## Abstract

Manipulating orthogonal circularly polarized (CP) waves independently in both reflection and transmission modes in a single metasurface is pivotal. However, independently controlling CP waves with different polarizations is difficult especially for both reflection and transmission modes. Here, we designed a receiver-transmitter metasurface with helicity-dependent reflection and transmission properties. Our design breaks the fixed phases of the geometry metasurface-carrying Pancharatnam-Berry operators by combining the receive and transmit antennas. To verify the effectiveness of the modulation, we designed three linear deflectors with: (a) reflection phase gradient, (b) transmission phase gradient, and (c) both of gradients to achieve anomalous reflection, anomalous refraction, and simultaneous anomalous reflection and refraction, respectively. As proof of the concept, a bifunctional meta-device with functions of anomalous reflection and focusing transmission for different incident CP waves was simulated and measured. Our findings offer an easy strategy for achieving arbitrary bifunctional CP devices.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Metasurfaces (MSs), composed of periodically or nonperiodically arranged subwavelength meta-atoms on an ultrathin surface, can effectively electromagnetic (EM) wavefronts by introducing abrupt phase changes [1]. Recently, MSs have gained tremendous interest in many areas such as anomalous reflection/refraction [1–3], focusing lens [4–7], polarization manipulation [8–9], propagating wave to surface wave transformation [10–12], photonic spin Hall effect [13–16], directional Janus functionalities [17], and so on [18–20]. More interesting physical properties are demonstrated in certain review articles [21–22]. MSs have provided a new route to design multifunctional devices, which improve their performance in device miniaturization and system integration [23–25]. Diversified functionalities have been integrated into a single device based on structural-phase MSs (controlling the phase of meta-atom by tuning the structure size) [26–29], geometric-phase MSs (controlling the phase by rotating the structure) [30–33], and mixtures of both [34–37]. For instance, Song et al. presented a general method that enables wavefront shaping with arbitrary output polarizations by encoding both phase and polarization information into pixelated metasurfaces [31]. In Ref. [32], Khorasaninejad et al. proposed a high-aspect-ratio titanium dioxide metasurface (MS) that can be fabricated and designed as metalenses with a numerical aperture of (NA) = 0.8. These powerful multifunctional devices have led to applications in the areas of on-chip photonic circuits [38–39], imaging [40–42], and information processing systems [43]. Some of the cited articles discuss multifunctional MSs that manipulate CP waves in the microwave regime [25,35,37,44]. For example, in Ref. [35], Ding et al. proposed a reflective dual-helicity decoupled coding metasurface to completely realize independent control of OAM vortices for two orthogonal helicities. In Ref. [37], Guo et al. proposed a single-layered spin-decoupled metasurface and its application to a dual-circularly polarized reflector antenna.

Multifunctional MSs have typically extended the wave-manipulation capabilities to the full space (reflection and transmission space). Very recently, our group achieved full-space wavefront manipulation using bifunctional MSs under excitations of linear waves [45]. However, it is a great challenge to realize the full-space wavefront manipulation for the excitations of CP waves. Some helicity-dependent MSs have been proposed to realize similar functionalities, i.e., focusing lens and diverging lens, or anomalous beam bending in transmission mode and reflection mode, respectively [46]. The intrinsically fixed Pancharatnam-Berry (PB) phases (±2*α* for left-handed circular polarization (LCP) and/or right-handed circular polarization (RCP) waves) in these MSs seriously limited their freedom to manipulate the CP wavefronts. Generally, once the phase for reflection wave is designed, the phase for the transmission wave is fixed. The phases for reflection and transmission waves are not independent and cannot be designed at will. Therefore, break the fixed phase relation in CP waves with different helicities is the key to realizing the free wavefront control in the full space.

