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Abstract
Metasurfaces have provided unprecedented degrees of freedom in manipulating electromagnetic (EM) waves and have been applied in the communication field. Growing communication demands require smaller and more versatile devices. However, there is still a gap in recent miniaturization versatile research. Here, we propose a design method to realize an ultrathin multifunctional metasurface by tailoring standing waves that formed on meta-atom both in longitudinal and transverse dimensions. Firstly, to guarantee high-efficiency coupling between incident waves and meta-atom, we place the metallic pattern at the peak point of longitudinal standing waves which formed by the interferences between incident and reflected waves via adjusting the substrate thickness. Then we can realize the diverse functions for different incident spin states by loading lumped elements at the standing wave peaks or nodes of the transverse surface currents. For this proof-of-concept, we demonstrate a spin-selective vortex beam generation metasurface with an ultrathin thickness 0.144λ0. The design can generate a vortex beam for right-handed circularly polarized (RHCP) waves with an efficiency above 80% in 14.0-23.0 GHz while it can achieve high absorption above 90% for left-handed circularly polarized (LHCP) waves in 13.8-23.3 GHz. To sum up, this method might help to design spin-selective metasurfaces with multifunctional integration and find applications in satellite communication, EM compatibility and others.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurface, which is usually composed of sub-wavelength artificial structures (meta-atoms) and can exhibit properties that do not exist in nature, has got tremendous progresses both in theory and design since its birth. Many canonical works have been conducted to obtain optimal electromagnetic characteristics. Mostly, the radar cross section (RCS) reduction is a frequent and practical research hotspot, which mainly includes absorption [1–3], scattering [4] and polarization conversion [5,6] for EM waves. In microwave communication, the planar filter frequency selective surfaces (FSSs) [7] are commonly used. In addition, many actively controllable metasurfaces [8,9] have been reported in recent years. However, in the trend towards miniaturization, the device size makes a limitation for functional integration. Therefore, the implementation as many described functions integration as possible in a limited size is an urgent problem.
Many previous works on the design of multifunctional metasurfaces have been reported in recent years. Wu et al. [6] took advantages of the Galinstan to design liquid-metal-based multifunctional polarization convertor, which can change reflected waves to three different polarization states through varying the arm length of L-shaped resonators. In photonics, Deng et al. [10] made a research about cascaded dielectric environment, which allows the wavevector-dependent tunneling of the slit cavity mode to different diffraction orders. This design allows waves to react different responses under different incidences. Huang and Xiao et al. employed the mutual coupling between the meta-atoms to induce spin-selective magnetic response to achieve the bifunction integration under different chiral incidences [11]. We found that the passive multifunctional designs are mainly concerned about the properties of waves, leveraging the different incident conditions. Compared with passive designs, the active designs pay more attention to multi-structure coupling through loading active elements. Li et al. [8] proposed a tunable metasurface that can switch perfect transparency to perfect absorption, and it was implemented by integrating two PIN diodes on the top and bottom of meta-atom and adjusting the bias voltages of diodes. Zhang et al. [12] achieved the dynamical polarization manipulation in terahertz by adjusting the Fermi energy of the embedded graphene through voltage biasing. The design can switch its output wave among cross-polarization, circular-polarization and co-polarization, modulating the polarization conversion ratio (PCR) from 2% to 95%. Actually, the most difficulty of active function-diverse devices including above works is the biasing circuit setup that will not exert any effect to normal performance. To overcome this limitation, a direct method to integrate the two functions is to design diverse responses for different spin states.
In this paper, we put our attention to standing waves of meta-atoms and on this basis put forward a method of designing functional metasurfaces with strong spin-selectivity. Firstly, we indicate the standing wave effect based on classical oscillator model and put the metallic pattern at the peak point of longitudinal standing waves to guarantee high coupling efficiency. Then we found the phase difference between reflected LHCP and RHCP waves will cause the transverse standing wave differences, which can be directly embodied by the surface current distributions on the meta-atoms. From these, it is logical to achieve spin-selectivity by loading lumped resistors at the node or peak positions of the transverse standing waves and therefore this makes it possible to realize diverse functions for different spin states. To verify the feasibility of this method, we designed, fabricated and measured a spin-selective vortex beam generation metasurface for RHCP waves while achieve significant absorption for LHCP waves. Generally, this method provides an alternative to the design of multifunctional metasurfaces and might find wide applications in the fields of satellite communication, EM shielding and compatibility, etc.
