Trifunctional metasurfaces: concept and characterizations

: Achieving multiple diversified functionalities in a single flat device is crucial for electromagnetic (EM) integration. While many recent efforts were devoted to designing multifunctional metasurfaces, most meta-devices realized so far typically exhibit only two functionalities. In this paper, we propose a generic strategy to design trifunctional metasurfaces, based on carefully designed single structure meta-atoms possessing polarization-controlled transmission/reflection properties. As a proof of our concept, we design and fabricate a trifunctional metasurface possessing simultaneously three distinct functionalities including beam splitting, deflecting, and focusing, and perform both far-field and near-field microwave experiments to demonstrate the predicted functionalities of the fabricated device. Experimental results are in good agreement with numerical simulations. These findings can motivate the realizations of high-performance multifunctional meta-devices in different frequency domains and with diversified functionalities.


Introduction
Electromagnetic (EM) integration plays a central role in modern science and technology, since it is believed to be a key to solve the increasing demands data-storage capacity and information processing speed of EM devices.The goals pursued by scientists and engineers along this development are to make devices as miniaturized as possible yet equipped with functionalities as many as possible.Metamaterials (MTMs), consisting of deepsubwavelength-sized EM microstructures arranged in periodic orders, break the limitation of natural materials [1,2].Through tailoring the microstructures of meta-atoms, MTMs can in principle exhibit arbitrary values of permittivity ε and permeability μ, which makes MTMs possess extraordinarily strong capabilities to control EM waves.But such systems are typically much thicker than wavelength, being inconvenient for EM integration and unfavorable for fabrications.Developed from the MTMs and frequency selective surface (FSS), metasurfaces, with elaborately designed meta-atoms and planar compatible size, have drawn much attentions recently [3,4].Many new physics and attractive optical phenomena were reported based on metasurfaces, such as generalized Snell's Law [5][6][7], propagating wave to surface waves conversion [8][9][10][11], planar holograms [12][13][14], focusing lenses [15][16][17][18][19], spin Hall effects [20][21][22][23].
Recently, many efforts have been devoted to designing multifunctional optical devices based on metasurfaces, which can combine two or more functionalities into one device.
A simple scheme developed in early years utilized the so-called "merged" meta-atoms to design multifunctional metasurfaces.In such a scheme, individual metasurfaces exhibiting their own functions are firstly designed and then multifunctional device is constructed by simply merging the structures together.This kind of idea makes the designed meta-atoms not so "compactable" and with low working efficiency [24][25][26][27][28]. Having understood the key issues in the "merging" concept, people then proposed a new strategy to design multifunctional metasurfaces.The key idea is to use single-structure anisotropic meta-atoms, which exhibit polarization-controlled transmission/reflection phase responses, as the basic building blocks to design multifunctional metasurfaces.Such meta-atoms typically exhibit low functionality cross-talking and high working efficiencies.Many sophisticated bifunctional metasurfaces exhibiting diversified functionalities designed based on this scheme have been proposed and fabricated, at frequencies ranging from microwave [29][30][31][32][33][34][35], terahertz [36], and to infrared region [10,37].However, the multifunctional meta-devices realized so far are bi-functional ones, since the independent polarization degree of freedoms are only two.
In this paper, for the first time, we propose a general strategy to design ultra-thin metasurfaces possessing simultaneously three different functionalities.The key idea is to fully utilize the distinct reflection behaviors of anisotropic multilayered meta-atoms to add a new freedom to design multifunctional metasurfaces.As a proof of concept, we experimentally realize a trifunctional meta-device in the microwave regime, which exhibits three distinct functionalities including beam splitting, deflecting and focusing.The experimental results are in good agreement with simulations and theoretical results, which collectively validate our theory.Our findings offer new possibilities to realize high-efficiency multifunctional metadevices working in the full space, which can lead to many exciting applications in different frequency domains.

