1. Introduction

Polarization is one of the fundamental properties of Electromagnetic (EM) waves. It is always desirable for microwave sensors and mm-wave systems to manipulate the polarization states of EM waves. The problems caused by the linearly polarized EM waves, such as the transmitter-receiver alignment and the Faraday rotation by the ionosphere and unknown orientation of source, can be eliminated by utilization of the circularly polarized EM waves [1-2]. To date various polarization convertors have been proposed. Conventional methods to fabricate polarization convertors mainly use optical gratings, anisotropic medias, the Brewester and Faraday effects [3–9]. Many concepts for the implementation of both transmission-type [10–16] and reflection-type [17–21] linear-to-circular polarization convertors using metasurfaces have been developed in previous literatures. What’s more, the polarization convertors based on metasurfaces have the advantage of scalable geometries when compared to the conventional polarization convertors. Therefore, they can be widely used in the polarization control devices from radio to optical frequencies.

In previous literature, various metasurfaces with anisotropic impedance, such as H-shaped metamaterial [16], polarization dependent electromagnetic band gap (PDEBG) [17], dipole array and meander lines [18-19], have been widely used to realize the reflection-type linear-to-circular polarization conversion. By virtue of anisotropy, the reflection phases of two orthogonal linearly polarized incident EM waves can be manipulated independently. For H-shaped metamaterial polarization convertor, the linear-to-circular polarization conversion can be obtained only in two very narrow frequency bands. By using PDEBG structure, two broad linear-to-circular polarization conversion bands can be obtained. In order to further improve the polarization conversion bandwidth of the convertors, the dipole array and meander lines are proposed to achieve the bandwidths of 60% and 93.8% respectively. However, the conversion bandwidths of these polarization convertors are still not wide enough, especially for wideband applications in microwave and optical regions.

In this study, we have designed and realized an ultra-wideband linear-to-circular polarization convertor based on a metaurface, which is able to convert the linearly polarized EM wave to a circularly polarized one in a 4.6:1 bandwidth (from 4.7 GHz to 21.7 GHz). As the proposed metasurface shows strong abilities to control the reflection phases of two orthogonal linearly polarized incident waves, the challenge of improving the bandwidth in previous works can be successfully solved.

2. Structures and experimental details

Figure 1(a) shows the top/side view of the unit cell of the proposed metasurface, where p = 9 mm, a = 4.4 mm, b = 2.3 mm, w₁ = 1 mm, w₂ = 0.9 mm, g₁ = 0.5 mm, g₂ = 1 mm, d₁ = 0.5 mm, t₁ = 3 mm, and t₂ = 4 mm. The gray regions are substrate and superstrate of the unit cell. The relative permittivity of both the substrate and superstrate is 2.2 with a loss tangent of 0.0009. The other regions are all perfect conductor. The unit cell of the proposed metasurface consists of two layers of dielectric. Two L-shaped patches, a patterned patch and a ground plane are printed on separate sides of the lower substrate. The two L-shaped patches are connected to the ground plane by two metallic vias. The upper dielectric acts as a superstrate. Figure 1(b) gives the photo of the fabricated prototype of the metasurface consisting of 26 × 26 unit cells with a total dimension of 234 mm × 234 mm. The schematic illustration of the AR measurement setup is shown in Fig. 1(c). The two horns have the same polarization. One horn is used as the transmitter while the other one is used as the receiver to receive the magnitude and phase of the reflected wave. By rotating the prototype with 90 degree, the reflection characteristics of the reflected waves can be measured with both u- and v-polarized incident waves. Then the AR can be calculated using the measured data. The simulated and measured axial ratio (AR) of the proposed structure illuminated by the y-polarized incident plane wave is given in Fig. 1(d). It can be seen that the simulated AR is less than 3 dB in the frequency range from 4.7 GHz to 21.7 GHz, in which there are five frequency points approximately 0. The 3-dB AR band is measured from 4 GHz to 18 GHz due to the restriction of the measurement conditions. It can be seen that the measured result shifts to the lower frequency band which is caused by the errors in implementation. However, the frequency shifting is small in consideration of the ultra-wide working band and a reasonable agreement between the simulated and measured results has been obtained in the designed frequency region.

