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Abstract
This paper presents a new design of linear-polarization metasurface converter with arbitrary polarization rotating angle. The linear-polarization conversion is achieved by first separating the linearly polarized incident wave into two orthogonal circularly polarized waves, then adding an additional phase to one of the circularly polarized waves, and finally recombining these two circularly polarized waves into a linearly polarized wave and reflecting it towards free space. A practical unit cell operating at 10 GHz with sandwich structure is applied to realize the linear-polarization metasurface converter, which consists of a top-layer square patch, a middle-layer ground plane, a bottom-layer 90° quadrature hybrid coupler, and two vias connecting the top layer and bottom layer. The proposed linear-polarization metasurface converter is analyzed theoretically and demonstrated by both simulating and experimental results.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces, the two-dimensional equivalent of bulky three-dimensional metamaterials, have been becoming a revolutionary technology in electromagnetic wave manipulation, due to their natural benefits of low-profile, low-cost, easy-fabrication and the flexible capability of electromagnetic wave transformation [1]. A variety of metasurface based applications have been reported, such as electromagnetic wavefront shaping [2–9], energy absorption [10–12], holography [13,14], analog mathematical computing [15], cloaking [16–18], camouflaging [19,20], nonreciprocity [21,22], frequency conversion [23,24], and simplified wireless communication and radar systems [25–29].
Manipulating the polarization of electromagnetic waves is crucial in many practical scenarios, such as radar cross-section (RCS) reduction [30,31], wireless communication [32–34], high-resolution imaging [35], and liquid crystal display (LCD) [36]. Conventionally, the polarization of an electromagnetic wave is controlled through the devices such as dichroic glasses, birefringent wave plates, and liquid crystals, which are generally bulky and have limited operating bandwidth [37–39], thus limiting their capability of integration within practical applications. Thanks to the attractive features of metasurfaces, a diversity of polarization converters have been studied using metasurface technology [37–48]. Nevertheless, most of the polarization converting metasurfaces are implemented by achieving desired resonating states for specified polarized incident waves, resulting in certain amplitude and phase responses and then further converting their scattering polarization, which usually have fixed functions with less flexibility.
In this paper, we propose a new design of metasurface based linear polarization (LP) converter. Different from conventional metasurface based polarization converters, the realization of proposed LP rotation may be divided into three steps: First, separating the LP incident wave into two waves with different circular polarization (CP), namely, left-hand circular polarization (LHCP) and right-hand circular polarization (RHCP). Second, introducing an additional phase to one of the CP waves, and finally recombining the two CP waves and radiating back to free space. During this procedure, the polarization rotating angle is fully determined by the additional phase introduced in the second step, and the rotating direction is controlled by adding the additional phase to the selected CP component. Those features make the proposed LP metasurface converter easy to achieve arbitrary angle rotation and arbitrary rotating direction by simply changing the value of added phase and switching the CP component to add the additional phase. What’s more, the proposed LP metasurface converter is insensitive to incident LP direction.
The rest of this paper is organized as follows. Section 2 establishes the general principle of the proposed LP metasurface converter. Then, section 3 presents a practical metasurface realization using a square patch and a quadrature hybrid coupler [49]. Next, section 4 provides the full-wave simulation results of the designed metasurface, and section 5 fabricates the designed metasurface and demonstrates the proposed design by experiment. Finally, section 7 concludes this paper.
2. Principle
Figure 1 provides the conceptual illustration of a reflective LP metasurface converter. A linearly polarized incident wave at frequency $\omega _0$, $\psi _{\textrm {i}}(t,\omega _0)$, whose electric field is $\boldsymbol{E}_{\textrm{i}}\boldsymbol{(t)}$, impinges on the metasurface based polarization converter. The linearly polarized wave interacts with the metasurface and is reflected back to the free space. The LP of the scattered wave $\psi _{\textrm {r}}(t,\omega _0)$ is rotated by an angle of $\theta$, with the electric field $\boldsymbol{E}_{\textrm{r}}\boldsymbol{(t)}$.
Fig. 1. The conceptual illustration of proposed reflective linear polarization (LP) metasurface converter with a reflecting rotating angle $\theta$.
