high polarization efficiency within a broad range of incident angles. Thus, polarization devices with high polarization efficiency, wideband, and high angular tolerance are highly desirable.
Rendering flexibility to metamaterials can make it possible to adhere flexible devices to all surfaces or wrap transparent and light metamaterials around objects, from which many terahertz and microwave applications[36–45] can significantly benefit. Kamali et al.[39] showed that cylindrical lenses covered with metasurfaces could be used as aspherical lenses to focus light onto a point by using a flexible substrate. Youn et al.[45] proposed and demonstrated an optically transparent and flexible microwave absorber that provided a method to use a three-dimensional (3D) design. Therefore, flexible metamaterials open up a whole new range of practical applications. Additionally, to the best of our knowledge, there is a lack of polarizer based on flexible metamaterials or metasurfaces at microwave bands.
In this paper, we design a reflective broadband linear polarizer composed of metallic disks and asymmetric arc metallic wires placed over flexible substrates. The long arc metallic wire resonator provides the main resonances. The short arc metallic wire and the metallic disk work as couplers to adjust the resonance frequencies and intensities. Both simulated and experimental results have demonstrated that the designed polarizer has a wide operating bandwidth from 11.3 GHz to 20.2 GHz under normal incidence of both x- and y-polarized waves. It can also keep high-efficient polarization conversion when the incident angle increases from 0° to 45°. The designed polarization device can also be applied for conformal design due to flexible substrates. The simulation and experiment results have demonstrated that our proposed polarizer can still keep high polarization conversion efficiency even when adhered to convex cylindrical surfaces. The proposed periodical metallic structure has great potential application values in the microwave, terahertz, and optic regimes.
2. Structure design and theoretical analysisFigure 1 shows the structure of the polarization converter used in the simulations and experiments. The polarizer is composed of four layers with the periodic metallic structure on the top and the metallic ground plane on the bottom separated by two flexible material layers. The
thick copper film is used as the metallic parts and polyethylene terephthalate (PET) is chosen as the flexible material with a thickness of d1=0.12 mm. The relative dielectric constant of PET is 2.86 with a dielectric loss tangent of 0.053. Because the thickness of PET is not enough for the microwave polarizer design, polyvinyl chloride (PVC,
) with a thickness of d2=2 mm is filled in the area between the PET layer and the ground plane. The top metallic unit cell is composed of three parts, the long arc metallic wire, the short arc metallic wire, and the metallic disk. As shown in Fig. 2(a), the final geometrical parameters of the unit cell are: w = 0.4 mm, r1 = r2 = 2.4 mm, r3 = 1.5 mm, α = 190°, and β = 33°. The designed polarizer consists of 48 × 48 square unit cells (5 mm ×5 mm). The top metallic structure can be regarded as an anisotropic metamaterial layer for its asymmetrical structure along the x-axis and y-axis.
To illuminate the polarization conversion theory, we assume that an x-polarized electromagnetic wave is normally incident on the polarization converter (the same as a y-polarized wave). The electronic field of the incident electromagnetic wave denoted as
can be decomposed into the u-polarized and v-polarized components denoted as
and
, respectively, as shown in Fig. 2(b). In this way, the electric field vector
in the incident wave and the reflected wave can be expressed as Eqs. (1) and (2), respectively
where
and
are the unit vectors in the
u-axis and
v-axis directions,
ruu or
rvv represents the co-polarization reflection coefficient, and
ruv or
rvu represents the cross-polarization reflection coefficient, respectively, at the
u-polarized or
v-polarized wave incidence. Due to the symmetric structure along the
u-axis, the amplitudes of
ruv and
rvu are near to 0, which means that no cross-polarized reflection exists at
u-polarized and
v-polarized EM wave incidences. According to these conditions, equation (
2) can be written as
where
and
.
Then, if conditions
are satisfied (
n is an integer), then
the polarization direction of the reflected light is transformed to the
y-axis.
