1 Introduction

Polarization is a very important and useful property of electromagnetic (EM) waves. Effective manipulation of EM waves from the microwave to optical frequency bands continues to receive much attention from researchers worldwide. Conventional methods of controlling wave polarization, such as through birefringence of natural materials and optically active materials, usually require a relatively long propagation distance to obtain sufficient phase accumulation. Hence, these conventional methods of manipulating polarization involve bulky devices. Alternative means of polarization control are needed for practical applications that are not so bulky. Fortunately, metasurfaces, which are two-dimensional metamaterials composed of sub-wavelength metamaterial unit cells [1], can tailor almost all of the basic properties of an EM wave, including amplitude, phase, polarization, and propagation modes. Based on metasurfaces, a variety of wave-manipulation effects have been realized in a wide frequency range, including negative refractive index [2], anomalous reflection and refraction [3–5], EM energy absorption [6], and digital beam steering [7]. Metasurfaces are also well suited in modulating the polarization of EM waves [8–18]. Recently, several polarization converters based on metasurfaces have been reported [19–21]. For example, Grady et al. [19] demonstrated a very efficient linear polarization converter using a cut-wire array based on the Fabry–Perot-like cavity in the terahertz band. A broadband circular and linear polarization conversion using thin birefringent reflective metasurfaces was reported in Ref. [20]. Shi et al. [21] proposed a linear polarization converter consisting of ring/disk resonators that use plasmon hybridization. Cheng et al. [22] have designed a reflective polarization converter using metallic disks and split-ring resonators operating in the terahertz region. An efficient multiband and broadband cross-polarization converter based on slotted L-shaped nanoantennas and operating in the terahertz band has also been reported [23]. Compared with the conventional polarization-manipulating device, these metasurfaces-based converters have advantages including sub-wavelength thickness, high-efficiency conversion, and wide working bandwidth. However, till now, dual-band and high-efficiency polarization converter operating at microwave frequencies still remains an issue for practical device applications.

In this paper, a dual-band and high-efficiency polarization converter can be realized based on metasurfaces in microwave frequency regime. The polarization conversion metasurfaces consist of a dielectric substrate sandwiched between double split-ring resonators (DSRR)/disk resonators and a ground plane that converts a given linearly polarized wave to its cross-polarized wave over two bands: Ku (11.5–20.0 GHz) and Ka (28.8–34.0 GHz). The converter can be regarded as a composite of DSRR and disk resonators, both of which have been demonstrated to convert the linearly polarized EM wave to its orthogonal direction [22, 24]. The electric response of the DSRR/disk is to generate five plasmon resonance modes that create the dual-band response and high polarization conversion efficiency. The simulated and experimental results indicated that this converter can convert a linearly polarized incident wave to its cross-polarized wave for both normal incident x- and y-polarized EM waves. The polarization conversion ratio (PCR) is above 0.94 for the Ku-band and 0.90 for the Ka-band. Additionally, at 10.568, 21.487, 27.054, and 34.958 GHz, a linearly incident polarized wave is converted to a circularly polarized wave that is left-handed or right-handed depending in frequency. Therefore, the proposed structure can also be used as a linear-to-circular converter. Furthermore, the dual-band and high-efficiency polarization can be sustained as the incident angle is increased to 45°. The converter is also polarization-selective in that only the x- and y-polarized waves can be converted.

2 Structure design and simulation

The unit cell of the proposed converter consists of metallic DSRR/disk resonators and a metallic ground sheet separated by a dielectric substrate, as shown in Fig. 1a, b. The substrate is TLA-6, with relative permittivity of 2.62, loss tangent of 0.0012, and thickness \(h = 2.0\;{\text{mm}}\). The periodicity of the metasurfaces unit cell is \(p = 4.0\;{\text{mm}}\). By a delicate parameter sweep process, the other geometric dimension parameters are as follows: \(a = 1.8\;{\text{mm}}\), \(b = 2.2\;{\text{mm}}\), \(r_{1} = 0.5\;{\text{mm}}\), \(r_{2} = 1.75\;{\text{mm}}\), \(r_{3} = 1.5\;{\text{mm}}\), \(r_{4} = 1.2\;{\text{mm}}\), \(r_{5} = 0.9\;{\text{mm}}\). The top metallic layer and the metallic ground sheet were modeled as copper films of thickness 0.035 mm and conductivity \(\sigma = 5.8 \times 10^{7} \;{\text{S}}/{\text{m}}\).

