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Functional integration is crucial and has become a research interest in recent years; however, available efforts suffer from low efficiency and narrow operating bandwidth. Here, we propose a novel strategy to design bifunctional meta-surface with high efficiency and largely enhanced bandwidth in reflection geometry. For demonstration, we designed and fabricated a bifunctional meta-surface which enables both focusing and anomalous reflection under different polarizations. The working bandwidth is significantly extended by using the dual-resonant three-turn meander-line resonator (TMLR) element which provides an almost consistent phase response within a large frequency interval. For potential applications, we engineered a bifunctional antenna by launching the designed meta-surface with proper feed sources. Numerical and experimental results coincide well, indicating bifunctionalities of high gain pencil-beam radiation (reflectarray) and beam steering radiation with comparable performances. Our results can stimulate the realizations of high-performance meta-surfaces and antenna systems.
© 2016 Optical Society of America
1. Introduction
Electromagnetic (EM) control plays an essential role in both science and technology, and has become a research spot with remarkable achievements. Conventional wavefront control devices are realized by natural materials [1] or man-made 3-D meta-materials [2–6], which surfer from bulky configurations and complex fabrication processes. Moreover, the achievable functionalities by these devices are strictly limited and the operating bandwidth is very narrow.
Gradient meta-surfaces (GMSs), proposed by Yu et al [7], have provided unprecedented capabilities in manipulating the amplitude, phase and polarization of EM wave. As a result, a wide range of applications over the entire electromagnetic spectrum have been explored and investigated in depth, including beam steering [7], subwavelength planar lenses [8,9], holograms [10,11], and other optical devices [12–17]. Despite these fruitful progresses, multifunctional meta-surface achieving simultaneously focusing and beam bending still remains one of the challenges, not to mention enhancing the working bandwidth. This is particular true because of the fact that realized multi-functionalities are either similar (e.g. focusing lenses in [18] and polarization-independent beam bending effects in [19, 20]) or with low efficiencies [21]. To the authors’ best knowledge, realizing multi-functionalities with very wide bandwidth in one single layer device, in addition to integrated lens antennas [22–24], has not been reported in an open literature.
In this paper, we propose a general strategy to realize bifunctional metasurface with high efficiency and also largely enhanced bandwidth. For demonstration, we design and measure a reflective bifunctional meta-surface at microwave regime, achieving both functionality of a focusing lens and a beam deflector under two orthogonal polarizations. Experimental results show that both realized functionalities exhibit high efficiency since our designed three-turn meander-line resonator (TMLR) possesses polarization-independent responses with very high isolation. Most importantly, the electrically small dual-resonant TMLR provides an almost consistent reflection phase responses as frequency varies and thus a desirable bandwidth. For practical applications, bifunctional antenna is implemented by carefully feeding the meta-surface with a proper source.
2. Mechanisms of bifunctional property and enhanced bandwidth
We first discuss our strategy to realize a bifunctional meta-device in a single slab. When conventional homogenous meta-surface consisting of a periodic array of elements in xoy plane was illuminated by a normally i-polarized (Ex or Ey) incident wave along z axis, the wave vector can be written as
where kxi represents the wave-vector along x direction, kyi denotes the wave-vector along y direction, k0 is the propagation constant in free space.Replace the conventional meta-surface with a GMS, the wave vector can be calculated as
where ξx and ξy denote the phase gradient along x and y directions introduced by the GMS, which can be further calculated asHere φx(x, y) and φy(x, y) represent the phase profiles at a position (x, y) along x and y directions, respectively. We can engineer φx(x, y) and φy(x, y) independently to realize required functionalities with very high efficiencies. Here, we discuss two special cases for better understanding the working mechanism of bifunctional meta-surfaces. For conventional reflective meta-surface GMS1 with constant phase distributions (φx(x, y) = C1, φy(x, y) = C2), shown in Figs. 1(a) and 1(b), mirror reflection occurs by normally illuminating the sample with Ex and Ey polarizations according to the Snell’s laws. For the GMS2 shown in Figs. 1(c) and 1(d), a parabolic phase profile along x direction and a linear gradient phase distribution along y direction are pre-arranged asHere F denotes the focal length. Both focusing and anomalous deflection functions can be realized under Ex and Ey excitations, respectively.