 

Fig. 1 (a) Top/side view of the unit cell of the polarization convertor. The gray region is a substrate and the other regions are all perfect conductor. The two L-shaped patches are connected to the ground by two metallic vias. (b) The fabricated prototype of the metasurface consisting of 26×26 unit cells with a total dimension of 234 mm×234 mm. (c) Schematic of measurement setup. (d) Simulated (black square) and measured (blue triangle) AR.

Download Full Size | PDF

3. Results and discussion

To understand the response of the proposed polarization convertor to the y-polarized incident EM wave, we decompose the y-polarized incident EM wave into two perpendicular components, u and v, which are introduced here along 45° direction with respect to x and y direction, as shown in Fig. 2(a). Then the linearly polarized incident plane wave can be expressed as

 

Fig. 2 (a) Schematic of the electric field decomposition. The red and blue arrows represent the incident plane waves and reflected plane waves, respectively. Inset shows the schematic diagram used to calculate the axial ratio of the reflected wave under a normally incident y-polarized wave. (b) Simulated reflection coefficients and phases of the unit cell illuminated by the incident plane wave with u polarization (blue triangle for reflection phase and black line for reflection coefficient) and v polarization (blue square for reflection phase and black dot for reflection coefficient).

Download Full Size | PDF

Assuming that the reflected coefficients along u- and v-axis are $r_u{e}^{i{\varnothing }_u}$ and $r_v{e}^{i{\varnothing }_v}$, respectively, the reflected wave can be expressed as

As a result, the linear-to-circular polarization conversion is obtained. Figure 2(b) shows the magnitudes and phases of the reflection coefficients of the proposed polarization convertor illuminated by u- and v-polarized incident plane waves respectively. It can be seen that $r_u\approx r_v\approx 1$ and the phase difference between ${\varnothing }_u$ and ${\varnothing }_v$ is close to $\pi /2$ in the frequency range from 4.7 GHz to 21.7 GHz. Hence an ultra-wideband linear-to-circular polarization conversion is achieved.

In order to understand the polarization states of the reflected waves better, the polarization ellipses of the reflected waves at the five peaks (f = 5.5, 8, 12, 16.3 and 20.5GHz) and one trough (f = 6.94GHz) within the 3dB-AR bandwidth for y-polarized incident wave are shown in Fig. 3. It can be seen that the principal axis directions of these polarization ellipses are all close to 0 degree. When the AR is close to 0dB, the polarization ellipse is approximate to a circle.

 

Fig. 3 Polarization ellipses at different frequencies

Download Full Size | PDF

There are three reasons that the phase difference between ${\varnothing }_u$ and ${\varnothing }_v$ can be relatively stable in such a wide frequency band. The first reason is that the unit cell with metallic vias can generate electric resonance in the lower frequency band when illuminated by the u-polarized incident plane wave. As shown in Fig. 4(a), the unit cell without metallic vias cannot realize good linear-to-circular conversion in the lower frequency band when compared with the proposed structure with metallic vias. Taking 7 GHz for example, we monitor the surface current distributions on the metallic parts of the unit cell with and without metallic vias. For the unit cell with metallic vias, the electric and magnetic resonances are generated when illuminated by u- and v-polarized incident plane waves, as shown in Fig. 4(b) and Fig. 4(c) respectively. As a result, the reflected phase difference between ${\varnothing }_u$ and ${\varnothing }_v$ is introduced. However, for the case of the unit cell without metallic vias, only magnetic resonance is generated, as shown in Fig. 4(d) and Fig. 4(e). Therefore, the phase difference will not be able to support a good linear-to-circular polarization conversion. By analyzing the current distributions of Fig. 4(b), it can be seen that the metallic vias introduce a longer current path since the patch and ground is connected by them. As a result, the electric resonance in a lower frequency band is generated.

 

Fig. 4 (a) Axial ratio comparison between unit cell with (black square) and without (blue triangle) metallic vias. (b) Simulated reflection coefficients and phases of the unit cell illuminated by the incident plane wave with u polarization (blue triangle for reflection phase and black line for reflection coefficient) and v polarization (blue square for reflection phase and black dot for reflection coefficient). (c) and (d) show the current distributions on the patches and ground of the unit cell with metallic vias under u-polarized and v-polarized incident plane waves, respectively. (e) and (f) show the current distributions on the patches and ground of the unit cell without metallic vias under u-polarized and v-polarized incident plane wave, respectively.