Fig. 1
figure 1

Unit cell of the proposed structure: a front view; b perspective view; c polarization of the incident wave; and d photograph of the experiment sample

Full size image

The DSRR/disk used in our design has a symmetric axis defined by the v-axis angle at 45° with respect to the x direction as shown in Fig. 1c. Therefore, the incident and reflected electric fields can be decomposed into two components parallel to the u- and the v-axis. Under illumination by a x-polarized or y-polarized wave, the reflected electric fields are polarized along the u- and v-axes and have almost the same amplitude. Accordingly, if we tune the structural parameters to yield a phase difference of 180° between these two components of the reflected wave, the reflected wave is rotated 90° to the incident wave, i.e., the x(y)-polarized incident wave is converted to a y(x)-polarized reflected wave. Moreover, if the phase difference generated by the two components of the reflected wave is 90° or −90°, the x(y)-polarized wave is converted to a circularly polarized wave.

A numerical simulation was performed using the commercially available software CST MICROWAVE STUDIO, which is based on the finite integration technique (FIT). In the simulation, periodic conditions are used in the x and y directions, and the absorbing boundary conditions are used for the z direction. The model is excited using a Floquet port with a linearly polarized wave at normal incidence.

To better understand the polarization conversion of the designed structure, we introduce the cross- and co-polarization reflectances \(r_{xy} = \left| {\varvec{E}_{xr} /\varvec{E}_{yi} } \right|\) and \(r_{yy} = \left| {\varvec{E}_{yr} /\varvec{E}_{yi} } \right|\), respectively, for y-polarized incidence; subscripts i and r indicate incident and reflected wave, respectively, and subscripts x and y indicate the polarization direction of the EM wave. The PCR is defined as \({\text{PCR}} = r_{xy}^{2} /\left( {r_{xy}^{2} + r_{yy}^{2} } \right)\) for the y-polarized incident wave [25]. The phase difference between \(\varvec{E}_{xr}\) and \(\varvec{E}_{yr}\) can be calculated from \(\Delta \varphi_{xy} = \arg (r_{xr} ) - \arg (r_{yr} )\); \(\Delta \varphi_{xy}\) can take arbitrary values within [−180°, 180°] depending on the frequency, indicating that all possible polarization states (i.e., circular, linear, and elliptic) are realizable for the reflected EM waves [26]. Hence, when \(r_{xy} = 1\) and \(\Delta \varphi_{xy} = 0^{ \circ }\) (or \(\Delta \varphi_{xy} = \pm 180^{ \circ }\)), the linearly polarized wave is converted to its cross-polarized wave; when \(r_{xy} = r_{yy}\) and \(\Delta \varphi_{xy} = \pm 90^{ \circ }\), the linearly polarized wave is converted to a circularly polarized wave.

3 Results and discussion

3.1 Simulation and experiment results

In experiments, the designed structures were fabricated into a 90 × 80 unit cell sample (360 mm × 320 mm) by the conventional printed circuit board (PCB) technique with the same structural parameters as the simulation model, and a part photography of the sample is shown in Fig. 1d. A double-side copper-cladding PCB board is etched with resonator patterns on the one side, while the copper cladding is kept on the other side. An Agilent E836B network analyzer and two linearly polarized standard gain horn antennas were used to transmit and receive the EM wave. The reflection measurement was calibrated by replacing the sample with a metal sheet of the same size.

