© L. Chen et al., Published by EDP Sciences, 2024

1 Introduction

In recent years, the demand for high-quality transmission among wireless devices is increasing significantly with the rapid development of communication systems. Polarization, which refers to the orientation of the electric field intensity vector of electromagnetic waves over time, plays a crucial role in various applications such as satellite communication, radar reception, and anti-interference. The emergence of metasurfaces has opened up new possibilities for manipulating the polarization states of electromagnetic waves [1]. Metasurfaces are two-dimensional metamaterials with a thickness much smaller than the wavelength [2], enabling precise control over the amplitude, phase, and polarization of electromagnetic waves [3–8]. Among various metasurface-based devices, polarization converters have gained significant attention. These devices can alter the polarization direction or state of transmitted or reflected waves, enabling the conversion between linear and circular polarizations, as well as between two orthogonal linear/circular polarizations. This flexible control over electromagnetic waves offers numerous possibilities for communication system design.

Polarization converters can generally be categorized into linear polarization converters [9–12], linear-circular polarization converters [13–16], and circularly polarized converters [17–20], depending on their applications. At the same time, the polarization rotator is also a type of polarization converter. For a wireless communication system with linear polarization converter, it can rotate the azimuth angle of incident linearly-polarized waves by a certain angle to match the polarization of the receiving and transmitting antennas, reducing energy loss caused by polarization mismatch.

According to the direction of wave propagation, polarization converters can be sorted into reflective type [21] and transmissive type [22]. Significant progress has been made in reflective polarization converters by various researchers. For instance, Huang et al. [23] proposed a reflective polarization conversion metasurface utilizing an oblique 45° symmetrical rectangle and concentric rectangular rings. This design achieved cross-polarization conversion within the frequency bands of 4.4–5.3 GHz and 9.45–13.6 GHz. Similarly, Kamal et al. [24] presented a dual-frequency reflective polarization converter composed of two square open resonant rings with different sizes. The nesting of these rings enhanced electrical resonance at higher frequency and strengthened the magnetic resonance between the open ring and the backplane at lower frequency. This design achieved cross-polarization conversion within the frequency bands of 5.4–9.0 GHz and 14.6–16.1 GHz.

Compared to reflective polarization converters, transmissive polarization converters are inevitable to face some challenges such as difficulty in design and narrow bandwidth. Nevertheless, they offer the advantage of the easier conformability with antennas, making them more suitable for practical applications. Additionally, transmissive polarization converters can be conveniently placed in front of the antenna radiation to convert the polarization of transmitted or received electromagnetic waves, facilitating easier assembly. For example, Xu et al. proposed a double-layer ultra-thin transmission polarization converter. Such converter consisting of two layers of orthogonally placed metal strips and metal vias, which can be rotated 90° and polarized for both x- and y-polarized incident waves, can only work at 8.79 GHz [25]. This frequency polarization converter can only work in single frequency, limiting its further applications.

To overcome the aforementioned limitations of existing linear polarization converters that most of them are only capable of operating at a single frequency, this study presents a design of dual-frequency polarization rotator. The proposed polarization rotator consists of two dielectric layers and three interconnected metal layers that are connected through coaxial metal holes. It can convert incident linearly polarized waves at any azimuth angle (the schematic demonstration of azimuth angle is marked as ϕ and depicted in Fig. 1) into counterclockwise 2ϕ linearly polarized waves, and achieve stable performance of polarization conversion at two frequency points.

Fig. 1 Schematic diagram of linear polarization conversion.

2 Design of the polarization rotator

The proposed polarization rotator is capable of rotating the transmitted linearly polarized wave at any angle by adjusting the azimuth angle of the incident electromagnetic wave. Figure 1 illustrates a schematic diagram of the incident electromagnetic wave. The blue and yellow lines represent the incident electric field at a relative azimuth angle of 0° and ϕ corresponding to x-axis, respectively. As the incident wave passes through the rotator, the transmitted electric field (pink line) remains linearly polarized but rotates counterclockwise by angle of 2ϕ.

In previous work [26], we used a pair of large rectangular metal patches that are orthogonal to each other to achieve stable polarization conversion. This design was capable of flexibly controlling transmitted linearly polarized waves at any incident azimuths, but only operating at a single frequency point of 11 GHz.