Download Full Size | PDF

The second reason is that the patterned patch at the center of the unit cell expands the 3-dB AR bandwidth of the proposed metasurface in the higher frequency region. The comparison of AR between the structure with and without the patterned patch is shown in Fig. 5. It can be seen from Fig. 5(a) that the structure without patterned patch has only five nodes and they are nearly the same with the first five nodes of the structure with patterned patch. According to Fig. 5(b), it can be seen that the patterned patch makes the reflection phase of the proposed structure illuminated by the incident plane wave with u polarization more stable at higher frequency. As a result, the patterned patch improves the upper frequency limit of the proposed metasurface.

 

Fig. 5 (a) Axial ratio comparison between unit cell with (black square) and without (blue triangle) the patterned patch at the center of the unit cell. (b) Reflection phases of the unit cell with (black lines) and without (blue scatters) the patterned patch illuminated by the incident plane wave with u polarization (solid line and blue square) and v polarization (black dot line and blue triangle).

Download Full Size | PDF

Finally, the superstrate makes the phase difference between the two orthogonal incident plane waves along u- and v-axis more stable. To further study the relationship between the polarization conversion efficiency and the thickness of the superstrate, the interference theory [22] can be used. As shown in Fig. 6(a), the y-polarized incident EM wave on the air-superstrate interface is partially reflected back to the air and partially transmitted into the superstrate. The transmitted y-polarized EM wave continues to propagate in the propagation phase $\beta =\sqrt{\epsilon }{k}_{0}d$ in the superstrate until it reaches the interface between the superstrate and the metallic patches. Since the metallic patches are connected to the ground sheet by the metallic vias, we treat the metallic structures and the dielectric substrate as a whole, regardless of the multiple reflection process among these structures. Thus, the transmitted EM wave is reflected on the superstrate-metallic patches interface back to the superstrate. Similar to the light propagation in a stratified media, the overall reflection is then the superposition of the multiple reflections. If superposition interference appears between the direct linear-to-circular reflection and its multiple reflections, the AR of the reflected wave will be very small and even approximately 0dB. With an optimized thickness of the superstrate, the overall reflected circularly polarized EM waves can be maximized in an ultra-wide frequency band. As a result, the ultra-wideband linear-to-circular polarization convertor is obtained. Figures 6(b) and 6(c) shows the comparisons of AR and phase difference between ${\varnothing }_u$ and ${\varnothing }_v$ among the polarization convertor with different thicknesses of superstrate. It can be seen that an optimized thickness of 4 mm can make the phase difference more stable and closer to $\pi /2$ in the whole operating band. Hence, the 3-dB AR bandwidth is wider.

 

Fig. 6 (a) Intuitive scheme of the multi-reflection under a normally incident y-polarized wave. (b) and (c) show the axial ratio and phase difference between ${\varphi }_u$ and ${\varphi }_v$ of unit cells with superstrate thickness of 2mm (black square), 4mm (red circle), and 6mm (blue triangle).

Download Full Size | PDF

The angular stability of the proposed polarization convertor has also been investigated. Figure 7 shows the simulated AR with the incident angle increasing from 0° to 20°. It can be seen that the upper cut-off frequency decreases with the increasing of the incident angle. When the incident angle increases to 20°, the AR of the proposed polarization convertor becomes larger than 3dB in the frequency range from 6.8GHz to 9.2GHz.

 

Fig. 7 Axial ratio of the proposed polarization convertor with the incident angles of 0° (black square), 10° (red circle), and 20° (blue triangle).

Download Full Size | PDF

4. Conclusion

In conclusion, a metasurface for realizing linear-to-circular polarization conversion has been proposed in this paper. The design of the metasurface is simple and ultra-wideband, which benefits from the multi-reflection and the utilization of metallic vias. The metasurface can convert the y(x)-polarized normally incident EM wave to a circularly polarized one. The 3-dB AR bandwidth of the proposed metasurface is 129% over 4.7GHz-21.7GHz. Both the simulated and experimental results prove that the proposed metasurface can convert the linearly-polarized incident wave to a circularly-polarized one in an ultra-wide band in microwave region. Our design can be applied to microwave sensors and mm-wave systems to manipulate the polarization states of EM waves.