In this paper, we first propose a receiver-transmitter (RT) [47–48] MS to independently control CP waves with different polarizations, which break the fixed phases for orthogonal CP waves [46]. The rotation of the receiver meta-atom (rotation angle *α*) can realize ±*α* phase shift for the incident CP waves with the opposite helicity, while the transmitter meta-atom (rotation angle *β*) can manipulate the radiated CP waves with ±*β* phase shifts. The combination of the receiver and transmitter meta-atoms can freely tune the transmissive CP waves with typical helicity. The phase ${{\varPhi }_r}$ of the reflected wave is controlled by the receiver rotation angle *α,* and the phase ${{\varPhi }_t}$ of the transmitted wave is controlled by the receiver rotation angle *α* and the transmitter rotation angle *β*. At the same time, the receiver meta-atom is a perfectly reflective PB structure for the incident CP waves with the opposite helicity, which can tune the reflection wave with a ±2*α* phase shift (see details in Section 2 of the Supporting Information). As a proof of concept, three beam deflectors were designed to achieve different beam bending performances for the transmitted and reflected CP waves. Moreover, a bifunctional meta-device was designed as demonstrated in Fig. 1, which can focus the incident LCP wave into a transmitted RCP wave and deflect the reflected RCP wave. Its working efficiency is very high for different CP waves. Our findings opened up a completely new way to realize high-efficiency multifunctional CP meta-devices working in full space.

## 2. Working principle and meta-atom design

The key to independent control of the orthogonal CP waves in full space is to break the fixed phase relation between the LCP and RCP waves. Suppose an LCP incident wave is received by an LCP microstrip antenna, the accumulated phase shift for the incidence is the sum of two contributions, ${{\varPhi }_{tot}}(r,\;\lambda ) = {{\varPhi }_p}(r,\;\lambda ) + {{\varPhi }_m}(r,\;\lambda )$, where, ${{\varPhi }_p}$ is the phase produced using the optical path and ${{\varPhi }_m}$ is the phase between the antenna patch and the feed port. We define the Receiver Patch 1, feed port, and Transmitter Patch 2 as Port 1, Port 2, and Port 3, respectively, as shown in Fig. 2(a). When the incident wave is received by an array of antennas with phase gradients, the transmitted wavefront can be controlled based on the generalized Snell’s law [1].

Here, $+$ and $-$ denote the RCP wave and LCP wave, respectively. As shown in the inset of Fig. 2(b), the designed LCP antenna Patch 1 (Receiver) can radiate only the LCP waves at a frequency of approximately *f*_{0} = 10 GHz. The antenna has a good matching property with a reflection coefficient lower than −15 dB. For such an antenna, ${{\varPhi }_m}_{12}$ (or ${{\varPhi }_m}_{21}$) can be tuned using the structure parameter (such as the antenna thickness ${h_s}$, patch size ${r_c}$, and slot size ${w_1}$ and ${w_2}$) and the rotation angle, *α,* of radiated Patch 1. More importantly, the phase shift is *α* due to the asymmetry of the antenna structure and antenna theory (see details in Section 1 of the Supporting Information). Figure 2(c) depicts the corresponding phase of ${{\varPhi }_m}_{12}$ as a function of the rotation angle *α*. A fixed phase shift of *α* can be observed against the working frequency. Namely, ${{\varPhi }_m}_{21} = \alpha$ can be obtained. Moreover, the amplitude is almost constant at approximately 0.94 because the antenna structure is not changed, as shown in Section 2 of the Supporting Information. The *α* phase shift is completely different from the PB operator, which should be highlighted. Although ${{\varPhi }_m}_{12}$ can be tuned using the rotation angle *α*, we should “read out” the phase information.