Figure 3 presents the simulated magnitudes and phases of ruu and rvv of the optimized polarizer based on Computer Simulation Technology (CST) Microwave Studio. It is clear that the magnitudes of ruu and rvv are close to 1 in Fig. 3(a), and the absolute value of phase difference
is close to 180° from 11.3 GHz to 20.2 GHz in the blue area in Fig. 3(b). So the conditions in Eqs. (4) and (5) are met, which means that the polarization direction of the reflected wave is rotated by 90° with the proposed polarizer. From the view of resonance,[33] the electric field along the v-axis can excite two magnetic resonances (I and III), and along the u-axis can excite one electric resonance (II). Here, the electric (magnetic) resonance does not necessarily mean out-of-phase (in-phase) reflection in Ref. [27], and the resonance type is judged through surface current distributions at the corresponding resonant frequency. Given the length of this paper, the current distributions at the three resonant frequencies are not presented here. In fact, the unit cell of the designed polarizer is a combined structure and it can excite multiple resonances. Moreover, main resonances are excited by the long arc metallic wire and the metallic disk because the resonance frequency of the short arc wire is out of the designed frequency band.
3. Simulation resultsTo verify the wideband property of the designed metasurface, full-wave simulations are performed with frequency domain solver in CST Microwave Studio. We set the periodic boundary conditions in x and y directions and open conditions along the z-axis. The polarization conversion ratio (PCR) can be defined as
where
rxx or
ryy is the co-polarization reflection coefficient, and
ryx or
rxy is the cross-polarization coefficient when
x-polarized or
y-polarized EM wave propagates along the
z-axis direction. Because of the symmetric structure along the
u-axis, PCR, co-polarization, and cross-polarization reflection coefficients are the same under the normal incidence of
x- or
y-polarized EM wave. We can find that
rxy and
ryx are higher than −1 dB, and
ryy and
rxx are lower than −10 dB in the frequency range from 11.3 GHz to 20.2 GHz in Fig.
4(a). It can also be seen from Fig.
4(a) that there are two resonant frequencies, one at 13.0 GHz and the other at 19.2 GHz. As shown in Fig.
4(b), PCR is higher than 90% from 11.3 GHz to 20.2 GHz under normal incidence. At the two resonant frequencies of 13.0 GHz and 19.2 GHz, the values of PCR are close to 100%. The simulation results demonstrate that the proposed polarizer can achieve wideband linear polarization conversion.
3.1. Impact of metallic disk radiusTo investigate the effects of the metallic disk on polarization conversion, we have carried out numerical simulations by changing the radius of the metallic disk. Figure 5(a) indicates that r3 can have great effects on the resonant frequencies and operating bandwidth under normal incidence of the y-polarized wave (the same as the x-polarized wave). With the increase of the radius of the metallic disk, the bandwidth decreases and the first resonant frequency shows a blue shift while there is a large red shift on the second and third frequencies. When r3 = 1.5 mm, the first two resonant frequencies come into one frequency. The above analysis is also available for the oblique incidence under θ = 40° as shown in Fig. 5(b), except that there are only two resonant frequencies under oblique incidence even if r3 varies from 1.1 mm to 1.6 mm. Additionally, we calculate the minimum PCR between the first resonant frequency and the last resonant frequency from the simulated results. As shown in Fig. 6, when the radius of the metallic disk r3 becomes longer, the minimum PCR gradually decreases under normal incidence, but it gradually rises when r3 is lower than 1.6 mm under θ = 40°. In particular, the minimum values of PCR are all higher than 90% under both θ = 0° and θ = 40° when r3 is 1.5 mm.
3.2. Incident angle insensitivity analysisThe most important criterion for obtaining a very weak angular dependence is to avoid coupling to propagating first negative diffraction orders, which is related to the unit cell periodicity p of the polarization conversion metasurface according to Braggʼs law.[46] In addition, the thickness of the substrate also exerts strong influence on the angle independence.[33] As shown in Fig. 7(a), the electromagnetic waves run back and forth in the dielectric substrates. The reflected coefficient on the boundary between the PET and PVC layer is
, where
and
represent the real parts of dielectric constants of the PET and PVC materials, respectively. Due to the thin thickness d1 of the PET and the small value of
, the two layers can be equivalent to one PVC layer with the thickness
in Fig. 7(b). The additional phase due to the oblique incidence is defined as
where
and
are the phases of the incident wave in the dielectric layer under oblique incidence and normal incidence, respectively,
γ represents the refraction angle, and
k0 is the wave number in the air. When other parameters are the same, thinner thickness leads to less additional phase, which would be beneficial to keep better polarization conversion ratio under oblique incidence.