Concept and design of meta-atom
We firstly describe our strategy to design the trifunctional metasurface.Different from the previous bifunctional metasurfaces with incident waves coming from one direction [31,34,36], our designed metasurface can independently control and completely reflect the xpolarized EM waves come from forward and backward direction, meanwhile it can also full control the transmitted y-polarized wave.The schematics are shown in Fig. 1.The metasurface behaves as a reflective beam splitter when excited by forward incident waves with polarizations Ê x   , as a beam deflector when excited by backward incident waves with polarizations Ê x   and as a transmissive focusing lens when excited by incident waves with polarizations Ê y   .The key of such trifunctional metasurface is to design the collection of meta-atoms which could independently control the orthogonality polarized waves with tailored phase covering the whole 2π range.Different from the geometric-phase systems [24][25][26][27][28], where the local symmetric axes of meta-atoms are rotated as a function of position, here the system that we consider is composed of meta-atoms exhibiting global mirror symmetries with respect to and operations.Thus, the EM characteristics of the meta-atom located at a position are described by two diagonal Jones' matrices: where xx r , yy r , xx t and yy t denote the reflection and transmission coefficients for the metaatom.In the purpose of independently control both sides of the reflective EM waves, a metallic grating is inserted into the middle of meta-atoms, as shown in Fig. 2(a), to filter xpolarized wave and let y-polarized wave pass.We therefore modified the Jones' matrices as: 0 0 ( , ) 0 ( , ) 0 ( , ) , ( , ) , ( , ) 0 ( , ) 0 0 0 0 where the ( , ) R x y  and ( , ) R x y  denote the reflection coefficients for the incident EM waves from the forward and backward direction, respectively.For simplicity, we consider these three ideal situations: (1) a totally reflective metasurface with =0  Then, we present the design of the meta-atom.It is easy to design a reflective meta-atom with 2π phase range [7,8,11] due to the Lorenz resonance between bottom metal background and reflection resonance structures.But for the transmission mode, compared with the reflective metasurface, the design of the ultrathin transmission phase gradient metasurface faces the challenges including not only the phase profile but also the transmission efficiency.To achieve full control of the wave-front, it has been theoretically and experimentally proved that multi-layers resonance structures are indispensable [29][30][31].
Here, as shown in Fig. 2 ).Layer A is an anisotropic metallic cross consisting of one reflection resonance bar (x-axis oriented) and one transmission resonance bar (y-axis oriented).Layer B is a metallic bar (y-axis oriented), which is used for transmissive resonance.Layer G is the pre-mentioned metallic grating designed for EM wave selecting.The different layers of experimentally fabricated sample are shown in Fig. 2(b).The slight difference in the design of transmissive resonance bars (layer A and B) is mainly to provide the freedom to modulate the coupling among different layers and to suppress the fluctuations in the transmission amplitude [33].
Next, let us discuss the scattering properties of the meta-atoms.Firstly, considering the reflection case.When incident by x-polarized EM waves, the coupling between Layer A and Layer G generates a magnetic resonance, which can dramatically control the reflection phase as a function of frequency.Figure 3(a) shows the finite difference time domain (FDTD) simulated spectra of the reflection magnitude and the phase of a typical meta-atom (periodically replicated) under x-polarization excitation.With the other fixed parameters being presented in Fig. 2(a), the size of the reflective resonator is set as 9 lr mm = .We can control the reflective resonances of both sides independently without affecting each other because of the grating layer G.In the frequency region (6-12 GHz), almost all of incident energy is reflected.And the reflection phase covers a range from −180° to 180° as frequency passes through the magnetic resonance [11].While for the transmission case, the y-polarized EM wave cannot "feel" the x-orientated metallic grating, so it can pass the Layer-G without any limitation.The coupling between different layers can further enhance the transmission by forming a series of Fabry-Perot transmissive modes.We therefore get a wideband transparent window with a transmission phase ( , ) t yy x y ϕ covers from the whole 360°, as plotted in Fig.

3(b).
Here, we note that although the metallic mesh is not a necessary element in designing of the meta-atoms, its presences can significantly reduce the mutual couplings among adjacent meta-atoms, which make our design robust and reliable [30,32].The characterization shown in Fig. 3 illustrates that such a meta-atom structure is an ideal building block to construct our metasurfaces to achieve the full-space wave-front control.Now that the reflection and transmission phases are dedicated by ( , ) − ° to 125° and the amplitudes are larger than 0.92 as the length of reflection resonance bar lr goes from 6mm to 11mm.While for the transmission case, the phase changes from 71 − ° to 422 − ° and the amplitude keeps large as the length of transmissive resonance bars lt (with all layers same) go from 4.5mm to 9.3mm.These characterizations make us easy to get any wanted phase.It is notable that during the geometric sweep, the transmission and reflection magnitudes remain a relative high level compared with the precious work based on different mechanism [5,6].