Figure 2 explains the general operating principle of the LP metasurface converter. An incident linearly polarized harmonic wave $\boldsymbol{\psi}_{\textrm{i}}(t)$ whose LP is in the $\boldsymbol{x}$ direction, namely,
impinges on the LP metasurface converter. The linearly polarized incident wave $\boldsymbol{\psi}_{\textrm {i}}(t)$ may be divided into two orthogonal circularly polarized waves, LHCP and RHCP, respectively,The metasurface interacts with the incident wave and adding an additional phase $\phi$ to one of the CP waves. If the additional phase $\phi$ is added to the RHCP wave, the reflected wave may be expressed as
The expression in the last equality of (3) shows that the reflected wave contains not only the $\boldsymbol{x}$ component but also $\boldsymbol{y}$ component. These two components are in phase but have different amplitudes, which demonstrates that the reflected wave is still linearly polarized but with a rotated angle. The polarization rotating angle $\theta$ may be simply derived by comparing the values of components in $\boldsymbol{x}$ and $\boldsymbol{y}$ directions,
Similarly, If the additional phase $\phi$ is added to LHCP, the reflected wave is expressed as
Then, the polarization rotating angle $\theta$ is obtained as
Equation (4) and (6) show that the LP rotating angle $\theta$ is half of the added additional phase $\phi$, and the rotating direction depends on which CP component $\phi$ is added. Since any linearly polarized wave can be naturally divided into two orthogonal circularly polarized wave as seen in (2), the theory here is perfectly valid for any linearly polarized incident wave with arbitrary polarization angle.
Fig. 2. Principle of proposed arbitrary linear-polarization metasurface converter, where an incident linearly polarized wave $\psi _{\textrm {i}}(t)$ with $\boldsymbol{x}$ polarization is divided into two circularly polarized waves, the two waves experience different reflective phases (RHCP experiences $\phi$ more phase shift than LHCP in this figure) and are recombined into a linearly polarized wave $\psi _{\textrm {r}}(t)$ with a rotated polarization angle $\theta$.
3. Metasurface unit cell design
A practical metasurface structure is designed to realize the proposed LP metasurface converter. Figure 3 depicts the layout of the metasurface unit cell with designing parameters. Figure 3(a) shows the side view of the unit cell, which is a sandwich structure formed by two Rogers 6002 substrates, whose dielectric constant is 2.94 and dissipation factor is 0.0012. It consists of a top layer metallic patch, a middle layer ground plane, a bottom layer circuit, and two metalized vias connecting the top and bottom layers. Figure 3(b) shows the top layer structure. It is a square patch with two feeding points, corresponding to the two orthogonal LP feeding positions, which are connected to the bottom layer through the two vias. The square patch is designed to be resonant at 10 GHz, so it can perfectly pick up the two orthogonal LP incident waves with $\boldsymbol{x}$ and $\boldsymbol{y}$ polarization at the two feeding points, respectively. Figure 3(c) shows the middle ground layer. It contains two circular slots on the ground to avoid shorting the two vias, which are connecting the top and bottom layers, to the ground. Figure 3(d) shows the bottom circuit layer. Its main part is a typical 4-port $90^\circ$ quadrature hybrid coupler with the following form scattering parameter matrix $[S_\textrm {c}]$ [49]:
Ports 2 and 3 of the coupler are connected to the two feeding points on the top patch layer through the vias, respectively. As a result, port 1 of the coupler receives the RHCP component of the LP incident wave, as $S_{12}=-j\frac {1}{\sqrt {2}}$, $S_{13}=-\frac {1}{\sqrt {2}}$, and port 4 of the coupler receives the LHCP component of the LP incident wave, as $S_{42}=-\frac {1}{\sqrt {2}}$, $S_{43}=-j\frac {1}{\sqrt {2}}$, hence, the two CP components in the incident wave are separated in ports 1 and 4 of the coupler. The additional phase $\phi$ added in one of the CP components for polarization rotation may be simply realized by adding an open-end microstrip line with the length,
in corresponding CP ports, where $k_0$ is the wave number of the guided wave in the microstrip line. Namely, $L_1=\Delta L, L_2=0$ are chosen for clockwise polarization rotation and $L_2=\Delta L, L_1=0$ are chosen for anticlockwise rotation. The factor of $\frac {1}{2}$ in $\Delta L$ is due to the fact that the open-end microstrip line works as a reflective phase shifter and therefore exhibits a double phase of $k_0\Delta L$. The waves reflected by the open-end microstip line and coupler are recombined on the top patch layer and reradiated to free space with a rotated polarization angle.Fig. 3. Metasurface unit cell realization with design parameters ($h= 0.76~\textrm {mm}, W_1=15.0~\textrm {mm}, W_2= 8.2~\textrm {mm}, W_3= 1.93~\textrm {mm}, d= 1.78~\textrm {mm}, L_4= 3.63~\textrm {mm}, W_4= 3.25~\textrm {mm}$). (a) Side view. (b) Top layer. (c) Middle layer. (d) Bottom layer.