Fig. 1 Schematics of functionalities of different meta-surfaces. Conventional mirror reflection responses of GMS1 (φx(x, y) = C1, φy(x, y) = C2) to (a) Ex and (b) Ey polarizations; GMS2 (, φy(x, y) = ξy) behaves as a focusing lens under (c) Ex polarization and a beam deflector under (d) Ey polarization.
To enlarge the operating bandwidth, we require similar slopes for the phase responses at different frequencies within a band. Therefore, we enforce the condition
where f1 and f2 are the lower and upper frequencies of the working band, fj denotes the frequency within the band. Our aim is to realize a large frequency interval (f2-f1), enabling a wide operating bandwidth. Next, we will show how to realize a high-performance bifunctional meta-surface with a wide bandwidth in a realistic system.3. Design and characterization of reflective bifunctional GMS
To realize a bifunctional GMS with wide bandwidth and high efficiency, we carefully design a TMLR element, as shown in Fig. 2(a). The TMLR element is a basic sandwich structure, consisting of a pair of orthogonal meander-line resonators, a 3-mm-thick FR4 spacer (εr = 4.3) and a metallic ground plane. The well known cross bar resonator (CBR) element in Fig. 1(b), two-turn meander-line resonator (TOMLR) in Fig. 1(c), four-turn meander-line resonator (FOMLR) in Fig. 1(d) and five-turn meander-line resonator (FMLR) element in Fig. 1(e) have the same parameters with the TMLR except for the turn numbers, which are utilized for a fair comparison. For analysis and characterizations, all numerical calculations and designs are conducted in the commercial FDTD solver CST Microwave Studio.
Fig. 2 Topology of proposed meta-atoms with different turns, EM simulation setup process and simulated reflection spectra. The top view of (a) TMLR, (b) CBR, (c) TOMLR, (d) FOMLR and (e) FMLR elements; (f) EM simulation setup process; (g) FDTD simulated spectra of reflection coefficient and phase; (h) FDTD simulated spectra of reflection coefficient ryy and rxy. The parameters are listed as: g = 0.2mm, c = 0.2mm, t = 0.2mm, px = py = 5.8mm.
For a special case with b1 = 4.5 mm, b2 = 4 mm, illuminating the five elements by normally incident y-polarized microwaves, Fig. 2(g) depicts the spectra of reflection amplitude and phase as a function of frequency. The reflection amplitude keeps nearly 1 for CBR, TOMLR and TMLR elements. However, it deteriorates seriously at some typical frequencies as the adopted turns of meander-line resonator increase (especially for FOMLR and FMLR). The cross polarization origins from the magneto-electric coupling due to the four-fold rotational symmetry of the elements which possess chirality. It increases with the turns of MLR because the increased turn enhances the localized currents along the meandered lines, see Fig. 2(h). Therefore, a tradeoff should be considered between the reflection amplitude (efficiency) and the accumulated phase. CBR element suffers an incomplete phase variation range of less than 360° since the single resonance property [28], which induces an imperfect wavefront control. Therefore, the compact TMLR is chosen as the final element by the tradeoff between high reflection and complete phase variation range (the TOMLR element is electrically large than TMLR). According to Fig. 2(g), dual resonance property appears at about f1 = 8.1 GHz and f2 = 13.4 GHz for the TMLR, which plays an essential role in extending the phase variation range [25]. The magnetic resonance f1 can be explained by the resonance between the middle bar and the ground plane, while the magnetic resonance f2 is mainly generated by the other two bars and the ground plane. Both resonances can be dictated by the geometrical parameters b1 and b2 of the structure. Since the incident wave polarized along y (or x) direction can only “see” the phase φy and φx, we can tune the reflection phases φy and φx independently and freely by varying the parameters b1 and b2, respectively, as shown in Fig. 3. Referring to Fig. 3(a), under excitation of Ey, φy undergoes a desirable phase-shift range over 360° as b1 increases. However, φx keeps consistent under excitation of Ex as b1 varies, as shown in Figs. 3(b) and 3(d), since φx is predominantly determined by other parameter b2. More importantly, almost consistent phase slope is observed, inducing an enhanced bandwidth according to Eq. (5). The working bandwidth, defined by the condition that the relative phase error changes within 30° compared with the phase profile at center frequency of f0 = 13 GHz shown in Fig. 3(c), is approximately evaluated as 5 GHz (10-15 GHz).Therefore, high reflection coefficients, a complete phase-variation range over 360°, the polarization-independent property and also a wide operating bandwidth guarantees the TMLR element a good candidate to design high-efficiency bifunctional meta-surfaces.