With mirror symmetry along the diagonal axis of the designed structure, the amplitude and phase for the co-polarization and cross-polarization reflected waves are the same regardless whether the incident wave is x- or y-polarized. Therefore, for brevity, we only demonstrate the simulation and experiment results for the y-polarized incident wave in Fig. 2. From Fig. 2a, it can be clearly seen that the simulated cross-polarization reflectance of \(r_{xy}\) is larger than 0.965 in the frequency range from 11.5 to 20.0 GHz, and the simulated co-polarization reflectance of \(r_{yy}\) is less than 0.23. For the experiment, in the frequency range from 12.10 to 20.70 GHz, the cross-polarization reflectance of \(r_{xy}\) is larger than 0.92, whereas the co-polarization reflectance of \(r_{yy}\) is less than 0.25. In Fig. 2b, in the frequency range from 11.5 to 20.0 GHz, both the simulated and experimental PCR are higher than 0.94, which means that the y-polarized incident wave can be efficiently converted to the x-polarized wave. The fractional bandwidth is about 54 % for frequencies from 11.5 to 20.0 GHz. Meanwhile, from Fig. 2a, for frequencies from 28.8 to 34.0 GHz, we observe that the simulated cross-polarization reflectance of \(r_{xy}\) is larger than 0.94, and the simulated co-polarization reflectance of \(r_{yy}\) is less than 0.27. For the experiment, the cross-polarization reflectance \(r_{xy}\) is larger than 0.90 for frequencies from 27.70 to 33.10 GHz, whereas the co-polarization reflectance of \(r_{yy}\) is less than 0.30. From Fig. 2b, the PCR rises above 0.90 for both simulation and experiment for frequencies from 28.8 to 34.0 GHz, which means most of the energy of the y-polarized incident wave is converted to a x-polarized wave. The fractional bandwidth is about 17 % in the frequency range from 28.8 to 34.0 GHz.

Fig. 2
figure 2

Experimental and simulated results under a y-polarized incident wave. a Reflectance of \(r_{xy}\) and \(r_{yy}\). b PCR

Full size image

Based on these results from simulations and experiments, the proposed metasurfaces can be functionalized as a dual-band and high-efficiency polarization converter. As shown in Fig. 2, the experimental results are in good agreement with the simulation results; nevertheless, there are slight differences. First, in the simulation, the unit cell boundary condition was used, which means that the physical size of the proposed structure is infinite. However, finite-size effects from the fabricated sample used in the experiment lead to edge diffraction, which can create differences between the experimental and simulated results. Second, fabrication tolerances are unavoidable, and the actual dielectric constant of the substrate material is slightly different from the value used in simulations. Third, the angle between the emitting and receiving antennas in the experiment process is nearly 5°, whereas in simulations, a vertical incidence is used that can lead to differences in results.

Figure 3 shows the simulated results for the phase difference \(\Delta \varphi_{xy}\) between \(\varvec{E}_{xr}\) and \(\varvec{E}_{yr}\), and the results of the ratio \({{r_{xy} } \mathord{\left/ {\vphantom {{r_{xy} } {r_{yy} }}} \right. \kern-0pt} {r_{yy} }}\) under y-polarized wave incidence. It can be seen that the co-polarization and cross-polarization of the reflected wave have the same amplitudes, \({{r_{xy} } \mathord{\left/ {\vphantom {{r_{xy} } {r_{yy} }}} \right. \kern-0pt} {r_{yy} }} \approx 1\), and a phase difference of \(\Delta \varphi_{xy} = \pm 90^{ \circ }\), at frequencies of 10.568, 21.487, 27.054, and 34.958 GHz. That is, the reflected waves are pure circularly polarized at these four frequencies. Figure 4 shows the polarization state of the reflected wave at several special frequencies under y-polarized wave incidence. The reflected wave is clearly rotated 90° with respect to the incident wave at the five frequencies of 11.825, 15.675, 19.204, 29.85, and 33.56 GHz. At 10.568, 27.054, and 34.958 GHz, the reflected wave is a right-handed circularly polarized wave, while the reflected wave is a left-handed circularly polarized wave at 21.487 GHz. At the other frequencies, the reflected wave is elliptically polarized wave.