Another Transmit Patch 2, which is an RCP antenna, is introduced at the other side of the LCP antenna, as shown in Fig. 2(a). Meanwhile, the phase of the incident wave can be tuned at a second time by simply rotating Transmitter Patch 2 by an angle of *β*. The geometry of the receiver-transmitter meta-atom is shown in Fig. 2(a). The meta-atom is composed of three metallic layers separated by two identical substrates. The middle metallic layer is a square patch with a circular hole (${d_h}$_{ }= 1.7 mm) at the center of the meta-atom. Patch 1 (receiver) is connected to Patch 2 (transmitter) through a metallized via-hole (${d_v}$* *= 0.7 mm) placed at the center of the meta-atom. To manipulate the transmitted wavefront, the LCP incident wave illuminates the Patch 1. When the incident LCP wave is received by Receiver Patch 1, the RF signal can be converted into a guided wave signal. Then, it passes through the metallized via-hole to Transmitter Patch 2. Transmitter Patch 2 transform this signal to the RCP wave. The good matching property of the Receiver and Transmitter Patch antenna makes it possible to obtain total transmission for an LCP wave with a very low insertion. As shown in Fig. 2(d), the phase ${\varPhi }({t_{ +{-} }})$ of the transmitted wave can cover the entire 360° when only rotating *β* from 0° to 360° while maintaining a constant *α *= 0°. Therefore, the phase ${{\varPhi }_m}_{32}$ between Port 2 and Port 3 can be denoted as ${{\varPhi }_m}_{32} = \beta$. To obtain a fixed transmitted phase ${\varPhi }({t_{ +{-} }})$, we have countless combinations of rotation angles *α* and *β*. Here, as depicted in Fig. 2(e), the transmitted phase ${\varPhi }({t_{ +{-} }})$ versus rotation angles, *α* and *β*, comparison demonstrates that the same transmitted phase can be obtained using different combinations of rotation angles, *α* and *β*. In conclusion, the phase ${\varPhi }({t_{ +{-} }})$ of the transmitted wave can be denoted as:

*x*-polarized and

*y*-polarized waves propagating along the

*z*direction, respectively. As shown in Fig. 2(g), it is necessary to mention that $|{{r_{xx}}} |= |{{r_{yy}}} |\approx 0.95$ and $|{{\varPhi }({r_{xx}}) - {\varPhi }({r_{yy}})} |= 180 \pm 10^\circ$ is observed at approximately

*f*

_{0}_{ }= 10 GHz.

Therefore, the designed LCP antenna Patch 1 can manipulate the RCP wave with the PB operator. To verify its ability to manipulate the RCP incident wave with the PB operator, the designed LCP antenna Patch 1 is illuminated by an RCP incident wave. Rotating Patch 1 with a step of *α* clockwise, the phase and amplitude of the reflected RCP wave are observed in Fig. 2(f). As expected, the proposed meta-atom achieved an accuracy phase shift of −2*α* for the phase of the reflected RCP wave, and almost all of the amplitudes are higher than 0.94, this indicates a very high efficiency for manipulating the RCP wave. Here, the phase of the reflected RCP wave ${\varPhi }({r_{ +{+} }})$ can be denoted as

## 3. Anomalous reflection and refraction effects in the same plane

To verify the completely free phase control ability of the proposed meta-atom, three typical beam deflectors are proposed to achieve different anomalous reflection and refraction effects. Deflector 1, Deflector 2, and Deflector 3 were designed to realize only reflection phase control, only transmission phase control, and a combination of reflection phase control and transmission phase control, respectively. The deflectors were composed of *N*×*N* meta-atoms, fixing *N *= 24, and each deflector is identical along the *y*-axis.

For Deflector 1, the phase gradients of the reflection and transmission waves were set to 45° and 0°, respectively. Therefore, the target phase distribution of the reflection wave is ${\varPhi }({r_{ +{+} }})$ = −2*α*(*n*) (*α* scanning from 0° to 360° with a step of 22.5° and *n* ranging from 1 to N), while the target phase distribution of the transmitted wave was ${\varPhi }({t_{ +{-} }})$ = 0. Here, *n* is the element number along the *x*-axis. According to Eq. (2), it can be deduced that *α*(*n*) =22.5(*n*-1). According to Eq. (1), *β*(*n*) can be denoted as *β*(*n*) = -*α*(*n*). As shown in Figs. 3(c) and 3(d), Receiver Patch 1 and Transmitter Patch 2 are arranged on the linear array according to the relative target phase distribution ${\varPhi }({r_{ +{+} }})$ and ${\varPhi }({t_{ +{-} }})$. A periodic boundary is applied in the *y* direction, and an open boundary is applied to the *x* and *z* directions. RCP and LCP illuminate the array along the *z* direction, respectively

