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Abstract
A multifunctional metasurface is capable of manipulating electromagnetic waves and achieving kaleidoscopic functions flexibly, which significantly improves the integration and utilization of a single metasurface and has become one of the hotspots in electromagnetics. However, the majority of designs to date can only operate for limited polarization states in half-space and are difficult to show diverse functions at the same time, which restrict the widespread applications of multifunctional metadevices. Herein, an inspiring strategy of a chiral transmission-reflection-selective bifunctional metasurface is proposed to generate two independent functions in co-polarized reflection channel for left-handed circular polarized (LCP) incidence utilizing rotation-induced geometric phase modulation and in co-polarized transmission channel for right-handed circular polarized (RCP) incidence utilizing scaling-induced propagation phase modulation, and both functions appear concurrently under arbitrary linear polarized (LP) incident waves. To verify the feasibility of this methodology, three proof-of-concept metadevices composed of a dual-mode orbital angular momentum (OAM) generator, a bifocal metalens and an integrated metadevice of OAM generator and metalens are constructed and their performances in simulations and experiments are in good accordance with the theoretical ones. This exotic design of bifunctional metasurface will open up a promising way for multifunctional metadevices in engineering applications.
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1. Introduction
Metasurfaces, planar artificial arrangements of sub-wavelength meta-atoms, have been continuously attracting enormous interest owing to their flexible controls in amplitude, phase and polarization state of electromagnetic waves [1–4]. And because of the distinguished properties of ultrathin thickness, low loss and simple fabrication [5,6], metasurfaces have shown practical applications from terahertz to visible domains, such as beam deflectors [7], achromatic focusing lenses [8,9], spoof surface plasmon polaritons couplers [10,11], vortex beam generation for wireless communication systems [12,13], antennas [14,15], hologram imaging [16,17] and so on and so forth [18–22].
In order to further improve the utilization and integration of single metasurface, the design of multifunctional metasurfaces has become a hot research issue in recent years. Metasurfaces with asymmetric transmission characteristics can show different responses by changing the propagation direction of incident waves [23–25]. Some efforts have also been devoted to achieve various functions in different frequency domains [25–27]. More striking, a series of designs are proposed to switch functions after changing the polarization state of incident waves. Metasurfaces can realize high-efficiency selection and get diverse responses for orthogonal linear polarized (LP) waves according to the principles of “Fabry-Pérot-like” cavity and scaling-induced propagation phase [28–31]. Nevertheless, propagation phase has the same effect on left-handed circular polarized (LCP) waves and right-handed circular polarized (RCP) waves [32]. Compared with propagation phase, rotation-induced geometric phase, also known as the Pancharatnam-Berry (PB) phase, is introduced for metasurfaces to generate opposite phase profiles in cross-polarized transmission channel or in co-polarized reflection channel under LCP and RCP illumination [33–35]. Consequently, the integrated design of propagation phase and geometric phase can make metasurfaces realize independent manipulation for orthogonal circular polarized (CP) waves, and some schemes of CP bifunctional metasurfaces was proposed based on this methodology [36–39]. However, most bifunctional metasurfaces can only work for two orthogonal polarization states, and their functions are confined in half-space and hard to be exhibited concurrently under single incidence condition because of the mutual interference between diverse functions, which limit the versatile simultaneous performances of bifunctional metasurfaces. It is generally known that LP waves can be regard as the composition of LCP and RCP waves with equal proportion [40,41]. Hence, if a CP bifunctional metasurface is designed to block LCP (or RCP) waves and transmit RCP (or LCP) waves at the same time, both functions can appear simultaneously under arbitrary LP incidence. This novel idea inspires us to construct the fire-new bifunctional metasurface.