Experimental results and discussion
As an example, we employ our meta-atoms to fabricate a trifunctional metasurface sample according to the design we mentioned above, which contains 24 × 24 meta-atoms with a total size of 288 × 288 mm 2 .Firstly, we consider the reflection case.Both sides of our metasurface can manipulate the x-polarized incident EM wave independently.
We start from the reflection case for the forward incident EM wave.The reflective metasurface for the forward incident EM wave was designed as a beam splitter.The top side is designed as a coding metasurface.A 1-bit coding metasurface with coding sequence 010101… is designed although the coding metasurface can utilized for multi-bit coding metasurface [38,39], low scattering surface [40,41] and holograms [42].According to the definition of coding metasurface [43,44], two meta-atoms with 180° phase difference are selected.The structure details of the optimized meta-atoms are summarized in the Table. 1 of Section 5.And every coding element 0 or 1 contains two same meta-atoms aims to provide stable EM response, as marked in Fig. 4(b) with dashed box.Theoretical splitting angle could be calculated by formula: where 0 λ is the wavelength of the incident EM wave and Γ is the periodicity of the coding sequence.The working frequency is set as 0 9 f GHz = , and the period of meta-atom is 12 p mm = .We can predict the reflective splitting angle 44 α = ° theoretically according to Eq. (3).To validate the coding metasurface, we depict in Fig. 4(a) that the FDTD simulated distributions of the reflection amplitude and phase of the designed metasurface.Then let us consider the reflection case for the backward incident EM wave.The reflective metasurface for the backward incident EM wave was designed as a beam deflector, and the phase profile was arranged as linearly distribution [5][6][7][8]: where 0 C is a constant, ξ is the phase gradient which determines the bending angle of the reflection EM wave.The same as the case of forward incident EM wave, the working frequency is 0 9 f GHz = , the period of meta-atom is 12 p mm = and totally six meta-atoms are selected to form a super-cell to satisfied Eq. ( 4).The structure details of the optimized meta-atoms are summarized in the Table.The full size of metasurface was designed with 24 × 24 meta-atoms and a total size of 288 × 288 mm 2 .There are totally four periods along x-axis and no phase variance along y-axis.Firstly, FDTD simulation was performed to examine our theoretical results.Figure 5(c) depicts the electric field distribution of reflected EM wave at the frequency of 0 9 f GHz = normally incident from the bottom side.The anomalous reflection angle can be recognized according to the far-field polar map of simulation result in Fig. 5(d).Next, with the fabricated sample in hand, microwave experiment was performed and the results were shown in Fig. 5(d).The sample was shined by x-polarized wave from the bottom side by a horn antenna and another horn antenna was used to receive reflected EM waves at different angle position.The measured results 26 θ ′′ = ° show a good agreement with FDTD simulation which prove the feasibility of our design.Finally, as for the transmission case, these meta-atoms are collected together to focus EM wave.For simplicity, a one-dimension flat focus lens is designed based on the following phase distribution [45]: where the wave vector is 0 is the focus length.According to Eq. ( 5), the phase distributions are changed along x-axis and keep fixed in y-axis.According to symmetry of Eq. ( 5), totally half of the full size meta-atoms are needed.We therefore select 12 meta-atoms which are satisfied Eq. ( 5) according to the parameters sweeping results in Fig. 3(d), as marked in Fig. 6(b) with dashed box.The structure details of the optimized metaatoms are summarized in the Table .3 of Section 5.The electric field distribution in x-o-z plane is also calculated by simulation, where we can find a focus point at z = 152mm, as shown in Fig. 6(c).In experimental result, the focus point can be obviously seen at z = 158mm, as shown in Fig. 6(d), which is in good agreement with numerical simulation result.Here, the deviation from the theoretical value (F = 150mm) is mainly due to the finite-size effect of our sample.