The target phase of ${\varPhi }({r_{ +{+} }})$ and ${\varPhi }({t_{ +{-} }})$, corresponding to the rotation angles *α* and *β*, are plotted in Fig. 3(a). According to the generalized law of reflection [1], the theoretical reflected angle is calculated to be ${\theta _r}$_{ }= 15.5°. The normalized simulated radiation pattern (normalized with the PEC Deflector) for Deflector 1 is shown in Fig. 3(b). The reflected wave ${r_{ +{+} }}$ is reflected to *θ *= 164.8° and the transmitted wave ${t_{ +{-} }}$ is not anomalously refracted, with reflected angle ${\theta _r}$ = 15.2°, which agrees well with the theoretical calculation. Then, we evaluated the working efficiency of Deflector 1. Efficiency is defined as the ratio of power carried by the anomalous reflected beam ${r_{ +{+} }}$ in the range of [90°, 270°] of the reflection side to that of the total power. We integrated the power in the corresponding regions. The simulated efficiency is approximately 92.5% at 10 GHz.

For Deflector 2, the target phase gradients of the reflection and transmission waves were set to 0° and 60°, respectively. Therefore, target phase distribution is ${\varPhi }({r_{ +{+} }})$ = 0 and ${\varPhi }({t_{ +{-} }})$ = 60(*n*-1). Here, *n* is the element number along the *x*-axis. Namely, *β*(*n*) = 60(*n*-1), *α*(*n*) = 0. As shown in Figs. 3(g) and 3(h), Patch 1 and Patch 2 are arranged on the linear array according to the target phase distribution ${\varPhi }({r_{ +{+} }})$ and ${\varPhi }({t_{ +{-} }})$, respectively. The target phase of ${\varPhi }({r_{ +{+} }})$ and ${\varPhi }({t_{ +{-} }})$, corresponding to the rotation angles *α* and *β*, are plotted in Fig. 3(e).

Based on the generalized law of refraction [1], the theoretical refracted angle is calculated to be ${\theta _t}$ = 20.9°. The normalized simulated radiation pattern for Deflector 2 is shown in Fig. 3(f). As shown, ${t_{ +{-} }}$ is refracted in the -*x* direction with *θ* = −20.7° and ${r_{ +{+} }}$ is not anomalously reflected, namely refracted angle ${\theta _t}$* *= 20.7°, which agrees well with the theoretical calculation. Then, we evaluated the working efficiency of Deflector 2. Efficiency is defined as the ratio of power carried by the anomalous refracted beam ${t_{ +{-} }}$ in the range of [−90°, 90°] of the transmission side to that of the total power. We integrated the power in the corresponding regions. The simulated efficiency is approximately 91% at 10 GHz.

For Deflector 3, the target phase gradient distributions of the reflection and transmission waves were set to 45° and 60°, respectively. Here, *n/m*, ranging from 1 to N, are the element numbers along the *x*-axis. Therefore, the target phase distribution of the reflection wave is ${\varPhi }({r_{ +{+} }}) ={-} 2\alpha (n)$ ($\alpha (n) = 22.5(n - 1)$). The target phase distribution of the transmission wave was ${\varPhi }({t_{ +{-} }}) = \alpha (n) + \beta (m)$ ($\beta (m) = 60(m - 1)$). Namely, ${\varPhi }({t_{ +{-} }}) ={-} 22.5(n - 1) + 60(m - 1)$ needs to be satisfied. Therefore, Patch 1 and Patch 2 are arranged on the linear array, as shown in Figs. 3(k) and 3(l), respectively. The theoretical reflected and refracted angles are calculated to be ${\theta _r}$ = 15.5° and ${\theta _t}$ = 20.9°. The target phases of ${\varPhi }({r_{ +{+} }})$ and ${\varPhi }({t_{ +{-} }})$, corresponding to the rotation angles, *α* and *β*, are plotted in Fig. 3(i). The normalized linear scaling simulated radiation pattern for Deflector 3 is shown in Fig. 3(j). As shown, the reflected wave ${r_{ +{+} }}$ is reflected in the + *x* direction with *θ* = 164.8° and ${t_{ +{-} }}$ is refracted in the -*x* direction with *θ* = −20.7°, with reflected angle ${\theta _r}$ = 15.2° and refracted angle ${\theta _t}$ = 20.7°. The simulation results agree well with the theoretical calculations. Then, we evaluated the working efficiency of Deflector 3. The simulated working efficiencies for anomalous reflection and refraction are 92.5% and 91%, respectively. Based on the above three deflectors, we can conclude that the proposed meta-atom can manipulate the orthogonal CP waves without fixed relations in full space.

