Abstract
We propose a method to control electromagnetic (EM) radiations by holographic metasurfaces, including to producing multibeam scanning in one dimension (1D) and two dimensions (2D) with the change of frequency. The metasurfaces are composed of subwavelength metallic patches on grounded dielectric substrate. We present a combined theory of holography and leaky wave to realize the multibeam radiations by exciting the surface interference patterns, which are generated by interference between the excitation source and required radiation waves. As the frequency changes, we show that the main lobes of EM radiation beams could accomplish 1D or 2D scans regularly by using the proposed holographic metasurfaces shaped with different interference patterns. This is the first time to realize 2D scans of antennas by changing the frequency. Fullwave simulations and experimental results validate the proposed theory and confirm the corresponding physical phenomena.
Introduction
In recent years, it has been shown that extreme controls of electromagnetic (EM) waves can be achieved by using metasurfaces. Due to advantages of smaller physical space and less lossy structures than bulk metamaterial^{1,2,3,4,5,6}, metasurfaces have found great potential applications in both microwave and optical frequencies. Similar to metamaterials, the metasurfaces are also modeled as subwavelength textures and several analysis methods have been established. Typically, the surface impedance or effective surface refractive index can be calculated analytically using the transverse resonance approach^{7}, from which surfacewave waveguides^{8} and lenses^{9,10,11} have been designed. To reduce the computational time in eigenmode simulations, a fast method was presented to calculate the surface impedance efficiently^{12}. Later, the printedcircuit tensor impedance surface^{13} has been analyzed using the modified transverse resonance technique and idealized tensor impedance boundary condition. Another method to model metasurface or metafilm is the generalized sheet transition condition^{14}, in which the small scatterers are characterized as electric and magnetic polarization densities. Based on this method, reflection and transmission coefficients of metafilms or metasurfaces have been obtained^{15,16}, promoting the study of metatransmission arrays^{17,18,19}. To control EM waves with more flexibility, the generalized Snell's law was proposed^{20} by introducing the abrupt phases on the interface of the two media. Based on similar ideas, a gradientindex metasurface was presented to convert propagating waves to surface waves efficiently^{21} and convert the circularlypolarized light to crosspolarized light^{22,23}.
On the other hand, due to the low profile and low loss, metasurfaces have great advantages in the design of surface aperture antennas. Based on the original analysis of sinusoidallymodulated reactance surface^{24}, the holographic antenna composed of surface impedance was proposed^{25}, which shapes the monopole source as a pencil beam in the farfield region and changes the linearlypolarized source to circularlypolarized radiation by using anisotropic surface impedance units. Later, a spiral leakywave antenna^{26} based on the modulated isotropic surface impedance implemented by corrugated dielectric or metallic patches on a grounded substrate can generate circularly polarized waves. Then the anisotropic tensor surface impedance formed by isotropic textures was used to realize circularlypolarized isoflux radiations^{27} for spacetoground data link applications in the Xband. In study of microwave imaging, a concept of metamaterial aperture has been presented for computational imaging^{28,29}, in which the randomaperture leakywave antennas composed of complementary electricinductorcapacitor elements have been used to generate multi beam radiation patterns. The metasurface antennas can also be tunable^{30,31} and conformal^{32,33} so that they are more functional and practical in many engineering applications.
In this work, we propose to control extreme EM radiations by using holographic metasurfaces, which can radiate multiple beams with the frequency sweeping in one dimension (1D) or two dimensions (2D) without using the complicated beamforming network^{34} and anisotropic structures^{35,36}. The proposed metasurfaces are composed of subwavelength quasiperiodic metallic patches on a grounded dielectric substrate, which can be shaped by mapping the variation of patch gaps to the surface impedance under the particular holographic interference. Once the interference pattern is recorded by the interference between reference waves and multibeam radiations on the metasurface aperture, according to microwave holography theory, the metasurface excited by the reference waves generated by a monopole antenna can reproduce the multiple beams as we desire. We demonstrate that the radiation waves generated by the holographic metasurface can accomplish 2D scans regularly with the change of frequency, which has not been realized in the earlier holographic metasurfaces and leakywave antennas.