Our designed polarizer has optimized the size and thickness of the unit cell; here, we make a comparison with some other reflection linear polarization converters in Table 1. In Table 1, BW indicates the operating absolute bandwidth (PCR
) of the metasurface. The parameters p and t are the unit cell periodicity of the polarization conversion metasurface and the dielectric substrate thickness of the metasurface, respectively.
(max) is defined as the maximum additional phase under the incident angle of 45° and
is the wavelength of the incident wave at the lowest operating frequency in the air. The incident angle dependence can be reduced by our designed polarization converter despite the fact that the bandwidth is reduced at the same time.
Table 1.
Table 1.
 Table 1.
Comparison with other wideband polarization conversion metasurfaces.
.
|
p/mm |
t/mm |
BW/GHz |
|
|
| [29] |
12.5 |
4.0 |
5.2–12.1 |
0.504 |
15.58° |
| [32] |
10 |
3 |
6.84–16 |
0.533 |
28.07° |
| [33] |
6.4 |
1.6 |
12.4–27.96 |
0.596 |
28.87° |
| Present study |
5 |
2.12 |
11.3–20.2 |
0.338 |
17.07° |
| Table 1.
Comparison with other wideband polarization conversion metasurfaces.
. |
Then, we study the polarization conversion of the optimized structure under the oblique incidence of y-polarized EM waves. Figure 8(a) presents that the first resonance becomes weaker and amplitudes of ryy at the last resonant frequency remain below −20 dB with the increase of θ from 0° to 45°. Meanwhile, figure 8(b) shows that the cross-polarization reflection coefficients are not greatly affected by the incident angle from 0° to 45°. The values of PCR are calculated from those simulated co- and cross-polarization reflection coefficients. As can be seen from Fig. 9(a), even if θ is increased to 40° and 45°, the values of PCR can still keep higher than 90% from 11.2 GHz to 20.3 GHz and over 85% from 11.2 GHz to 20.5 GHz, respectively. BW remains nearly unchanged as θ increases from 0° to 45°. The simulated results further demonstrate that our designed polarization converter can work well with a wide range of incident angles. Furthermore, compared with the symmetric structure composed of the split-ring resonators and metallic disk resonators (together hereinafter referred to as DSRRs) in Ref. [31], our proposed asymmetric structure can avoid the split of the bandwidth which is caused by the absorption, as shown in Figs. 9(a) and 9(b).
3.3. Current distributionsFrom the perspective of resonances, the surface current distributions are given in Fig. 10 at resonant frequencies under r3 = 1.4 mm and r3 = 1.5 mm (different resonant numbers as shown in Fig. 5(a) and similar minimum PCR values in Fig. 6) to explain the physical mechanism of the reflected linear polarization converter. There are three resonances at 12.5 GHz, 14.0 GHz, and 19.8 GHz when r3 = 1.4 mm. The surface current distributions at these resonant frequencies on the top metallic structure and metallic ground sheet are shown in Figs. 10(a)–10(c). The top metallic structure forms an equivalent surface current at 12.5 GHz and 14.0 GHz, which is antiparallel to the current flowing on the bottom ground plane. In this case, an equivalent circulating current is formed between the top metallic structure and the metallic ground, and magnetic resonances are created at those two resonant frequencies. On the contrary, the surface current on the top metallic structure is parallel to the current on the ground plane at 19.8 GHz, which can be regarded as an electric dipole that can excite the electric resonance. Under r3 = 1.5 mm, there is a magnetic resonance at 13.0 GHz and an electric resonance at 19.2 GHz in the same analytical way, as shown in Figs. 10(d) and 10(e).
We can find that the current on the metallic ground sheet at 14.0 GHz in Fig. 10(b) is much weaker than that at other resonant frequencies, which means that the magnetic resonance at 14.0 GHz is easily broken. Moreover, with the increase of the incident angle, the magnitude of the electric field along the u-axis and v-axis (y-polarized wave decomposed into the two directions) would decrease, which would lead to the weaker magnetic resonance. Thus, the second resonant frequency would disappear when the incident angle θ = 40° as shown in Figs. 5(a) and 5(b).