## 4. Full-space bifunctional meta-device design and experiment

According to the unique property described in the above section, we designed a bifunctional meta-device operating at *f _{0}* = 10 GHz using 15×15 meta-atoms. With the well-designed meta-atom, we designed a bifunctional meta-device that deflects RCP incident wave to the +

*x*direction with an angle of 15.4° and converts the LCP incident wave into an RCP transmitted focusing wave. To achieve this goal, we set the phase gradient to 45° for the anomalous reflection and focal length

*L*= 110 mm for the focusing wave at

*f*= 10 GHz.

_{0}In the reflection mode, the phase gradient Δ*Φ* = 45° is only arranged in the *x* direction. Therefore, the phase distribution on every row should satisfy ${{\varPhi }_{{r_{ +{+} }}}}(m,n) ={-} 2\alpha (m,n)$, where *m* and *n* are the meta-atoms arranged along the *x* and *y* directions, respectively. According to the above analysis, it can be deduced that $\alpha (m,n) ={-} 22.5(m - 1)$*.* Therefore, the phase distribution of ${{\varPhi }_{r +{+} }}(m,n)$ should yield the following equation:

*m*,

*n*) should be compensated by a phase difference $\Delta {{\varPhi }_{t +{-} }}(m,n) = {{\varPhi }_{t +{-} }}(m,n) - {\varPhi }(0,0)$ accumulated from the lens, yielding the following phase distribution:

*p*is the periodicity of the meta-atom,

*L*is the focal length, and

*m*and

*n*are the meta-atom positions along the

*x*and

*y*directions, respectively.

Figure 4(c) describes the target phase distribution according to Eq. (4). According to Eq. (1), to achieve the target phase distribution, the rotation angle of Transmitter Patch 2 at meta-atom location (*m*, *n*) should be obtained using the following equation:

*β*(

*m*,

*n*) along the

*x*and

*y*directions is depicted in Fig. 4(d). In addition, the amplitude of the reflected wave ${r_{ +{+} }}$ and transmitted wave ${t_{ +{-} }}$ are depicted in Figs. 4(e) and 4(f), almost all of which are all higher than 0.93. This amplitude distribution makes it very efficient in manipulating reflected and transmitted waves.

Then, the bifunctional meta-device is fabricated using the standard printed-circuit-board technology. The meta-device is composed of 15×15 meta-atoms, which exhibits a total volume of 210×210×3 mm^{3}, corresponding to 7*λ*_{0}×7*λ*_{0}×0.1*λ*_{0}. Figures 4(a) and 4(b) demonstrate the receive and transmit sides of the fabricated sample. To validate our design, we first examine our sample functionality as an anomalously reflective meta-device. Illuminating the meta-device by RCP wave radiated from an RCP horn antenna at the normal incidence, we detected the electric-field (E-field) distributions at the reflection space using a monopole and recorded the local E-field using a vector field network analyzer (Agilent E8362C PNA), as schematically shown in Fig. 5(a).

We measured the deflection performance of our meta-device under the illumination of an RCP wave. Figures 5(c) and 5(d) depict the measured scattering field intensities as a function of the detection angle and frequency. It clearly shows that, within a frequency interval from 9.5 to 10.3 GHz, most of the RCP reflected waves are deflected to an anomalous angle, described perfectly using the generalized Snell’s law [solid stars in Fig. 5(c)]. Obviously, the best performance is found at the working frequency *f _{0}* = 10 GHz, where the normal-mode reflection disappears nearly completely, while the anomalous reflection reaches a maximum. Then, we evaluated the working efficiency of our meta-device. Efficiency is defined as the ratio of power carried by the anomalous reflected beam

*r*

_{++}in the range of [−90°, 90°] of the reflection side to that of the total power. We integrated the power in the corresponding regions, and the simulated and measured efficiencies are approximately about 92.5% and 91% at 10 GHz, respectively.