In this work, we propose a strategy to construct ingenious chiral transmission-reflection-selective bifunctional metasurfaces, whose meta-atoms consist of double-layered chiral structure and four-layered square patch structure. The double-layered chiral structure can reflect LCP waves and transmit RCP waves into co-polarized waves with relatively high efficiencies. The wavefronts of LCP reflected waves are controlled based on geometric phase principle by rotating the double-layered chiral structure with appointed angles, and the wavefronts of RCP transmitted waves are modulated based on propagation phase principle by adjusting the dimensions of meta-atoms’ two structures. A dual-mode orbital angular momentum (OAM) generator, a bifocal metalens and an integrated metadevice of OAM generator and metalens are established to demonstrate our theoretical designs. Both simulated and measured results verify that the elaborate bifunctional metadevices can achieve independent functions for LCP and RCP waves, and show both functions under x-polarized incidence and y-polarized incidence, showcasing that they are also effective for arbitrary LP incident waves, as described in Fig. 1.
Fig. 1. Schematic of the proposed chiral transmission-reflection-selective bifunctional metasurface, which can achieve two independent functions (F1 in reflection channel and F2 in transmission channel) simultaneously under arbitrary LP incident waves.
2. Meta-atom design and basic principles
By way of fabricating chiral transmission-reflection-selective materials, a number of helical stereo structures are designed to block CP waves with same handedness as the helices and transmit CP waves orthogonal to it [42–44], but they are difficult to apply in practice because of large thickness, low amplitude/phase control and complex processing method. Inspired from helical stereo structures, a double-layered chiral structure is designed with the assistance of the commercial software CST MICROWAVE STUDIO, which consists of two layers of F4B dielectric substrate with the thickness of d1 = 2 mm (${\varepsilon _r}$=2.65, loss tangent is 0.001) and two metallic rectangular patches with $\alpha $=60$^\circ $ angle etched on two substrates respectively, as shown in Fig. 2(a). The double-layered chiral structure shows giant chiral transmission-reflection-selective characteristics because the angle between two rectangular patches makes this structure act as the metamirrors to block LCP waves and have no effect on RCP waves, so it can reflect LCP incident waves and transmit RCP incident waves with relatively high efficiencies (detailed in the Supplement 1).
Fig. 2. Designs and simulations of meta-atoms. (a) The schematic view of the meta-atom containing double-layered chiral structure and four-layered square patch structure, where p = 7 mm, d1 = 2 mm, d2 = 1 mm, α=60$^\circ $. (b) Simulated co-polarized transmission amplitudes and phases under RCP incidence and co-polarized reflection amplitudes and phases under LCP incidence of No. 14 meta-atom with different rotation angles $\theta $ (the details of No. 14 meta-atom are provided in the Supplement 1). (c) Simulated co-polarized transmission amplitudes and phases under RCP incidence and co-polarized reflection amplitudes under LCP incidence of selected 24 meta-atoms in meta-atom library. And the insets are the bottom views of the meta-atoms.