In order to achieve stable polarization rotation at two frequencies, a dual-frequency transmission polarization rotator unit-cell is established in the commercial electromagnetic simulation software CST, and the full-wave simulation is carried out. The periodic boundary condition is utilized in the x and y directions, and the open boundary condition is utilized in the z direction. The frequency domain solver with linearly polarized incidence along the +z direction is adopted to calculate the performance of the proposed unit-cell. The unit-cell of the proposed polarization rotator is illustrated in Figure 2. It comprises two dielectric layers and three metal layers interconnected by four coaxial metal holes. The metal layer is colored in yellow, while the F4B dielectric substrate with a dielectric constant of 2.65 and a loss tangent of 0.001 is depicted in blue. The upper metal layer includes two large and two small rectangular metal patches. Two large rectangular metal patches are positioned orthogonally along the x- and y-axes, respectively, and two small ones are also positioned orthogonally along the x- and y-axes, respectively. Similarly, the lower layer contains two rectangular metal patches along the y-axis and two rectangular metal patches along the x-axis. Two rectangular metal patches along the y-axis are identical to the configuration of the upper layer, and the ones along the x-axis are rotated by 180° relative to the top layer. The middle metal layer acts as a shared ground plane for the upper and lower layers. Detailed parameters of the proposed unit-cell are listed in Table 1.

To verify the performance of the proposed unit-cell, electromagnetic simulation software is used. The simulation results are plotted in Figure 3. To validate the polarization stability at two frequencies, the incident wave azimuth angles are set as 0°, 30°, 60°, and 90°. From Figure 3, we can observe that the amplitude of polarization conversion exceeding 0.95 is obtained at 12 GHz, and the corresponding co-polarization reflection coefficient remains below 0.1. Similarly, at 17 GHz, the amplitude of polarization conversion above 0.94 with the co-polarization reflection coefficient below 0.1 is achieved. The polarization conversion and reflection coefficient exhibit stable behavior at both 12 GHz and 17 GHz. The results demonstrate that the proposed structure is capable of achieving stable polarization conversion for electromagnetic waves with different incident azimuth angles.

The give further insight into the mechanism of the proposed polarization rotator, the distribution of electric fields vector of two neighboring unit-cell in the yoz plane is analyzed in Figure 4. The incident azimuth angles are set as 0°, 30°, 60°, and 90, respectively. From Figure 4, it can be observed that the azimuth angles of the corresponding transmitted electric field vectors at 12 GHz are 0°, −30°, −60°, and −90°, respectively. This indicates that the angle between the transmitted and incident electromagnetic wave at 12 GHz is 2ϕ. Similarly, at 17 GHz, the corresponding transmitted electric field vectors are witnessed as −180°, −210°, −240°, and −270°, implying that the angle between the transmitted and incident electromagnetic wave at 17 GHz is also 2ϕ. Furthermore, we can also obtain from Figure 4 that the electric field strength at the input and output terminals remains nearly the same demonstrating little energy loss during transmission. Hence, the proposed polarization rotator successfully achieves polarization conversion at two frequency points for arbitrary incident azimuth angles of 2ϕ.

Fig. 2 Schematic demonstration of the proposed unit-cell. (a) Three-dimensional view. (b) Explored view. (c) Top view.

Fig. 3 The (a) transmission and (b) reflection coefficients under incidence polarized at the azimuth angle of 0°, 30°, 60°, 90°.

Fig. 4 The distribution of electric fields vector of two neighboring unit-cell under incidence polarized at the azimuth angle of (a) 0°, (b) 30°, (c) 60°, and (d) 90° at 12 GHz and 17 GHz in the yoz plane.

3 Analysis of the principle of polarization conversion

To analyze the principle of polarization conversion, we define the incident electric field of a linearly polarized wave as [26]:

$$E^{ui}=u{E}^{ui}{e}^{j\left(wt-kz\right)}=\left[\begin{array}{c}\hfill E^{ui}\cos \varphi e^{j\left(wt-kz\right)}\hfill \\ \hfill E^{ui}\sin \varphi e^{j\left(wt-kz\right)}\hfill \end{array}\right]\text{,}$$(1)

where E^ui represents the electric field amplitude of the linearly polarized incident wave, ϕ represents the azimuth of the incident electric field relative to the x-axis, and u represents the unit vector of the incident electric field of the linearly polarized wave.