Fig. 3 Phase responses of the proposed TMLR under excitation with different polarizations. The 2-D color map of the phase profile as functions of b1 and frequency illuminating by (a) Ey and (b) Ex; the blue symbols in (a) represent the magnetic resonances with the reflection phase being 0° or 360°. The phase curves of different frequencies under excitation of (c) Ey and (d) Ex.
The well-optimized TMLR can provide arbitrary phases φy and φx by carefully tuning b1 and b2 under different polarizations, which offers us the possibilities to design two distinct phase functions. Here, for instance, we design and fabricate a bifunctional meta-surface with the phase profiles satisfying Eq. (4), where F = 70 mm and ξy(y) = 0.5k0 are pre-designed at the center frequency f0 = 13 GHz, respectively. As can be seen in Fig. 4(a), the fabricated sample consists of 24 × 24 well-selected cells with a total dimension of 139.2 mm × 139.2 mm, corresponding to 6.03 λ0 × 6.03 λ0, where λ0 is the wave length at the frequency of f0. The related phase distributions for Ey and Ex polarizations are depicted in Figs. 4(b) and 4(c), respectively.
Fig. 4 (a) Photograph of the fabricated sample of our bifunctional meta-surface and the corresponding phase distributions for (b) Ex and (c) Ey polarizations.
Then, we experimentally evaluate the focusing effect of the bifunctional meta-surface. Shining the sample by a wide horn antenna (2-18 GHz), the Ex field at yoz plane with an area of 140 × 100 mm2 is recorded by a 15 mm-long monopole antenna which is connected to the vector network analyzer (Agilent E8362C), with the results shown in Fig. 5. The designed meta-surface enables the outgoing uniform wavefront to be converged over a wide frequency range from 10 to 15 GHz. The decent focusing effect comes from the strong phase compensating capacity and the exact design. At the center frequency of f0 = 13 GHz, the scattering field is largely enforced at F = 70 mm, evaluating by the maximum energy intensity along z axis (not given here for brevity), which coincides well with the theoretical value (F = 70 mm). Apart from the center frequency, especially at 10 and 15 GHz, the focusing effects deteriorate, resulting from the intrinsic chromatic aberrations and the reduced phase compensation capacity [30]. We further investigate the maximum Ex amplitude along z axis as a function of frequency with the results shown in Fig. 6. With a perfect phase profile at f0 = 13 GHz, the electric field amplitude is larger than those of other frequencies. Meanwhile, the half-power bandwidth, ordered by the contour line of 0.707, is measured from 9.85 to 15.6 GHz, indicating a comparable bandwidth of the proposed meta-lens. In addition, the measured enforced Ex field distribution at the focal plane of z = 70 mm (in the inset of Fig. 6) demonstrates the high-efficiency of the designed meta-lens. The realized 3-D focusing effects show advances than those of reported 2-D focusing lens [31, 32], which should be highlighted.
Fig. 5 Measured electric field distributions in yoz plane at different frequencies. The electric field distributions at (a) 10 GHz, (b) 11 GHz, (c) 12 GHz, (d) 13 GHz, (e) 14 GHz, (f) 15 GHz.
Fig. 6 The normalized Ex-field amplitude as a function of frequency. The Ex-field distribution at z = 70mm at f0 = 13 GHz is shown inset.