Fig. 3
figure 3

Phase difference \(\Delta \varphi_{xy}\) between \(r_{xy}\) and \(r_{yy}\), as well as the ratio \({{r_{xy} } \mathord{\left/ {\vphantom {{r_{xy} } {r_{yy} }}} \right. \kern-0pt} {r_{yy} }}\)

Full size image
Fig. 4
figure 4

Polarization ellipses of reflected waves at the twelve special frequencies under y-polarization incidence. The axis represents the magnitude of the reflected electric field (normalized by the electric field magnitude of the incident wave) along the x- and y-axes

Full size image

3.2 Polarization conversion for different angles of incidence

The above analysis shows that the proposed converter has advantages of dual-band and high-efficiency polarization conversion under normal incidence; however, in practical applications, the EM wave is usually incident onto converter with an oblique incident angle. Therefore, the relationship between the angle of incidence and polarization conversion performance needs to be investigated. Figure 5a, b gives the simulated cross-polarization reflectance of \(r_{xy}\) and the co-polarization reflectance of \(r_{yy}\), respectively, under different angles of incidence (\(\theta\)). The angle of incidence has a very small influence on the dual-band performance of polarization conversion. When the angle is increased to 30°, the high-efficiency polarization conversion is maintained over the two bands of Ku (11.5–20.0 GHz) and Ka (28.8–34.0 GHz). However, the performance worsens at \(\theta = 45^{ \circ }\), with the PCR above 0.68 in the Ku-band and above 0.70 in the Ka-band. Therefore, the dual-band and high-efficiency performance of the converter can be sustained over a wide range of angles of incidence. Such tolerance to the angle of incidence provides convenience in practical applications.

Fig. 5
figure 5

Simulated results of reflectance for different angle of incidences: a simulated magnitudes of \(r_{xy}\), b simulated magnitudes of \(r_{yy}\)

Full size image

3.3 Polarization conversion for differently polarized incident waves

To investigate the sensitivity to polarization, we analyzed the polarization conversion of the proposed converter under normal incident wave with different polarizations. Figure 6a, b gives the simulated cross-polarization reflectance of \(r_{xy}\) and the co-polarization reflectance of \(r_{yy}\) for different polarizations; here, \(\varphi\) is the angle between electric field (\(\varvec{E}\)) and y-axis. We could clearly see that the dual-band and high-efficiency polarization conversion can be achieved for \(\varphi = 0^{ \circ }\) (or \(\varphi = 90^{ \circ }\)). However, the polarization conversion clearly worsens as \(\varphi\) increases, indicating that the converter exhibits polarization selectivity in that it converts only the x- and y-polarized waves efficiently.

Fig. 6
figure 6

Simulated results of reflectance for differently polarized incident waves: a simulated magnitudes of \(r_{xy}\), b simulated magnitudes of \(r_{yy}\)

Full size image

3.4 Physical mechanism of the polarization converter

To understand the physical mechanism of the proposed converter, we analyzed the plasmon resonance modes of the DSRR/disk using CST Microwave Studio software. In the simulation, periodic boundary conditions are used in both the x and y directions, and absorbing boundary conditions are used for the z direction. A Floquet port is used to excite a u (v)-polarized wave at normal incidence, as well as to simulate the co-polarization reflectance of \(r_{uu}\)(\(r_{vv}\)) in the frequency range from 9 to 40 GHz. In Fig. 7, the co-polarization reflectance for the incident wave polarized along the u- and v-axes clearly shows that there are in total five plasmon resonance modes that are excited by the electric field components along the u- and v-axes. The three plasmon resonance modes (i), (iii), and (iv) are excited by the v-polarized \(\varvec{E}_{v}\), whereas the plasmon resonance modes (ii) and (v) are excited by the u-polarized \(\varvec{E}_{u}\). Therefore, when the y-polarized wave is incident, these five modes can be excited simultaneously because the incident electric fields of the y-polarized wave can be decomposed into u-polarized \(\varvec{E}_{u}\) and v-polarized \(\varvec{E}_{v}\).