When the linearly polarized incident wave is transmitted through the element in the +z direction, the incident electric field E^ui will be decomposed into two electric field components that are orthogonal to each other along the x-axis and y-axis, respectively. These two mutually orthogonal electric field components will be received by two pairs of perpendicular metal patches on the upper layer of the unit-cell, because the radiating metal patches distributed along the x- and y-axes are rotated by 180° and the same as the metal patches at the receiving end, respectively. This makes the co-polarized transmitted electric field components along the x- and y-axes obtain an additional phase difference of 180°. The corresponding Jones matrix can be described as:

$$E^{ut}=\left[\begin{array}{cc}\hfill T^{xx}\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill T^{yy}\hfill \end{array}\right]\left[\begin{array}{c}\hfill E^{uix}\hfill \\ \hfill E^{uiy}\hfill \end{array}\right]=\left[\begin{array}{c}\hfill T^{xx}{E}^{ui}\cos \varphi e^{j\left(wt-kz+\alpha \right)}\hfill \\ \hfill T^{yy}{E}^{ui}\sin \varphi e^{j\left(wt-kz+\alpha +\pi \right)}\hfill \end{array}\right]\text{,}$$(2)

where T^xx and T^yy represent the co-polarized transmittance of the horizontally and vertically polarized components under linear polarization incidence, respectively, and α represents the transmission phase under linear polarization. Based on the characteristics of the polarization rotator and the fact that two perpendicular pairs of metal patches at the radiating and receiving ends of the element have the same geometric parameters, the transmission phase α is the same as the co-polarized transmittance T^xx (T^yy). When T^xx and T^yy are both equal to 1, the equation (2) can be converted as:

$$E^{ut}=\left[\begin{array}{c}\hfill E^{ui}\cos \varphi e^{j\left(wt-kz+\alpha \right)}\hfill \\ \hfill E^{ui}\sin \varphi e^{j\left(wt-kz+\alpha +\pi \right)}\hfill \end{array}\right]=\left[\begin{array}{c}\hfill E^{ui}\cos (-\varphi )e^{j\left(wt-kz+\alpha \right)}\hfill \\ \hfill E^{ui}\sin (-\varphi )e^{j\left(wt-kz+\alpha \right)}\hfill \end{array}\right]\text{.}$$(3)

In this case, two components of the electric field at the radiating end of the element combine with each other to form E^ut, which radiates into free space. By comparing the equations (1) and (3), we can find that the linear polarized wave with ϕ incident azimuth has been converted into a linear polarized wave with a transmitted azimuth angle of −ϕ. Therefore, the unit-cell can achieve a polarization conversion at an angle of 2ϕ counterclockwise.

In order to further illustrate the principle of the designed polarization rotator, the surface current vectors of the top and bottom layers are analyzed. We name the large metal patch distributed along the x- and y-axes on the top layer as A and B, respectively, the small metal patch distributed along the x- and y-axis as a and b, respectively. Similarly, the bottom metal patch is named A^′, a^′, B^′, b^′. The corresponding surface current vector distributions on the top and bottom layers of the unit-cell at 12 and 17 GHz are presented in Figure 5 and Figure 6, respectively, with the azimuth angles of the incident wave set as 0°, 30°, 60°, and 90°. As can be seen from the figures, when ϕ = 0°, only the E^x electric field component of the incident wave is received by A and A^′ at both frequency points, and a strong induced current is formed on the patch surface. Besides, the E^x component is almost not induced by the metal patches B and B^′. In this case, the E^x component of the electric field is significantly dominant at both frequencies, while the E^y component can be considered to be negligible, indicating no obvious polarization conversion at an incident azimuth angle of 0°.

When ϕ = 30° or 60°, the metal patches marked as A, a, B, and b at the receiving end will receive the E^x and E^y electric field component of the incident wave, and generate the induced current of corresponding components. When the metal patches at the radiating end reaches the metal patches through the coaxial metal hole, A^′ and a^′ (B^′ and b^′) will generate E^x (E^y) electric field components with almost the same induced current intensity as that of A, a, B, and b, indicating negligible loss caused by the induced current during transmission at 12 and 17 GHz. In this case, the incident and transmitted electric field vectors are symmetrical with respect to x-axis, and the polarization conversion with azimuth angle of 2ϕ is realized.

In order to verify the polarization conversion performance of the arbitrary linear polarization rotator proposed in this study, a periodic array composed of the proposed elements is constructed and a corresponding prototype is fabricated, as shown in Figure 7. The size of the fabricated sample composed of 15 × 15 identical elements is 196.5 mm × 196.5 mm. By rotating the horn on one side by 0°, 30°, 60°, and 90°, while rotating the horn on the other side by corresponding 0°, −30°, −60°, and −90° in turn, the transmitted polarization conversion can be obtained. For the sake of measuring the reflection coefficient, two horns are set on the same side of the sample. By simultaneously rotating two horns by 0°, 30°, 60°, 90°, the co-polarized reflection coefficient of the sample can be obtained. The measured results are shown in Figure 8. From the test results, we can obtain that when the ϕ varies from 0° to 90°, it has almost no effect on both transmission coefficient and reflection coefficient. The measured transmission coefficients are close to 0.95 and 0.94 at 12 GHz and 17 GHz, respectively, and the measured co-polarization reflection coefficient is close to 0.1, coinciding well with the simulation curve. Inevitably, there are some slight deviations attributed to fabrication and assembly errors, as well as measurement uncertainty. Whereas, these deviations have little effect on the performance of the polarization rotator. The measured results demonstrate that the proposed polarization rotator is capable of maintaining stable polarization transition at two frequencies, even for linearly polarized incident waves with different incident azimuths.

