High-efficiency dual-modes vortex beam generator with polarization-dependent transmission and reflection properties

Vortex beam is believed to be an effective way to extend communication capacity, but available efforts suffer from the issues of complex configurations, fixed operation mode as well as low efficiency. Here, we propose a general strategy to design dual-modes vortex beam generator by using metasurfaces with polarization-dependent transmission and reflection properties. Combining the focusing and vortex functionalities, we design/fabricate a type of compact dual-modes vortex beam generator operating at both reflection/transmission sides of the system. Experimental results demonstrate that the designed metadevice can switch freely and independently between the reflective vortex with topological charge m1 = 2 and transmissive vortex with m2 = 1. Moreover, the metadevice exhibits very high efficiencies of 91% and 85% for the reflective and transmissive case respectively. Our findings open a door for multifunctional metadevices with high performances, which indicate wide applications in modern integration-optics and wireless communication systems.

a single metasurface, respectively. As shown in Fig. 1(a), shining an x-polarization quasi-spherical wave normally onto our metasurface, a reflective vortex beam generator with topological charge m 1 = 2 can be obtained. Meanwhile, for a y-polarized incident wave, our metadevice can work as a transmissive vortex beam generator with m 2 = 1 (see Fig. 1(b)). Moreover, our metadevice can work with very high efficiencies since our meta-atom is totally reflective for x-polarization incident wave and completely transparent for y-polarization EM wave with arbitrary phase profiles, respectively. Our findings can not only set up a new platform to design compact and integrated vortex beam generator, but more importantly, they also provide a powerful guideline to design other metadevices with other functionalities or in other frequency domains.

Working principle and meta-atom design
In order to realize the above mentioned dual-modes vortex beam generator, we need to design an appropriate meta-atom which can control the transmitted and reflected waves efficiently and independently. In our recent research, we proposed such a meta-atom, which can meet the above requirements 33 . Here, we describe its working principle briefly. For a system with mirror symmetry, its EM property can be described by two diagonal Jones , with r xx , r yy , t xx and t yy being the reflection and transmission coefficients with polarizations along two principle axes x and ŷ, respectively. In a lossless system, we can obtain | | + | | = r t 1 xx xx 2 2 and | | + | | = r t 1 yy yy 2 2 due to the energy conservation. Here, we consider two ideal conditions. Firstly, for an x-polarized incident wave, we can completely suppress the transmission power Secondly, for a y-polarization, we can enlarge the transmission part | | = t ( 1 ) yy and block all the reflection | | = r ( 0 ) yy . These two conditions are independent and can be combined to manipulate the transmitted and reflected waves simultaneously.
Then we discuss how to design such a desirable meta-atom. Here, meta-atoms in multilayer geometry (with deep-subwavelength total thicknesses) are found as alternative candidates. Each single layer exhibits perfect EM transmission at a particular frequency due to the interaction between the patch resonator and the opaque mesh. Mutual interactions between different layers can realize high transmission amplitude as well as the large transmission-phase variation range covering 360°. . At x direction, we connect the metallic stripes at bottom two layers to block the x-polarized incident wave, while the metallic stripes at upper two layers have small size to tune the reflected wave. In our design, the parameter d 1 and d 2 can be tuned to control the number of magnetic resonances and expand the design freedom. At y direction, the metallic patch structures have the same size, which can enhance the transmission and enlarge the phase-shift range due to the coupling among different layers [44][45][46][47][48] . To demonstrate our concept, we fabricate a microwave sample, which consists of periodic array of such special meta-atoms, with its top and bottom views shown in Fig. 2(b). The measured  reflection coefficient under an x-polarized EM wave is plotted in Fig. 2(c). We can see that the reflection amplitude | | r xx reaches near 1 at the target frequency of f 0 = 10.5 GHz, indicating high reflection for our meta-atom. The reflection phase ϕ xx r varies from −180° to 180° as the frequency changes from 7 GHz to 13 GHz. Under a  Fig. 2(d). Moreover, the transmission phase ϕ yy t covers 360° range as frequency varies. Finite-difference-time-domain (FDTD) simulation results agree well with the measured cases.
After characterizing the EM response of this typical meta-atom, we can immediately understand that the phases ϕ ϕ ( and ) xx r yy t can be tuned by changing the geometric structural details. Figure 2(e-h) illustrate, respectively, how ϕ xx r , | | r xx , ϕ yy t , and | | t yy vary against the parameters a, d 1 and d 2 , with frequency fixed at 10.5 GHz. Obviously, ϕ xx r is sensitive to d 1 and d 2 but insensitive to a, while ϕ yy t behaves oppositely. At the top of Fig. 2(e-h), reflection response of the designed metasurface is determined by two magnetic resonances which is generated by varying d 1 and d 2 simultaneously (d 1 = d 2 ). While at the bottom of Fig. 2(e-h), it is determined by the single magnetic resonance generated by changing the parameter d 1 and fixing d 2 = 11 mm. Changing the structural parameters within the restricted spaces (5 mm < d 1 < 10.8 mm, d 2 = 11 mm and 8.2 mm < d 1 = d 2 < 9 mm and 4 mm < a < 8.5 mm), we find that the variations of the two phases ϕ ϕ ( and ) xx r yy t already cover the whole 360° range, while simultaneously the reflection/transmission amplitudes (| | r xx and | | t yy ) remain at very high values (| | r xx >0.92, | | t yy >0.85), which ensures the high working efficiency of the designed metasurface. With arbitrary phase distribution, coupled with high reflection/transmission amplitude of the meta-atom, we can achieve required functionalities as expected.