Fig. 7
figure 7

Co-polarization reflectance for an incident wave polarized along the u- and v-axes of the proposed structure. Insets show the corresponding polarization of the incident wave

Full size image

To understand how the plasmon resonance modes contribute to the dual-band polarization conversion for our proposed converter, we analyzed their surface current distributions at the corresponding resonance frequencies of the DSRR/disk using the CST Microwave Studio software. Maps of these surface current distributions are given in Fig. 8. At the plasmon resonance frequencies of 11.097 and 28.673 GHz as shown in Fig. 8a, d, each arc can be considered as a dipole resonator that couples to the \(\varvec{E}_{u}\) component to produce a 0° phase shift. However, at these two resonance frequencies, the structure does not resonate with the \(\varvec{E}_{v}\) component, and hence, a 180° phase shift is produced by the ground plane. In contrast, at the plasmon resonance frequency of 15.745 GHz, as shown in Fig. 8b, a 0° phase shift is produced by the dipole resonators that couples to the \(\varvec{E}_{v}\) component, whereas the \(\varvec{E}_{u}\) component is reflected from the ground plane giving a phase difference of 180° between the two orthogonal components. At the plasmon resonance frequency of 21.539 GHz, as shown in Fig. 8c, both the outer and inner arcs are coupled with the \(\varvec{E}_{u}\) component, which is reflected off with a 0° phase shift, and the \(\varvec{E}_{v}\) component is reflected off by the ground plane, with a 180° phase difference. At the plasmon resonance frequency of 34.364 GHz, as shown in Fig. 8e, both the outer and inner arcs couple to \(\varvec{E}_{v}\), producing a 0° phase shift, whereas the \(\varvec{E}_{u}\) component is reflected off the ground plane, and therefore, the phase difference between the two orthogonal components is 180°. All five plasmon resonance modes are excited by an electric response, resulting in a dual-band behavior for our proposed converter. As shown in Fig. 9, the relative phase difference of the u-polarized and v-polarized waves is roughly \(1 8 0^{\text{o}}\) over the two bands, Ku (11.5–20.0 GHz) and Ka (28.8–34.0 GHz), which implies that the linearly polarized wave is converted to its cross-polarized wave. Moreover, at 10.568, 27.054, and 34.958 GHz, the phase difference is about 90° and the reflected wave is right-handed circularly polarized. At 21.487 GHz, the phase difference is about −90°; the reflected wave is left-handed circularly polarized.

Fig. 8
figure 8

Surface current distributions on the DSRR/disk for y-polarized incident wave at the five plasmon resonant frequencies (in GHz). a 11.097, b 15.745, c 21.539, d 28.673, and e 34.364, f schematic of the decomposed electric fields

Full size image
Fig. 9
figure 9

Relative phase of the co-polarization reflectance for an incident wave along the u- and v-axes of the proposed structure

Full size image

4 Conclusions

In summary, we have numerically and experimentally demonstrated a dual-band and high-efficiency polarization conversion converter. The converter can convert a linearly polarized wave to a cross-polarized wave for two distinct bands: Ku (11.5–20.0 GHz) and Ka (28.8–34.0 GHz). It also can convert the linearly polarized wave to a circularly polarized wave at four other frequencies. The PCR is above 0.94 in the Ku-band and 0.90 in the Ka-band. Furthermore, the proposed converter can achieve dual-band and high-efficiency polarization conversion with angles of incidence up to 45°. The proposed converter also exhibits polarization selectivity with only the x- and y-polarized waves being converted. The physical mechanism was investigated by studying the simulated surface current distributions in the unit cell. Because of the efficient dual-band performance, the proposed converter may have great potential in sensor applications, antennas, and related applications.