We employ the Jones matrix to analyze different reflection/transmission amplitude and phase responses for orthogonal CP waves [37,39]. For the transmission fields, because the cross-polarized transmission amplitudes of the double-layered chiral structure under LP incidence approach zero, the Jones matrix under Cartesian coordinate system can be simplified as $T_0^{LP} = \left( {\begin{array}{cc} {{T_{xx}}}&0\\ 0&{{T_{yy}}} \end{array}} \right)$. Here, ${T_{xx}} = {t_{xx}} \cdot {e^{i \cdot \varphi _{xx}^t}}$ and ${T_{yy}} = {t_{yy}} \cdot {e^{i \cdot \varphi _{yy}^t}}$ denote the co-polarized transmission coefficients under x-polarized incidence and y-polarized incidence respectively, where ${t_{xx}}$ and ${t_{yy}}$ are co-polarized transmission amplitudes, and $\varphi _{xx}^t$ and $\varphi _{yy}^t$ are co-polarized transmission phases. After rotating two rectangular patches with an angle $\theta $ and changing LP basis to CP basis, the CP transmission coefficients can be described as follows (the specific derivation process of transmission and reflection can be found in the Supplement 1):
where ${T_{LL}} = {t_{LL}} \cdot {e^{i \cdot \varphi _{LL}^t}}$ and ${T_{RR}} = {t_{RR}} \cdot {e^{i \cdot \varphi _{RR}^t}}$ are defined as co-polarized transmission coefficients under LCP incidence and RCP incidence respectively, and ${T_{LR}} = {t_{LR}} \cdot {e^{i \cdot \varphi _{LR}^t}}$ and ${T_{RL}} = {t_{RL}} \cdot {e^{i \cdot \varphi _{RL}^t}}$ are considered as cross-polarized transmission coefficients. According to Eqs. (1)–(3), RCP waves’ co-polarized transmission phase $\varphi _{RR}^t$ has nothing to do with rotation angle $\theta $, indicating that $\varphi _{RR}^t$ is only determined by scaling-induced propagation phase. Therefore, a four-layered square patch structure is placed under the double-layered chiral structure and designed to ensure that the propagation phase distribution of $\varphi _{RR}^t$ can cover $2\pi $, whose F4B dielectric substrate’s thickness is d2 = 1 mm, as described in Fig. 2(a). If we intend to maximize the co-polarized transmission amplitude ${t_{RR}}$ and minimize the cross-polarized transmission amplitude ${t_{LR}}$, co-polarized transmission amplitudes and phases under LP incidence should meet the requirements of ${t_{yy}}$/${t_{xx}}$=1 and $\varDelta {\varphi ^t}$=$\varphi _{yy}^t$-$\varphi _{xx}^t$=0, and Eqs. (1)–(3) will be rewritten as follows: For the reflection fields, the CP reflection coefficients can be analyzed by Jones matrix in the same way and derived as follows: From Eqs. (6)–(8), LCP waves’ co-polarized reflection phase $\varphi _{LL}^r$ depends on rotation-induced geometric phase and scaling-induced propagation phase. In fact, the arrangement and corresponding dimensions of meta-atoms cannot be changed when the transmission function is well designed, so we can only make use of geometric phase modulation to realize the reflection function. Because most of the LCP energy is reflected by the double-layered chiral structure and almost unaffected by the four-layered square patch structure, $\varphi _{LL}^r$ can be obtained by rotating two rectangular patches together with appointed angle. As shown in Fig. 2(b), we verify that the changes of $\varphi _{RR}^t$, ${t_{RR}}$ and ${r_{LL}}$ can be ignored when rotating two rectangular patches and the change of $\varphi _{LL}^r$ is almost twice the rotation angle $\theta $. And we find if meta-atom’s co-polarized reflection amplitudes and phases under LP incidence satisfy the requirements of ${r_{yy}}$/${r_{xx}}$=1 and $\varDelta {\varphi ^r}$=$\varphi _{yy}^r$-$\varphi _{xx}^r$=180$^\circ $, it can achieve efficient co-polarized reflection and eliminate cross-polarized reflection under LCP incidence, which can be described in Eqs. (9)–(11). Based on the analyses of transmission/reflection amplitudes, a meta-atom library of 24 different meta-atoms is built by precisely optimizing the dimensions of structural components to satisfy the aforementioned requirements (the optimization process of a meta-atom is given in the Supplement 1 and the detailed dimension parameters of selected 24 meta-atoms can be found in Table S1). At 14 GHz, the average transmission amplitude ${t_{RR}}$ and the average reflection amplitude ${r_{LL}}$ of selected 24 meta-atoms are 0.79, and the transmission phases $\varphi _{RR}^t$ cover $2\pi $ and have a variation step of about $\pi /12$, which are presented in Fig. 2(c). It is worth noting that every meta-atom has an unequal initial reflection phase $\varphi _{LL}^{{r_0}}$ (the specific phases are listed in Table S1), and we will compensate for the initial phase difference between different meta-atoms by rotating the extra angle when we establish the bifunctional metadevices.3. Designs and simulations of three bifunctional metadevices
According to the previous mechanism analysis and meta-atom design, RCP transmission phase $\varphi _{RR}^t$ and LCP reflection phase $\varphi _{LL}^r$ are independently controlled by propagation phase and geometric phase respectively, which helps us design diverse functions for RCP transmission waves and LCP reflection waves and show both functions simultaneously for arbitrary LP incidence. Three metadevices are proposed to verify our design theory.