Experimental Results and Discussions
The proposed meta-atom is very suitable to achieve bifunctional metadevices working at both reflection and transmission sides of the metasurfaces. Here, we construct a bifunctional vortex beam generator as an example. Different from currently reported vortex beam generator 1-16 , our design can not only realize vortex beams with different topological charges, but also with very high efficiencies, which results from the independent manipulation of vortex beams based on the polarization-dependence of the metasurfaces. To ensure a compact structure, we excite the metasurface with a self-made Vivaldi antenna, which can radiate quasi-spherical waves at a wide frequency range 49 . Thus, the metasurface should incorporate two distinct phase profiles of a lens and a vortex plate, which can be calculated as with F 1 and F 2 being two focal lengths which can be chosen freely and arbitrarily, m 1 and m 2 denoting the topological charges which are integers. Here, we set F 1 = F 2 = 60 mm to ensure efficient integration of different functionalities. Moreover, m 1 = 2 and m 2 = 1 are chosen to demonstrate independent control of vortex modes. The designed metasurface consists of 16 × 16 meta-atoms and exhibits a total size of 176 × 176 mm 2 , with the pictures shown in Fig. 3(a) and (b). To validate our design, we show in Fig. 3(e,f) the FDTD calculated continuous phase distributions and discrete phase profiles at each meta-atom, which agree well with the theoretical values in Eq. (1). The corresponding high reflection-transmission amplitude distributions shown in Fig. 3(g,h) (|r xx | > 0.92, |t yy | > 0.86) indicate high working efficiencies of our metadevice. With the fabricated sample in hand, the next step is to characterize the performances of the metadevices through microwave experiments. We firstly characterize its reflection functionality. As illustrated in Fig. 4(b), the designed vortex beam generator is excited by an x-polarized Vivaldi antenna. The electric field of the system is detected at the reflection side by a waveguide antenna and recorded by a vector-field network analyzer (Agilent E8362C PNA). Referring to the measured Re(E x ) and phase distributions at xoy plane (30 cm behind the sample) shown in Fig. 4(c) and (d), we can see clearly that pure vortex beams with m 1 = 2 are generated by integrating x-polarized waves reflected by meta-atoms at different positions. The amplitude null in the center of the 3-D radiation pattern in Fig. 4(e) demonstrates once again the excellent vortex effect for a second time. The measured 2-D radiation pattern at xoz plane agrees well with the simulated case, indicating that the amplitude in the azimuth (θ = 0°) is lower than −28 dB. Based on the far-field measurements, we can quantitatively examine the working efficiencies of our device. Here, there are three channels to propagate the energy of the incident waves: scattering to the transmission part, absorption and conversion to vortex beams by the reflection energy. For the reflective functionality, the working efficiency can be estimated by the formula η = 1 − T − A, where T and A describe the scattering energy to the transmission side and absorption, respectively. The transmission energy can be evaluated by integrating the energy at the transmission part of the far-field pattern, where T is found of 7% (5%) for measurement (simulation). The absorption is calculated as 2% (1.5%), estimated by integrating the total scattering energy with and without metasurfaces. Therefore, the numerical and experimental efficiency is estimated as 91% and 93.5%, respectively.
We secondly characterize the transmission property of our metadevice. Rotating the feeding Vivaldi antenna by 90°, our system can behave as a transmissive vortex beam generator with m 2 = 1. Similar to the experimental configuration of the reflection functionality, we measure the electric field distributions at the transmission part (30 cm in front of the designed metadevice) (see Fig. 4(a)). The pure Re(E y ) distribution in Fig. 5(a) and spiral trend of phase distribution in Fig. 5(b) demonstrate the excellent characteristic of vortex beam. Referring to the 3-D radiation pattern in Fig. 5(c), the deep dip at the center further validates the good performance of the designed system. Observation from the measured and simulated 2-D radiation patterns at xoz planes indicate that the gain is lower than −22 dB and −23 dB at the specular direction, respectively. The working efficiency can be described as η = 1 − R − A, with R denoting the reflection energy. R is computed by integrating the power at the reflection part of the designed system. Thus, the efficiency of the transmissive vortex beam is evaluated as 86% (89%) for measurement (simulation). Compared with the reported multi-modes vortex beam generators 1-16 , our design exhibits very high working efficiencies since the interferences among different modes are reduced based on the polarization-dependent property of the metadevice.
Finally, we estimate the working bandwidth of our dual-modes vortex beam generator. The bandwidth is defined by −10 dB level of specular radiation for the far-field pattern. The bandwidth for the reflection functionality is found as 1.6 GHz (9.6-11.2 GHz). The corresponding Re(E x ) and phase distributions at lower and higher frequencies of the band are shown in Fig. 6(a-d). Within the working frequency interval, the reflected waves can be successfully converted to vortex beams and keep at very high working efficiencies. Outside the working frequency range, specular reflections would increase significantly. The bandwidth of the transmission functionality varies from 9.5 GHz to 11 GHz. Similarly, the transmissive waves can be converted to pure vortex beams within the bandwidth, demonstrated by the pure Re(E y ) and spiral phase distributions at two edges of frequency band shown in Fig. 6(e-h).

Conclusion
To summarize, we proposed a new kind of dual-modes vortex beam generator by using well designed metasurfaces with polarization-dependent transmission and reflection properties. The designed vortex beam generator can not only manipulate the operating modes (topological charges) freely and independently but also can work at both sides of the metadevice. Both near-field and far-field characterizations demonstrate the good vortex effects. More importantly, the designed vortex beam generator exhibits very high working efficiencies (91% for the reflective mode and 85% for the transmissive case). Our findings pave the road to realize high-efficiency metadevices with mode-manipulation properties, which are crucial importance in modern EM integration. Data availability statement. All relevant data are within the paper.