Fig. 5 Surface current vector distribution of the top (top panel) and bottom (bottom panel) layers of the unit under incidence polarized at the azimuth angle of (a) 0°, (b) 30°, (c) 60°, and (d) 90° at 12 GHz.

Fig. 6 Surface current vector distribution of the top (top panel) and bottom (bottom panel) layers of the unit-cell under incidence polarized at the azimuth angle of (a) 0°, (b) 30°, (c) 60°, and (d) 90° at 17 GHz.

Fig. 7 (a) Experimental set-up, (b) front view and partial zoomed-in view, and (c) bottom view of the proposed rotator.

Fig. 8 Measured (a) transmission and (b) reflection coefficients at different incident azimuths.

4 Conclusion

In this paper, we design a dual-frequency polarization rotator capable of controlling arbitrary linearly polarized incidence. This rotator is mainly connected by three metal layers and two dielectric layers through coaxial metal holes, so that the proposed unit-cell can maintain a stable polarization conversion effect at two frequency points. By analyzing the strength of electric field and the induced current vector of the unit, the structure can convert the linearly polarized wave into a transmitted one with a counterclockwise rotation of 2ϕ under the condition that the incident azimuth angle is ϕ different. The polarization conversion efficiency up to 0.95 and 0.94 can be achieved at lower and higher frequencies, respectively, indicating negligible energy loss. Finally, a prototype of the proposed structure is fabricated and tested. The measured results are consistent with the simulation ones. We envision that the proposed design can facilitate the utilization of polarization rotator in various wireless communication systems.

Funding

This work was supported in part by the China Postdoctoral Science Foundation under Grant 2022M720063, in part by the Natural Science Foundation of Jiangsu Province of China under Grant BK20220440, in part by the National Natural Science Foundation of China under Grant 62301262, and in part by the Startup Foundation for Introducing Talent of the Nanjing University of Information Science and Technology under Grant 2021r040 and 2022r076.

Conflicts of interest

The authors have nothing to disclose.

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Author contribution statement

Conceptualization, L.C.; Methodology, L.C.; Validation, L.C.; Formal Analysis, L.C.; Investigation, L.C.; Resources, G.D. and S.W.; Data Curation, L.C.; Writing – Original Draft Preparation, L.C. and X.L.; Writing – Review & Editing, L.C. and X.L.; Visualization, L.C. and X.L.; Supervision, G.D., X.L. and S.W.; Funding Acquisition, G.D. and X.L.

References

All Tables

All Figures

	Fig. 1 Schematic diagram of linear polarization conversion.
In the text

	Fig. 2 Schematic demonstration of the proposed unit-cell. (a) Three-dimensional view. (b) Explored view. (c) Top view.
In the text

	Fig. 3 The (a) transmission and (b) reflection coefficients under incidence polarized at the azimuth angle of 0°, 30°, 60°, 90°.
In the text

	Fig. 4 The distribution of electric fields vector of two neighboring unit-cell under incidence polarized at the azimuth angle of (a) 0°, (b) 30°, (c) 60°, and (d) 90° at 12 GHz and 17 GHz in the yoz plane.
In the text

	Fig. 5 Surface current vector distribution of the top (top panel) and bottom (bottom panel) layers of the unit under incidence polarized at the azimuth angle of (a) 0°, (b) 30°, (c) 60°, and (d) 90° at 12 GHz.
In the text

	Fig. 6 Surface current vector distribution of the top (top panel) and bottom (bottom panel) layers of the unit-cell under incidence polarized at the azimuth angle of (a) 0°, (b) 30°, (c) 60°, and (d) 90° at 17 GHz.
In the text

	Fig. 7 (a) Experimental set-up, (b) front view and partial zoomed-in view, and (c) bottom view of the proposed rotator.
In the text

	Fig. 8 Measured (a) transmission and (b) reflection coefficients at different incident azimuths.
In the text