Firstly, a dual-mode OAM generator is constructed, which can generate vortex beam carrying OAM mode with topological charge of ${l_r}$=1 in co-polarized reflection channel under LCP illumination and ${l_t}$=-2 in co-polarized transmission channel under RCP illumination, as shown in Fig. 3(a). The reflection and transmission phase distributions of this bifunctional metasurface for corresponding CP incident waves are calculated as follows [45]:
where $({x,y} )$ is the coordinate of designed metasurface. By matching $\varphi _{RR}^t$ of each selected meta-atom with $\varphi _{RR}^t({x,y} )$ in Eq. (13), 24 meta-atoms are arranged to form the initial metasurface, which can satisfy the demand of bifunctional metasurface’s transmission phase. Considering meta-atoms’ phase compensation $\varphi _{LL}^{{r_0}}({x,y} )$ at each position of the initial metasurface, we should rotate every meta-atom’s two rectangular patches with the angle $\theta ({x,y} )={-} (\varphi _{LL}^r({x,y} )- \varphi _{LL}^{{r_0}}({x,y} ))/2$ to meet the required reflection phase distribution. A dual-mode OAM generator composed of 19${\times} $19 meta-atoms is established after above operations, and we simulate the phase distributions in xoy plane at z = 200 mm for LCP illumination and z=-200 mm for RCP illumination. The simulated results in Figs. 3(b)–3(c) indicate that the designed metadevice can generate vortex beam with the OAM mode ${l_r}$=1 under LCP incident waves and ${l_t}$=-2 under RCP incident waves at 14 GHz. We also estimate that the efficiencies of this dual-mode OAM generator are 51.5% and 52.8% under LCP incidence and RCP incidence respectively (the method of evaluating metadevices’ efficiencies are given in the Supplement 1) [39]. The interferences between adjacent meta-atoms, discrete phase distributions and limited transmission/reflection amplitudes of meta-atoms restrict the efficiencies of the metadevices.Fig. 3. Dual-mode OAM generator. (a) The function sketch map of dual-mode OAM generator. Simulated phase distributions of Ex component in xoy plane (b) at z = 200 mm under LCP incident waves propagating along -z direction (c) at z=-200 mm under RCP incident waves propagating along -z direction (d) at z = 200 mm under RCP incident waves propagating along + z direction (e)-(f) at z = 200 mm and z=-200 mm under x-polarized incident waves propagating along -z direction (g)-(h) at z = 200 mm and z=-200 mm under y-polarized incident waves propagating along -z direction.
In theory, two beams of vortex waves with different OAM modes will be generated simultaneously under arbitrary LP incidence because LP waves can be decomposed into LCP waves and RCP waves with the same proportion. As a demonstration, the metadevice is simulated under x-polarized incidence and y-polarized incidence respectively, and the results are shown in Figs. 3(e)–3(h). We can see that two different phenomena of LCP incidence and RCP incidence appear at the same time under LP illumination.
More interesting, we find the meta-atoms possess the characteristic of reciprocity (detailed in the Supplement 1), which means that meta-atom’s transmission response is invariant after changing the propagation direction of incident waves, but the phase distributions of the same metasurface are opposite from the perspective of + z direction and -z direction. Hence, the vortex beam carrying OAM mode with opposite topological charge can be generated when the incident direction is changed. As shown in Fig. 3(d), the designed metadevice generates vortex beam with the OAM mode ${l_t}$=2 when RCP incident waves illuminate onto the metadevice along + z direction, whose efficiency is approximately 50.0%. All in all, this OAM generator can actually generate three OAM modes by switching the polarization state and propagation direction of incident waves.