2. Design and analysis
2.1 Standing waves on reflective meta-atoms
The standing waves on finite metallic structures are resulted from directional movement of free electrons driven by external electric fields, and the fields are confined within the cavity formed by the borders of the metallic structures. When the electrical size of the effective cavity satisfies $t = \mathrm{n\lambda }/2$, both nodes and peaks of the standing waves which perform as surface current distributions will be formed on the structure (Fig. 1). Locally strong surface current means that EM powers are concentrated at that location where is peak point. The EM response of metallic structures can be described with the canonical Drude model or Lorentz model [13–15]. For finite-size metallic structures of meta-atoms, they can be treated as electric or magnetic dipoles. When transient external electric field $ \vec{E}=E e^{j \omega t} $ is applied on them, the dipoles will be driven to make forced motions which can be described with Lorentz model [15].
Fig. 1. Schematically illustration of standing waves that exists both in the longitudinal dimension (due to interference between incident and reflected waves) and in the transverse dimension (surface currents distribution on the top metallic pattern of a meta-atom).
Supposing that the intrinsic natural frequency of the dipole is ${\omega _0}$ and the positive particle (which is assumed to be stationary since its movement is far slower than that of electron) is the origin of the coordinate, we can derive the oscillation equation of the dipole by considering the collisions between dipoles,
Due to the interferences between incident and reflected waves, standing waves not only exist in transverse dimension but also in longitudinal dimension. Actually, the conventional ${\lambda _0}/4$ substrate thickness for reflective surface can also be considered as one of the most typical uses of standing waves, so as the top metallic pattern should be placed at the peak point of longitudinal standing waves. In this way, the top metallic pattern can fully “sense” external EM fields, which makes it possible to achieve near-unity efficiency of the metasurfaces of interests. Due to such longitudinal standing waves, the amplitude will exhibit periodic rise-and-fall (Fig. 4(b, d)) along the propagation direction of EM waves. For a given substrate thickness, the wavelengths of standing waves (${\lambda _{S - N}}$, ${\lambda _{S - S}}$) have significant influences to the operating bandwidth of reflective metasurfaces.
2.2 Surface current difference for LHCP and RHCP waves
The standing waves commonly exist for different incidences and visually perform in current distributions. However, the current distributions are absolutely different under different incident spin states.
When a circularly polarized (CP) beam illuminates the meta-atom, the Jones matrix of scattered waves from an anisotropic meta-atom in the backward direction can be written as [16]:
Fig. 2. Two typical meta-atoms of reflective metasurfaces: (a) and (d) d show detailed structures of the two meta-atoms and their structural parameters (Px1= Py1 = 5.50mm, l1 = 5.00mm, l2 = 3.50mm, w = 0.50mm, t1 = 2.30mm; Px2= Py2 = 8.00mm, r1 = 1.35mm, r2 = 2.15mm, α=90°, t2 = 2.4mm); (b) and (e) shows the surface current distributions on the top metallic patterns of the two meta-atoms for LHCP and RHCP waves. (c) (f) The reflection coefficients of two reflective meta-atoms with lumped resistors (L-R) and without lumped resistors (None). (rRL represents the cross-polarization reflectivity under RHCP incidence, rRR represents the co-polarization reflectivity under RHCP incidence; the rLR, rLL have the similar means under LHCP incidence.)
Fig. 3. EM response of the S-shaped meta-atom: (a) definitions of the initial angle (${\alpha _0} = \pi /4$) and the orientation angle $\mathrm{\alpha }$; (b) Phase response of the meta-atom versus the orientation angle (with two typical values of $\varphi $).