Results
Theory and analysis
The surface impedance is defined as the ratio of electric to magnetic fields near a surface. Hence, the perfectly electric conducting (PEC) and perfectly magnetic conducting (PMC) surfaces are physically zeroimpedance and highimpedance surfaces, respectively. We can design a metasurface by forming quasiperiodic gradient distribution of surface impedance. According to microwave holography theory, the desired radiation beam can be produced by using a reference wave to excite holographic interferogram, which is generated by the interference between the reference wave and radiation wave. The interferogram equation is given as^{37} in which Ψ_{ref} is the reference wave and Ψ_{obj} is the object wave. To design the surfaceaperture radiations, we use the distribution of surface impedance to embody the whole surface interferogram. We rewrite Eq. (1) to describe the distribution of surface impedance as where X and M indicate the average value of surface impedance and the modulation depth, respectively, and “*” represents the conjugate operation. To build up the object wave (or radiation wave), we should use the reference wave to excite the interference pattern in determining .
In our design, the basic unit of metasurface is a subwavelength metallic patch on a grounded substrate, as shown in Fig. 1(a). We extract the surface impedance of the metasurface via its dispersion curve. When the surfacewave vector k_{t}_{ }passes through a unit cell, the phase difference across the unit is ϕ = k_{t}a, which can be acquired under eigenmode simulations, where a is the period of the unit cell. Then the surface refractive index is given as n = c/v_{t} = k_{t}c/ω_{t}, where c is the light speed in free space and ω_{t} is the surface angular frequency. Combining with the equation of surface impedance Z = jZ_{0}k_{z}/k of the transversemagnetic (TM) modes, we obtain the relation between the unit phase difference and surface impedance as where Z_{0} is the impedance in free space. Therefore, once the unit phase difference is acquired through the eigenmode simulation, we can calculate the surface impedance. The gap between square patches (see the orange area in Fig. 1(a)) determines the value of surface impedance. When slowly varying the gap sizes to obtain different surface impedances, the structure is considered as quasiperiodic.
From the nine dispersion curves with changing gap sizes shown in Fig. 1(b), we calculate nine values of surface impedance at 17 GHz, from which the following equation is fitted using cubic polynomials to describe the relationship between surface impedance and gap size: Then we determine the values of X and M as 197.5 and 36.5, respectively, from the simulated values of surface impedance.
According to the holographic antenna theory, once the interference pattern is recorded by the interaction between reference wave and multibeam radiation wave on the metasurface, we can reconstruct the multiple beams as we desire. We choose a monopole antenna placed in the center of metasurface to produce the reference wave, which is written as where n is the effective surface refractive index and r is the distance from the origin to the surface radiation unit. For doublebeam radiation, the object wave (i.e. the desired radiation wave) can be defined as in which and are wavenumber vectors of the two beams with the elevation and azimuth angles θ_{1/2} and ϕ_{1/2}, respectively, and is the spatial location vector. In particular, when θ_{1} = θ_{2} = 30° and φ_{1} = 45°, φ_{2} = 135°, Eq. (6) is rewritten as in which the positive and negative exponential terms indicate the radiation waves propagating to the two sides of the normal direction on the metasurface. To obtain the doublebeam radiation shaped by Eq. (7), the interferogram generated by Eq. (2) should be excited by the reference wave defined in Eq. (5).
We will show later that the proposed holographic metasurface is equivalent to the 2D leakywave structure. To radiate EM waves more efficiently, we define the “1” order leakywave radiation without other Floquet modes participating the interference by synthetically considering the unit design and radiation frequency. In fact, the forward and backward waves in leaky waves mean that the radiation directions are uniform and nonuniform with the propagation of surface waves. If we place the monopole antenna in the center of metasurface as excitation, the fullwave simulation results reveal that the leakywave (objectwave) radiation pattern may generate the sag like “rabbit's ears” in the far fields, as shown in Fig. 2(a). This phenomenon is caused by the slightly radiating deviation of forward and backward modes, which is attributed to the inaccuracy of effective surface refractive index that determines the distribution of surface currents. The surface currents excited by the monopole antenna will not be completely the same as the reference wave so that the forward and backward waves have different radiation directions, as illustrated in Fig. 2(a).