Secondly, a bifocal metalens is established, which can achieve beam focusing with ${F_r}$=150 mm in co-polarized reflection channel under LCP incidence and ${F_t}$=100 mm in co-polarized transmission channel under RCP incidence, as shown in Fig. 4(a). The reflection phase distribution under LCP incidence and transmission phase distribution under RCP incidence of this bifunctional metadevice are described as follows [9]:
where ${k_0}$ is the value of wave vector in free space at 14 GHz. According to Eqs. (14)–(15), we construct the bifocal metalens in the same way as the dual-mode OAM generator, and simulate the ${E_x}$ component of reflection/transmission electric fields in xoz plane for LCP/RCP incident waves, as shown in Figs. 4(b)–4(c). It can be clearly seen that the electric fields are strengthened at z = 150 mm under LCP incidence and at z=-100 mm under RCP incidence. The full width at half maximum (FWHM) of normalized energy is used to describe the size of the focal spot [46], and Fig. 4(d) indicates the FWHMs of this bifocal metalens under LCP incidence and RCP incidence are about 1.08${\lambda _0}$ and 0.77${\lambda _0}$ respectively, which demonstrates that it can generate high-quality focus spots in two opposite directions. And the focusing efficiencies of the bifocal metalens are calculated as 55.0% and 52.4% for LCP incidence and RCP incidence. For x-polarized and y-polarized incident waves, the electric fields distributions show two focal points at z=-100 mm and z = 150 mm, as indicated in Figs. 4(e)–4(f). And it is easier to understand that other arbitrary LP waves can also achieve this effect because of the isotropy of designed metalens.Fig. 4. Bifocal metalens. (a) The function sketch map of bifocal metalens. Simulated Ex field distributions in xoz plane (b) under LCP incidence (c) under RCP incidence (e) under x-polarized incidence (f) under y-polarized incidence. (d) Simulated normalized energy distributions in xoy plane at z = 150 mm under LCP incidence for bifocal metalens, at z=-100 mm under RCP incidence for bifocal metalens and at z=-100 mm under RCP incidence for the integrated metadevice of OAM generator and metalens, which are represented by 1, 2 and 3 respectively.
Finally, an integrated metadevice of OAM generator and metalens is proposed, which can generate vortex beams carrying OAM mode with topological charge of ${l_r}$=1 under LCP incident waves and achieve beam focusing with ${F_t}$=100 mm under RCP incident waves, as shown in Fig. 5(a). The phase distributions of this integrated metadevice should obey the Eqs. (16)–(17) as follows:
Fig. 5. The integrated metadevice of OAM generator and metalens. (a) The function sketch map of the integrated metadevice of OAM generator and metalens. Simulated phase distributions of Ex component in xoy plane at z = 200 mm (b) under LCP incidence (c) under x-polarized incidence (d) under y-polarized incidence. Simulated Ex field distributions in xoz plane (e) under RCP incidence (f) under x-polarized incidence (g) under y-polarized incidence.
As illustrated in Figs. 5(b) and 5(e), the vortex beam carrying the OAM mode ${l_r}$=1 is generated under LCP incidence, and the converging beam with the focal length ${F_t}$=100 is generated under RCP incidence at 14 GHz. The efficiencies of producing vortex beam and converging beam are 52.0% and 50.6%, and the FWHM of this focus spot shown in Fig. 4(d) is 1.07${\lambda _0}$. As described in Figs. 5(c), 5(d), 5(f) and 5(g), these two phenomena appear at the same time when x-polarized and y-polarized waves illuminate onto the integrated metadevice, which demonstrates that arbitrary LP waves can produce these two completely different functions concurrently. In addition, we use this integrated metadevice of OAM generator and metalens to evaluate the bandwidth of the bifunctional metadevices we designed, and we find this metadevice keeps good performances in 12-16 GHz (the simulated results are presented in Supplement 1).