Furthermore, it can be seen that most of the current distributes on the long arc metallic wire and metallic disk and a little on the short arc metallic wire, which confirms long arc metallic wire and metallic disk make greater contributions to resonances.
It is also necessary to point out that the y-polarized wave (the same as the x-polarized wave) could excite all the three resonant modes (I), (II), and (III) in Fig. 3(a) because the electric field of it can be decomposed into two components along the u-axis and v-axis, respectively. These resonant modes would generate resonance frequencies of different positions and numbers through mutual coupling.
3.4. Conformal performanceTo study the conformal performance, the designed polarizer and the pure metallic sheet are bent on convex cylindrical surfaces respectively with different curvature radii R = 250 mm and R = 500 mm, as shown in Figs. 11(a), 11(b) and 11(c), 11(d). We define
as the co-polarization radar cross section (RCS) and
as the cross-polarization RCS under the y-polarized plane wave
where
D is the distance from the metasurfaces to the observation points,
and
are the scattered and incident electric fields, respectively, and
and
are electric fields along the
x-axis and
y-axis, respectively. RCS can be used to analyze the polarization conversion of our designed polarizer on curved surfaces with the same
D based on Eq. (
9). Figure
11(a),
11(c) and
11(b),
11(d) show the simulated 3D bistatic RCS including co-polarization RCS
and cross-polarization RCS
under normal incidence of
y-polarized EM wave with our designed polarizer and the same shaped metal cylindrical metallic sheets, respectively. For metallic curved sheet, main scattered energy distributes in the co-polarization component and little in the cross-polarization component, as can be seen in Figs.
11(b) and
11(d). In contrast, cross-polarization RCS is much higher than co-polarization RCS in the main scattered area for our designed polarizer under
R = 250 mm and
R = 500 mm in Figs.
11(a) and
11(c), which indicates that our proposed polarizer conformal on the curved surface can achieve polarization conversion. Besides, in the column titled with cross-polarization of Figs.
11(a) and
11(c), when
R increases from 250 mm to 500 mm, the energy of the scattered wave propagating along the +
z-axis would increase and the beamwidth of the lobe along the +
z-axis in the
xoz plane would be narrower, which indicates that the energy of the scattered wave would be more concentrated.
4. ExperimentsTo experimentally show properties of the proposed polarization converter, some prototypes are fabricated on PET substrate and stuck on the PVC substrate with these parameters d1 = 0.12 mm, d2 = 2 mm, w = 0.4 mm, r1 = r2 = 2.4 mm, r3 = 1.5 mm, α = 190°, and β = 33°. Figure 12 shows the photo of the fabricated prototype and the measurement setup. The sample is placed in the front of the horn antennas surrounding by absorbing materials, and the horn antennas are fixed on the two vertical arms of the rotating pedestal. The centers of the sample and horn antennas are set at the same height. One horn antenna is used as the source and the other is used for receiving reflected waves to obtain the co- and cross-polarization reflective coefficients by rotating the receiving antenna by 0° and 90°. Both antennas are connected to an Agilent vector network analyzer (N5245A). The horizontal arms connected to the rotating pedestal can be rotated to obtain the reflective coefficients under different incident angles. However, the separation angle between the two antennas is set to be 5° firstly because of their overlap positions under normal incidence. It should be noted that the metal ground sheet is also measured for the sake of normalization.
Figure 13 and 14 illustrate the simulated and measured reflective coefficients, which indicate that the experiment results are in good agreement with numerical predictions. We can clearly observe two resonant frequencies when the incident angle varies from 5° to 45°. PCR is also given in Fig. 15(a), which is in good agreement with the simulation. Moreover, in order to show the conformal feature of our proposed polarizer, some arc foams have been made and the sample is stuck on the different convex cylindrical surfaces of them and tested. Limited by the testing condition, the measured bistatic RCS cannot be obtained at present and we use S-parameters to evaluate the polarization conversion. The same cylindrical metal ground sheets are measured for the sake of normalization without taking influences of scattering waves brought by the cylindrical structure into consideration. Figure 15(b) shows the calculated PCR from the measured results. The designed polarization converter can keep high polarization conversion efficiency from 11.9 GHz to 20.0 GHz even it is bent on convex cylindrical surfaces.