Fig. 4. The influences of loading manners of lumped resistors: (a) and (c) illustrate different loading manners under LHCP and RHCP incidences; (b) gives the absorption of N- and S-shaped meta-atom for the middle-loading manner under 18GHz incidence. (d) gives the absorption of N- and S-shaped meta-atom for the sides-loading manner under 25GHz incidence. (A.E. means absorption efficiency. S-M for S-Shaped middle-loading; S-S for S-Shaped sides-loading; So as the similar means to N-S, N-M).
The difference under two spin states (LHCP and RHCP) can be further derived in the view of their orthogonal components. The circularly polarized waves can be written as
We have discussed the standing waves on two typical reflective meta-atoms and the current difference under two incident CP waves. The surface currents modulated by standing waves behave as cosine distributions and there is a $\pi /2$ phase difference between the currents exited under the two spin states. This means that for a given location on the structure, it is the wave peak for one spin state while the node for the other. In addition, many previous works have indicated that the meta-atoms can maintain their reflective properties when their orientation angles are changed [5]. The phase resonances of these structures are linearly dependent on the orientation angles. Furthermore, the reflection amplitude can be tailored by modulating the cavity thickness whereas the resonance phase variation can be achieved through rotating the meta-atom. Under this consideration, the differences under the two spin states provide a foundation for creating spin-selectivity.
3. Vortex beam generation metasurface with spin-selectivity
To verify the above postulation, we still consider the N-shaped and S-shaped meta-atoms. As is shown in Fig. 2(b) and (e), it is obvious that the shape centers of two structures are peaks for LHCP waves while are nodes for RHCP waves. Spin-selective functions can be achieved by making use of the different EM responses under two spin states. The propagation of EM waves is a process of constant iteration of electromagnetic fields. If some losses (electric, magnetic or both) are introduced in the iterative process of the electromagnetic fields, the wave propagation can be interrupted as stated by Poynting theorem [17]. The simplest method of introducing loss is loading lumped resistors at the high-amplitude current locations. Combined with our illustrated above, loading lumped resistors at given locations may achieve high-efficiency absorption for one spin state but a high-efficiency reflection for the other.
To demonstrate this, we put the lumped resistors at different locations of the two shapes. Due to the metal ground plate, there is no transmitted light after EM wave has impact on the meta-atom. All power reflects, presents different polarized states (Fig. 2(c,f)). The spin-selectivity absorption performance of N-shaped is similar, but not identical, to that of S-shaped for the same spin state. With the same geometric dimensions, for EM waves coupled into the structure, electron movements are constrained within the metallic structure or in the area between the metallic structure and ground plane (metal ground plate). The different patterns act variant sensitivity for two meta-atoms. For S-shaped meta-atom, the middle-lumped resistor makes a strong wideband coupling and further achieve the good absorption in 13.0-24.0GHz for LHCP (Fig. 2(f)). In sharp contrast, there is a poor absorption performance for RHCP wave incidence (sides-lumped). And the N-shaped meta-atom is the opposite as the S-one (Fig. 2(c) and Fig. 4(b, d)). Therefore, one should select suitable meta-atoms for a specific spin-selectivity and the prescribed functions.
Incident waves with LHCP and RHCP spin states lead to the phase differences of surface currents on the meta-atoms. This lays the foundation for achieving spin-selectivity, that is, only one of the two spin states can be left to achieve a prescribed function. To demonstrate this, we designed a vortex beam generation metasurface that selects RHCP waves while absorbs LHCP waves, as is shown in Fig. 5. Compared with classical CP wave, the vortex beam has a strong directivity and a faster transmission rate. Thus, it has a bright future in wireless communication. The vortex beam can be described as [18],
where $A(r )$ is the amplitude. r is the distance between any point on the EM wave and the axis. $\varphi $ is the azimuth. l is number of cycles a wave front rotates in a period. Therefore, the EM vortex can be achieved by introducing the phase factor ${e^{ - il\varphi }}$. The phase distribution of meta-atom is where $({x,y} )$ is coordinate of some meta-atom on the surface. Supposing the $l$=2, the phase of meta-atoms should cover -2$\pi $ to 2$\pi $. We design reflective metasurface which serves as a vortex convertor ($l$=2) for RHCP waves while as an absorber for LHCP waves, composed of 17×17 S-shaped meta-atoms.Fig. 5. Schematic demonstration of the vortex beam generation metasurface with spin selectivity. The metasurface can absorb LHCP waves, only leaving reflected RHCP waves. Plus phase modulations on the metasurface, vortex beam can be generated upon reflection for RHCP waves.