4. Experiment and discussion
As shown in Fig. 6(a), three samples of the proposed bifunctional metadevices with the same size as the simulation models are fabricated to validate our designs in the experiments. Firstly, the metallic structures are etched on five F4B dielectric boards using printed circuit board (PCB) technology. And then, the elaborate dielectric boards are aligned according to the design of multilayer metasurfaces and assembled with adhesives. Finally, the samples are reinforced through the hot press. The near-field experimental setups consist of the experimental platform, Agilent E8363B vector network analyzer (VNA), motion controller, LP horn antenna and scanning coaxial probe, as displayed in Fig. 6(b). At 14 GHz, the gain of the LP horn antenna is 20.1 dB, and its corresponding S11 is measured to be less than -20 dB. The LP horn antenna connects port 1 of VNA to emit electromagnetic waves, which is placed 30${\lambda _0}$ away from the samples to keep the incident waves to be quasi-plane waves. And the scanning coaxial probe controlled by the motion controller connects port 2 of VNA to detect the electric field distributions in corresponding measured planes.
Fig. 6. Samples, near-field experimental setups and experimental results. (a) The fabricated samples of three metadevices. (b) The near-field experimental setups. Measured Ex phase distributions of the dual-mode OAM generator in xoy plane (c)-(d) at z = 200 mm and z=-200 mm under x-polarized incidence (e)-(f) at z = 200 mm and z=-200 mm under y-polarized incidence. Measured Ex field distributions of the bifocal metalens in xoz plane (g)-(h) under x-polarized incidence (i)-(j) under y-polarized incidence. Measured (k)-(l) Ex phase distributions in xoy plane at z = 200 mm under x-polarized incidence and y-polarized incidence and (m)-(n) Ex field distributions in xoz plane under x-polarized incidence and y-polarized incidence of the integrated metadevice of OAM generator and metalens.
The experimental results indicate that the dual-mode OAM generator can produce vortex beam with the OAM mode ${l_r}$=1 in reflection channel and ${l_t}$=-2 in transmission channel under x-polarized and y-polarized incident waves at 14 GHz, as shown in Figs. 6(c)–6(f). For the bifocal metalens, the reflected waves are highly focused at about z = 150 mm and the transmitted waves are focused at about z=-100 mm under LP incidence, as presented in Figs. 6(g)–6(j). And when LP waves illuminate onto the integrated metadevice of OAM generator and metalens, the vortex beam carrying OAM mode ${l_r}$=1 and the converging beam with the focal length ${F_t}$=100 are generated simultaneously, as shown in Figs. 6(k)–6(n). Some small divergences between measured electric field distributions and simulated results are due to the inevitable deviations in sample processing and the interferences of test environment. But overall, the experimental results basically agree with the simulation results and further demonstrate the effectiveness of our proposed bifunctional metadevices.
5. Conclusion
In this paper, we propose the innovative designs of chiral transmission-reflection-selective bifunctional metasurfaces, which can realize two independent functions in co-polarized reflection channel for LCP incidence and in co-polarized transmission channel for RCP incidence, and show both functions simultaneously under arbitrary LP incidence. A dual-mode OAM generator, a bifocal metalens and an integrated metadevice of OAM generator and metalens validate the practicability of our theories in the simulations and experiments. Significantly, the meta-atom can be designed to reflect RCP waves and transmit LCP waves when rotating the second rectangular patch of the double-layered chiral structure clockwise with 60° relative to the first rectangular patch, indicating that this methodology has superior serviceability and design freedom. Moreover, our strategy further improves the utilization and integration of metasurfaces, and opens a new avenue for controlling the wavefronts of multifunctional metadevices, which can find practical applications in detection, imaging and communication systems.
Funding
National Natural Science Foundation of China (61901508, 61971435, 61971437).
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.
Supplemental document
See Supplement 1 for supporting content.
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