The optimization of surface refractive index n can avoid the “rabbit's ear” phenomenon by enforcing θ_{1} = θ_{2} in Fig. 2(a), but it is more complicated. Here, we present a sidefeeding method, as shown in Fig. 2(b). The interferogram shaped by the holographic metasurface is generated by Eq. (2), which is combined with Eq. (4) to determine the relation to describe the gap size versus position on the metasurface. Fig. 3(a) illustrates the interferogram generated by the interference between doublebeam radiation (Eq. (7)) and reference (Eq. (5)) waves at 17 GHz. Based on the fullwave simulations by commercial software, CST Microwave Studio, the reproduced waves are demonstrated in Fig. 3(c). We also show that the doublebeam radiations can make 1D scan with the change of frequency (16–18 GHz), as clearly observed in Figs. 3(b) – (d).
To explain the phenomenon of frequency scanning by the 2D metasurface, we now show the equivalence of the holographic reproduction and “1”order leakywave radiation. For simplicity, we analyze a singlebeam radiation defined by Ψ_{obj} = e^{−jkxsin(θ)}, which will interference with reference wave Ψ_{ref} = e^{−jknx} to generate the interferogram as To obtain periodicity of the holographic distribution of surface impedance along the x direction, we define k_{0}nxk_{0}x sin(θ) = 2π, and the corresponding period is determined as which can be rewritten as The above result is exactly the same as that in the “1”order leakywave radiation^{12}. Here, θ is the radiation direction of the holographic reproduction. It is obvious that the object wave can accomplish the beam scanning controlled by frequency, and the corresponding radiation direction is given as where k′, n′ and θ′ are the same as those in Eq. (8) but under different operating frequencies.
We introduce the concept of surfacewave phase gradient to explain the above phenomenon. For simplicity, we still analyze the singlebeam radiation defined by and , which generate the interferogram as Here, we assume that the sinusoidal phase distribution () of interferogram generated by the impedance units is approximately invariant by changing frequencies since the higher and lowerimpedance areas of the interferogram are fixed. Hence we only need to concern the object wave term in processing the holographic reproduction. If we excite the interferogram by reference wave defined as , where k′ and n′are the wave number in free space and effective refractive index, then the phase of surfacewave front becomes Φ = k′n′r−k_{0}nr + sin(θ)k_{0}[x cos(φ) + y sin(φ)]. By calculations, the surfacewave phase gradient ∇Φ is given as where , and are unit vectors. Hence the surface wave front is generated by the interference of two surface waves and , and the phase of wave front in the x direction is written as where φ is the angle between r and x directions. Thus, the x component of effective surface wave number at the particular frequency is which is corresponding to the wave number of the “1” order leakywave. Likewise, the y component of effective surface wave number at the particular frequency is Thus, the amplitude and azimuth angle of the effective surface wave number are given as
As a consequence, the elevation angle of the main radiation direction is expressed as According to Eq. (18), if we change the object wave as (φ = 45°; the interferogram is defined in the area of x>0 and y>0), in which “+” and “−” represent the backward and forward modes of leaky waves, we find that the azimuth angle of main radiation direction will be unchanged with frequencies under the circumstance of , which can accomplish 1D scanning controlled by frequency, as shown in the simulation results in Fig. 3.
This method can be generalized to produce multibeam radiations by recording interferograms in several subareas, each of which radiates a single beam. For instance, in fourbeam radiations, the overall interferogram is generated by mirroring the metasurface pattern in the first quadrant to other quadrants. The object wave is then given as in which we determine φ = 45° to satisfy the condition of , and the azimuth angles of the desired four beams are 45°, 135°, 225°, and 315°, respectively. When we set θ = 45°, the corresponding interferograms and simulation results for forward and backward modes are presented in Figs. 4(a) and (b). Although the feeding point is located in the center of the overall metasurface, for each radiation beam, it is the side feeding in the subarea. Hence the earlier “rabbit's ears” phenomena are avoided. From Fig. 4, we notice that the fourbeam radiations in the backward mode are scanned in 1D direction with increasing elevation angles as the frequency becomes larger; while the four beams in the forward mode are scanned with decreasing elevation angles.