4. Full-wave simulation results
Figure 4 plots the full-wave simulation results of the proposed LP metasurface converter design with the help of Ansys Electronics. Figure 4(a) plots the magnitudes of the co-polarized and cross-polarized reflection coefficients, $|S_{xx}|$ and $|S_{yx}|$, for different $L_1$ when $L_2$ is fixed to 0, where different $L_1$ is corresponding to different phase shift $\theta$ added to the RHCP component, as shown in Fig. 2. It shows that when $L_1$ increases from 0, corresponding to $0^\circ$, to 4.8 mm, corresponding to $90^\circ$, $|S_{xx}|$ reduces from 1 to 0, while $|S_{yx}|$ increases from 0 to 1, approximately, which demonstrates that the amount of $\boldsymbol{y}$-polarized scattered wave converted from incident $\boldsymbol{x}$-polarized wave by the LP metasurface converter increases as $L_1$ increases, and hence the reflected linealy polarized wave rotating angle $\theta$ increases. Similarly, if $L_1$ is fixed to 0, different $L_2$ is corresponding to different phase shift $\theta$ added to the LHCP component, as shown in Fig. 2.
Figure 4(b) plots the phases of co-polarized and cross-polarized reflection coefficients, $\angle S_{xx}$ and $\angle S_{yx}$, for the two cases $L_1=3.2~\textrm {mm}, L_2=0$ and $L_1=0, L_2=3.2~\textrm {mm}$. It shows that the co-polarized and cross-polarized reflected waves are approximately in phase when $L_2=0$ mm, and out of phase when $L_1=0$ mm, which demonstrates that in both cases the polarization of reflected waves are linear. However, when $L_1=2.4$ mm, the reflected LP rotates clockwise, while when $L_2=0$ mm, the reflected LP rotates anticlockwise.
Fig. 4. Scattering parameters from full-wave simulation. (a) Magnitudes of reflection coefficients for different $L_1$, when $L_2=0$. (b) Phases of reflection coefficients for the cases $L_1=0$ and $L_2=0$.
5. Experimental demonstration
A LP metasurface converter with $3\times 5$ elements and reflected polarization rotating phase $\theta =45^\circ$ is designed and fabricated based on the proposed concept. In order to achieve the designed rotating angle $\theta$, $L_1=2.4$ mm and $L_2=0$ mm in Fig. 3 are chosen to design the LP metasurface converter. Figure 5 presents the fabrication prototype of the LP metasurface converter, where Fig. 5(a) shows the top view and Fig. 5(b) shows the bottom view of the LP metasurface converter prototype.
Fig. 6 provides the experimental demonstration of the fabricated LP metasurface converter. Figure 6(a) shows the experimental setup. The testing LP metasurface converter is placed in front of a piece of absorbing material. A pair of linearly polarized antennas are chosen as the transmitting and receiving antennas, respectively. The distance between the antennas and the metasurfce converter is around 80 cm. The two excitation ports of the two antennas are connected to a vector network analyzer (VNA) to measure the scattering parameters. During the measurement, the transmitting antenna is fixed, while the receiving antenna is set to have the same polarization direction as the transmitting antenna in the initial stage and then the receiving antenna is rotated manually with the rotating angle $\alpha$ to measure the scattered wave. Figure 6(b) plots the measured normalized $|S_{21}|$ against different rotating angles $\alpha$ of the receiving antenna and its comparison with ideal and full-wave simulated results. The measured results is plotted with interpolation using least square method. It shows that the measured result agrees with the ideal and simulated results. When $\alpha =42.2^\circ$, the measured $|S_{21}|$ arrives the maximum, which is very closed to the designed value $45^\circ$ and demonstrates the proposed concept and design. The small deviation of LP rotating angle may be introduced by the fabrication resolution, the undesired scattering from the surrounding environment, and the edge effect of the metasurface with a finite size.
Fig. 5. Fabricated prototype of the proposed LP metasurface converter. (a) Top view. (b) Bottom view.
Fig. 6. Experimental demonstration of proposed LP metasurface converter. (a) Experimental setup. (b) Comparison between ideal, simulated and measured normalized $|S_{21}|$ for different receiving antenna rotating angles $\alpha$.
6. Comparison and discussion
Finally, the comparison between this work and other reported works is provided in Table 1. It is clearly observed that different from other works that are based on the different resonating states for different incident components, the proposed LP metasurface converter is realized with the antenna-circuit-antenna design, which separates the process of incidence picking up and wave processing, leading to flexible LP rotating angle.
Table 1. Comparison between reported work and this work.
In addition, it is worth mentioning that the operating band and bandwidth of the proposed LP metasurface converter are fully determined by the operating bands and bandwidth of the microstrip antenna and the $90^\circ$ hybrid coupler. By designing wideband or multiple band picking-up antenna and coupler components using various modern technologies [49,50], the operating band and bandwidth may be further improved.
7. Conclusion
We have presented a new design of LP metasurface converter. This LP metasurface converter is insensitive to incident wave polarization direction and may be easily implemented to achieve arbitrary polarization rotating angle by adjusting the additional microstrip line length connecting to the coupler ports. The proposed LP metasurface converter is analyzed theoretically and demonstrated by both full-wave simulation and experimental verification. This LP metasurface converter may find wide potential applications in RCS reduction, wireless communication, and imaging systems.
Funding
National Key Research and Development Program of China (2017YFA0100203).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request
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