Next, we examine our sample functionality as a transmitted focusing lens. Shining LCP waves radiated from an LCP horn antenna onto the sample, we employed a monopole antenna to measure the electric-field distributions at its transmission side, as shown in Fig. 5(a). The experimental setup used to measure the focusing wave are shown in Fig. 5(b). First, to validate the functionality of focusing a transmitted wave, a meta-device is simulated using FDTD. A curve is placed along the *z*-axis to evaluate the power field on the curve to obtain the focal point. As depicted in Fig. 5(e), the maximum power distribution is approximately *L* = 110 mm, and the measured focal length (*L* = 109 mm) matches well with the theoretical design (*L* = 110 mm) and FDTD simulation result (*L* = 110 mm). The simulated electric-field distributions right on the focal plane at *z* = 110 mm [inset of Fig. 5(e)] reinforces the excellent focusing performance. To further evaluate the focusing effect, we measured and then depicted the normalized power distribution on the line (*y *= 0, *z *= 109 mm) in Fig. 5(f). The focal spot size, which is defined as the width over which the peak power drops by half, is equal to 15 mm (0.5*λ*_{0} at 10 GHz), which illustrates a good focusing effect.

To demonstrate the functionality of focusing transmitted waves clearly, Figs. 5(g) and 5(i) plot the simulated and measured Re(*E _{x}*) distributions at the

*xoz*plane at 10GHz, respectively. Moreover, the simulated and measured Re(

*E*distributions at the

_{x})*yoz*plane at 10 GHz are shown in Figs. 5(h) and 5(j). Good agreement between the numerical and experimental results demonstrates the excellent focusing effects. Then, we evaluated the absolute focusing efficiency, which is defined as the ratio between the power carried by the focal spot and that of the incident beam. Direct measurement of the meta-device working efficiency is technically impossible, we used a two-step method to approximately evaluate it, following the strategy established in Ref. [28]. The absolute working efficiency can be calculated as $\eta = \frac{{{P_{tra}}}}{{{P_{tot}}}} \times \frac{{{P_{foc}}}}{{{P_{tra}}}}$. The first term,

*P*/

_{tra}*P*represents the ratio between the power carried by the totally transmitted waves and that of the incident one. The second term,

_{tot}*P*/

_{foc}*P*is defined by the ratio between the power taken by the focal point and that of the focal plane, which can be obtained by two integrations run over the areas occupied by the focusing spot (the dashed-line circle in the inset of Fig. 5(e)) and the meta-device. As a result, the absolute efficiency of the focusing lens is 83% for the measured result. Therefore, the incident LCP wave is indeed focused on the RCP transmitted wave, which agrees reasonably with the theoretical one.

_{tra}## 5. Conclusions

We theoretically and experimentally proposed a novel and easy RT metasurface, which is based on Receiver-Transmitter, to achieve complete control of the reflection and transmission phases for orthogonal CP waves independently. The reflection and transmission phases are tuned using the angles *α* and *α*+*β*, respectively. Based on this meta-atom, arbitrary phases for the LCP and RCP waves were achieve. Using a set of proposed meta-atoms, a bifunctional meta-device with anomalous reflection in reflective mode and wave focusing in transmission mode was finally simulated, fabricated, and measured. The bifunctional meta-device makes it possible to manipulate orthogonal CP waves without locked phase relations between reflected and transmitted waves. Our findings open new possibilities for realizing high-efficiency multifunctional CP meta-devices working in full space.

## Funding

Natural Science Foundation of Shaanxi Province (2019JQ-013); Postdoctoral Innovation Talents Support Program of China (BX20190293); National Natural Science Foundation of China (61901512); National Natural Science Foundation of China (61871394).

## Disclosures

The authors declare no conflicts of interest.

See Supplement 1 for supporting content.

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