Conclusion
In conclusion, we have proposed an alternative type of metasurface that possesses high freedom to integrate three distinct functionalities.We have designed and fabricated the metasurface in the microwave regime (with a total thickness 0.18λ , which is much less than the wavelength) and experimentally demonstrated that it can simultaneously realize the beam splitting, deflecting and focusing functionalities in transmission and reflection modes, depending on the input polarizations.Our findings open the door to realizing multifunctional metadevices with full-space control abilities in different frequency domains, which are important in modern integration-optics applications.

Tables
Corresponding tables.

Fig. 1 .
Fig. 1.Schematics and working principles of the trifunctional metasurfaces.The metasurface behaves (a) as a reflective beam splitter when excited by forward incident waves with polarizations Ê x   , (b) as a beam deflector when excited by backward incident waves with polarizations Ê x   , and (c) as a transmissive focusing lens when excited by incident waves with polarizations Ê y   .
= .Moreover, the phase associated with these three EM responses are denoted by be freely tuned by varying the structural details of the meta-atoms.If the meta-atoms with all these three desired phase profiles can be designed, multi-functional full space control meta-devices can be realized.
(a), we propose the A-B-G-B-A five-layer structure with A and B being two kinds of MTM layers and G being the metallic grating, which could independently control orthogonality EM waves.The metal structures are separated by the 1.5-mm-thick F4B dielectric spacers (with 2.65 0.01 i ε = +

Fig. 3 .
Fig. 3. (a) FDTD simulation results of the reflection coefficients versus frequency.The reflective resonance geometric parameter is set as lr = 9mm.(b) FDTD simulation of the transmission coefficients versus frequency.The transmissive resonance geometric parameter is set as lt = 7.0mm.(c, d) The scattering coefficients versus geometric parameters.The other parameters are kept fixed while sweeping the variant.(c) The reflection magnitude and phase versus geometric parameter lr.(d) The transmission magnitude and phase versus geometric parameter lt.

.
The resonance positions are shifted by changing the geometric sizes, mainly the length of resonance bars, and goes through a full phase period at the design frequency.Obviously, the geometric parameter lt and lr correspond to transmission phase ( .Geometric parameters are swept in simulation and the scattering coefficients versus geometric parameters at the designed frequency 09  f GHz = are shown in Fig.3(c) and Fig.3(d).In reflection case, the phase changes from200

Figure 4 (
b) is the top-view picture of the designed metasurface.FDTD simulation was performed and electric field distribution was calculated in Fig.4(c).According to the far-field polar map of simulation result in Fig.4(d), we can figure out that the x-polarized wave incident from the top side are reflected into two beams with angle 44.1 α ′ = ° .As show in Fig. 4(d), the experimentally retrieved far-field reflection angle is 42 α ′′ = °, which is in good agreementwith their corresponding theoretical one.

Fig. 4 .
Fig. 4. Design, fabrication and characterizations of the coding reflective metasurface.(a) Simulated magnitude and phase distribution of whole metasurface.(b) Picture of the top view of the fabricated sample.The dashed box shows the coding element 0 and 1. (c) FDTD simulated electric field distribution in x-o-z plane.(d) The simulated and experimental measured far-field polar map.

=
2 of Section 5. We therefore get the phase gradient 0 with c is the speed of light.In theory, the anomalous To validate the deflector, the magnitude and phase distributions of the meta-atoms in whole metasurface are shown in Fig.5(a) and Fig.5(b) is bottom view picture of the fabricated metasurface.

Fig. 5 .
Fig. 5. Design, fabrication and characterizations of the anomalous reflective metasurface.(a) Simulated magnitude and phase distribution of whole metasurface.(b) Picture of the bottom view of the fabricated sample.Insert dashed box shows the super-cell with 6 meta-atoms.(c) FDTD simulated electric field distribution in x-o-z plane.(d) The simulated and experimental measured far-field polar map.

Fig. 6 .
Fig. 6.Design, fabrication and characterizations of the transmissive flat meta-lens.(a) Magnitude and phase distribution of the designed one-dimension focus metasurface (b) The picture of the fabricated sample.Insert dashed box shows half (12 meta-atoms) of the flat focus meta-atoms.(c) FDTD simulation result of the focus effect.(d) Microwave experimental result of the focus effect.