The simulation was conducted by CST studio, with circular polarized plane wave port as the excitation source, which was placed 400mm far from the plate. The near-field monitor was placed between the excitation source and plate, 200mm far from the plate to measure the electric filed along the y-axis. The phase of cross profile is consistent with theoretical design, which covers -2$\pi $ to 2$\pi $ and show up a helical distribution. That means the topological number of charges carried by the beam is 2 which is satisfied with the previous designed work. As is shown by the simulated results, from 13.8GHz to 23.3GHz, high-efficiency absorption reached 90% can be achieved for LHCP wave. Besides, the metasurface can convert RHCP incident wave to vortex beam from 14.0GHz to 23.0GHz.
4. Experimental verification
A prototype was fabricated and measured, with the same area as that used in the simulation. We placed the horn antenna 600mm far from the plate, and approximated the point-emitting beam as plane wave. The probe which as a near-field monitor was configured as simulation to collect the component of the electric field in the y direction. The absorption performance for LHCP was measured with free space method. The two circular polarized horn antennas were placed in front of the plate to be excitation source and receiving end. All operations were taken place in anechoic chamber to reduce the influence of surroundings. As are shown in Fig. 6, the measured results agree well with simulated results, which convincingly verifies the design method.
Fig. 6. (a) The simulated and measured electric filed components along y-axis at z = 200mm in the xoy-plane under RHCP incidences (normalized results). (b) The absorption simulated and measured results of fabricated metasurface under LHCP incidences. (c) and (d) The measurement conditions of electric fields and S-parameters. The near-fields was measured with probe detection and S-parameters was measured with free space method. Put the circular polarized horn antenna as the excitation and received end.
A key factor for reflective vortex convertor, the reflection efficiency, defined as the ratio between the energy carried by CP wave with the same handedness and that carried by incident wave, can be described as [19],
5. Conclusions
In this paper, we proposed a method of designing spin-selective reflective metasurface, which performs discriminatively for different incident CP waves, based on tailoring standing waves both in longitudinal and transverse dimensions. Firstly, to guarantee near-unity efficiency of the prescribed function, the top metallic pattern of reflective meta-atom was placed at the peak point to fully couple incident waves. Then, the EM response difference of reflective meta-atoms under two spin states (RHCP and LHCP waves) is utilized to realize spin-selectivity, that is, only one spin state is left to achieve the prescribed function while the other is totally absorbed. For this proof-of-concept, we designed, fabricated and measured a vortex beam generation metasurface for RHCP waves, which can achieve high-efficiency plane-to-vortex beam conversion for RHCP wave and significant absorption for LHCP wave. The beam conversion efficiency can exceed above 80% in a 48.6% relative bandwidth (13.0-24.0GHz). Meantime, the absorption effect for LHCP incident wave reaches 90% absorption from 13.3 to 23.8GHz. The measurement is consistent with simulation and confirms the feasibility of the method. To sum up, this method provides an alternative of designing functional metasurface with high spin-selectivity and might help to the fields of satellite communication, EM shielding and compatibility, etc.
Funding
National Key Research and Development Program of China (2017YFA0700201); Natural Science Foundation of Shaanxi Province (2020JM-351, 2021JQ-363); National Natural Science Foundation of China (61901508, 61971435, 62001504, 62101588, 62101589).
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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