Helicity-dependent metasurfaces employing receiver-transmitter meta-atoms for full-space wavefront manipulation

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.

Here, it can be assumed that an incident LCP wave propagates along the +z direction. Then the incident wave's electric field can be described as: According to the antenna theory, the signal received by the Receiver Patch 1can be described as: Where Φ p is the accumulated phase transmitted from the radiated source by optical path. Meanwhile, the transmission phase from the Receiver Patch 1 (Port 1) to the waveport (Port 2) is denoted as When the Receiver Patch 1 rotate clocklwise with α angle, the incident wave under u-v axis can be described as According to the antenna theory, the signal received by the Receiver Patch 1can be described as: where Φ p is the accumulated phase transmitted from the radiated source. Meanwhile, the transmission phase from the Receiver Patch 1 (Port 1) to the waveport (Port 2) is denoted as Therefore, the phase gradient Φ m21 denoted as Therefore, there is a phase gradient Φ m21 =α when rotating the Receiver Patch 1 with the angle α. This is a key point for proposed meta-atom working in the transmission mode, which is very different from the PB theory.

Additional FDTD simulation of the designed meta-atom
The proposed meta-atom is composed of Receiver and Transmitter CP patch. For the Receiver CP patch, there are two choices: LCP and RCP. For the transmitter CP patch, can be LCP or RCP antenna.
Therefore, there are four cases (Case 1, Case 2, Case 3, and Case 4 ) of receiver and transmitter can be denoted as Table S1, where r ij represents the reflected wave when illuminating by j-polarization and receiving by i-polarization and t ij represents the transmitted wave when illuminating by j-polarization and transmitting i-polarization Here, + and − denote the RCP wave and LCP wave, respectively.
For example, in Case 1, the receiver is a LCP patch antenna and transmitter is RCP patch antenna. In this case, the RCP incident wave can be reflected by Receiver and the reflected wave is still RCP wave.
Therefore, r ++ is achieved. Meanwhile, the LCP incident wave is received by the LCP Receiver (Patch 1) and is converted into guided wave signal. And then it passes through the metallized via-hole to the Transmitter (Patch 2). Due to the RCP Transmitter, the guided wave signal is radiated into RCP wave.
Therefore, t +-is achieved. The other cases ( Case 2 , Case 3, and Case4 ) are depicted in Table S1.
Next, the Receiver-transmitter corresponding to Table S1 is depicted in Fig. S2.

Case 1 analysis:
For the Case 1, Receiver Patch 1 is a LCP patch and Transmitter Patch 2 is RCP patch. Therefore, RCP reflected wave and RCP transmitted wave can be obtained under the illumination of RCP and LCP incident wave. After that, the meta-atom is simulated and analyzed using FDTD. And the simulated results are shown in Fig. S3. From the Fig. S3, relative phase Φ(r ++ ), phase Φ m21 of transmitted coefficient from Port 1 to Port 2, the phase Φ m32 of transmitted coefficient from Port 2 to Port 3, and transmitted phase Φ(t +-) can be described as: To demonstrate the operation process of the reflection mode clearly, we scan α from 0° to 360° with a obvious that Φ(r ++ ) is able to realize the range of -2α degree with α varying from 0° to 180° and Φ(r ++ ) 6 does not change with β varying from 0 to 360 degree in Fig. S4(a). It indicates that phase of reflected wave r ++ is controlled only by α not β. Therefore, we can manipulate the phase of r ++ by changing the α from 0° to 180° to obtain the reflected phase from 360° to 0°. Fig. S4(b) demonstrates that the amplitude of r ++ is almost a constant about 0.95 with varying α and β, leading to manipulate wavefront of r ++ with very high efficiency. To demonstrate the operation process of the transmissive mode clearly, we scan β from 0° to 360° with a step of 22.5° while scan α from 0° to 360° with a step of 22.5°. The transmitted phase and amplitude versus α and β are shown in Figs. S4(c) and S4(d), respectively. Fig. S4(c) demonstrates that Φ(t +-) can cover the range of 0°-360° by rotating α, or β, or both of them. More interesting, the same Φ(t +-) can be achieved by totally different combinations of rotation angle α and β, which means our receiver-transmitter meta-atom can control the CP waves with different chirality freely in the full space.
And Φ(t +-) agrees well with the theatrical one based on Equation (S9). As shown in Fig. S4(d), the amplitude of t +-is almost a constant about 0.94 with the variation of α and β, which means a very high transmitted efficiency.

Case 2 analysis:
For the Case 2, Receiver Patch 1 is LCP patch and Transmitter Patch 2 is LCP patch. Therefore, RCP reflected wave and LCP transmitted wave can be obtained under the illumination of RCP and LCP incident wave. According to the Case 1 analysis, the same methods are used to demonstrate the characteristics of meta-atom in Case 2. By FDTD simulation, reflected phase Φ(r ++ ), phase Φ m21 of 8 transmitted coefficients from Port 1 to Port 2, the phase Φ m32 of transmitted coefficients from Port 2 to Port 3, and transmitted Φ(t --) can be described as: We scan α from 0° to 360° with a step of 22.5° while scan β from 0° to 360° with a step of 22.5°. The

Case 3 analysis:
For the Case 3, Receiver Patch 1 is RCP patch and Transmitter Patch 2 is RCP patch. Therefore, LCP reflected wave and RCP transmitted wave can be obtained under the illumination of LCP and RCP incident wave According to the Case 1 analysis, the same methods are used to demonstrate the characteristics of meta-atom in Case 3. Reflected phase Φ(r --), phase Φ m21 of transmitted coefficient from Port 1 to Port 2, phase Φ m32 of transmitted coefficient from Port 2 to Port 3, and transmitted phase Φ(t ++ ) can be described as: We scan α from 0° to 360° with a step of 22.5° while scan β from 0° to 360° with a step of 22.5°. The and S6(d), respectively. The simulated results are in good agreement with the theatrical calculation based on Equations (S16)-(S19). from Port 1 to Port 2, the phase Φ m32 of transmitted coefficient from Port 2 to Port 3, and transmitted phase Φ(t -+ ) can be described as: We scan α from 0° to 360° with a step of 22.5° while scan β from 0° to 360° with a step of 22.5°. The  For the redesigned Deflector 1, reflected/refracted angle / r t θ θ were set to 45° and 0°, corresponding to the phase gradient 119° and 0°, respectively. Therefore, the target phase distribution of the reflection wave is ( ) Φ r ++ = -2α(n) (α scanning from 0° to 360° with a step of 59.5° and n ranging from 1 to N), while the target phase distribution of the transmitted wave was ( ) Φ t +− = 0. Here, n is the element number along the x-axis. According to Eq. (2), it can be deduced that α(n) =59.5(n-1). According to Eq.
(1), β(n) can be denoted as β(n) = -α(n). As shown in Figs. S8(c) and S8(d), Receiver Patch 1 and Transmitter Patch 2 are arranged on the linear array according to the relative target phase distribution ( ) Φ r ++ and ( ) Φ 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 ( ) Φ r ++ and ( ) Φ t +− , corresponding to the rotation angles α and β, are plotted in Fig. S8(a). The normalized simulated radiation pattern (normalized with the PEC Deflector) for Deflector 1 is shown in Fig. S8(b). The reflected wave r ++ is reflected to θ = 135° and the transmitted wave t +− is not anomalously refracted, with reflected angle θ r = 45°, which agrees well with the target reflection angle.