From Eq. (18) and (19), if , we can realize extreme controls of the multibeam radiations, in which the azimuth angle (ϕ′) and elevation angle (θ′) of the leaky waves can be simultaneously scanned with the change of frequency. In this case, the object wave with fourbeam radiations is defined as in which we determine φ = 135°and θ = 45° to satisfied the condition . The corresponding interferogram and simulation results of the fourbeam radiations with 2D frequency scanning are demonstrated in Fig. 5. We clearly observe that the fourbeam radiation patterns are scanned in both azimuth and elevation directions as the operating frequency changes. The detailed scanning properties are summarized in Table 1, from which we notice that the simulation results have good agreements to the theoretical analysis. The little deviation may be caused by the inaccuracy of effective surface refractive index and approximate condition of sinusoidal phase distribution under different frequencies. Compared to the conventional holographic leakywave radiations that can only accomplish 1D frequency scanning, the proposed method and holographic metasurface have greatly enhanced the capabilities to reach 2D frequency scanning.
Fabrication and Measurement
To validate the proposed method experimentally, we fabricate a sample of the holographic leakywave metasurface shown in Fig. 3 to show the frequency scanning properties of two beams. The sample of the doublebeam metasurface has a dimension of 240 × 240 mm^{2}, containing 6400 unit cells. In fabrication, we choose commercial printed circuit board (FR4) as the dielectric substrate and choose copper with tinning as the ground. The experimental setup in anechoic chamber to measure the far fields is illustrated in Fig. 6(a), and the measured farfield radiation patterns with the 1D frequency scanning in azimuth direction of the doublebeam holographic metasurface are demonstrated in Fig. 6(b).
The detailed doublebeam scanning parameters of the holographic metasurface from theoretical analysis, simulation and experimental results are presented in Table 2. We clearly observe that the experimental results have good agreements to numerical simulation and theoretical predictions. We do not measure the fourbeam radiations with 2D frequency scanning due to the much complicated experimental process based on our current measurement system, but the simulation results in Fig. 5 and Table 1 have verified the good performance to make extreme controls of EM radiations only by frequency.
Discussion
We proposed an efficient method to design holographic leakywave metasurfaces to perform complicated multibeam radiations with frequency scanning. We presented two approaches to record the desired interferograms, one of which is recorded on the whole metasurface with side feeding, and the other of which is recorded on several subdomains of the metasurface with central feeding. According to theoretical analysis, the first approach can accomplish 1D frequency scanning, while the second can reach 1D and/or 2D frequency scanning. Numerical simulation and experiment results show that the radiation beam directions in the far fields can be coded by frequency instead of complicated feeding network. The proposed method has potential applications in the satellite communications and radar systems, and can be extended to the millimeter wave and THz regimes.
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Acknowledgements
This work was supported by the National Science Foundation of China (60990320, 61138001,61171026 and 60990324), National High Tech (863) Projects (2011AA010202 and 2012AA030402), 111 Project (111205) and the Natural Science Foundation of the Jiangsu Province BK2012019, and 20130202 Guangxi Experiment Center of Information Science, Guilin University of Electronic Technology.
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Affiliations
State Key Laboratory of Millimeter Waves, School of Information Science and Engineering, Southeast University, Nanjing 210096, China
 Yun Bo Li
 , Xiang Wan
 , Ben Geng Cai
 , Qiang Cheng
 & Tie Jun Cui
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Contributions
Y.B.L. and T.J.C. conceived the idea, did the theoretical calculations, and wrote the manuscript. Y.B. Li designed the samples and performed the measurements. X.W., B.G.C. and Q.C. involved in the simulations and measurement. All authors contributed to the discussions.
Competing interests
The authors declare no competing financial interests.
Corresponding author
Correspondence to Tie Jun Cui.
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