Next we experimentally evaluate the other function of the designed meta-surface. As seen in Fig. 4, three super cells with −45° phase gradient are arranged along y direction. According to the generalized Snell’s law [7], the anomalous reflection angle obeys strictly the condition of
Figure 7(a) depicts the FDTD simulated Ey-field distribution in xoz plane at frequency of f0 = 13 GHz when the designed meta-surface is illuminated by a normally incident y-polarized plane wave. The anomalous wavefront is clearly seen with a deflection angle θr = 29.7°, which coincides well with the theoretically calculated value (θr = 29.8°) according to Eq. (6). Then we measure the angular power distributions as functions of detection angle and working frequency. Within a large frequency interval from 9 to 15 GHz, most of the reflected waves are deflected to an anomalous angle, coincides well with Eq. (6) (blue stars in Fig. 7(b)). Obviously, the best performance is found at the working frequency f0 = 13 GHz, where the normal-mode reflection disappears completely while the anomalous reflection reaches a maximum. Furthermore, we calculate the absolute efficiency, which is defined as the ratio between the power carried by the anomalous beam and that of the incident wave. Our experimental results show that the maximum efficiency reaches about 92% at f0 = 13 GHz. Moreover, the half power bandwidth, ordered by the efficiency better than 0.5, extends from 9 to 14.8 GHz, which is comparable with other reported meta-surfaces [7, 12, 13].
Fig. 7 Numerical and experimental results of the anomalous reflection effect. (a) FDTD simulated Ey-electric field under illuminating of a normal y-polarized wave. (b) Measured scattered-wave intensity map as functions of frequency and detection angle. (c) Measured absolute efficiency as a function of frequency.
4. Applications to bifunctional antenna
The designed bifunctional meta-surface achieves a free switch between the focusing lens and anomalous reflection under different polarizations, which shows a potential application to design bifunctional antennas. Because the designed meta-surface can focus the incident plane wave to its focal point under an Ex polarization, quasi-spherical wave emitted from a source placed at its focal point can also be collimated to a plane wave instead, enabling high directivity of a reflectarray. As shown in Fig. 8(a), a self-made Vivaldi antenna, radiating quasi-spherical waves with a broad bandwidth (7-18 GHz), is utilized as the feed source. We optimize the length l = 68 mm to obtain best antenna performances in the final design. In the experimental process, four dielectric screws is used to fix an exact length between the designed meta-surface and the feeding antenna, and the foam is applied to provide a supporting frame without affecting the antenna performance. We measure the 2-D radiation patterns through the far-field measurement system in an anechoic chamber. Figure 8(c) depicts the FDTD simulated 3-D far field pattern at the frequency of f0 = 13 GHz. The achieved narrow-beam patterns are completely distinguished from the broad-beams of the Vivaldi antenna [29]. Figure 8(b) plots the simulated (measured) radiation gain of the proposed reflectarray antenna and the bare Vivaldi antenna. The best performance of the reflectarray antenna appear at the center frequency of f0 = 13 GHz with the measured gain of 24.1 dB. The 1-dB bandwidth is investigated with 16.42% (12.3-14.5 GHz) and 12.03% (12.5-14.1 GHz) for the numerical and experimental results, respectively. A simple calculation shows that more than 11.8 dB increment has been achieved over a quite broad band from 10 to 15 GHz. Note that the aperture efficiency is evaluated with respect to the utmost directivity calculated through the equation η = G/Dmax = G/(4πPQ/λ02) × 100%, where P and Q denotes the aperture size, G is the realized gain. A competitive aperture efficiency of 60.26% (52.48%) is obtained for the simulation and measurement at f0, respectively [24–27]. Figure 8(d) shows the simulated and measured 2-D far-field patterns in E-plane against the elevation angle (H-plane is not given for brevity). Narrow-beam is detected as expected, and the simulated (measured) half power beam width (HPBW) is about 9.2° (9.2°) in E-plane and 10.3° (10.5°) in H-plane at 13 GHz. The front-to-back (F/B) ratio is better than 25 dB (22 dB), and the levels of side-lobe is about 25.8 dB (18.3 dB) in both E- and H-planes. Moreover, the cross-polarization levels are better than 25 dB for both simulation and measurement. The competitive antenna gain, wide operating bandwidth and the relative high aperture efficiency reveal that the proposed reflectarray antenna is a good candidate for high data communication systems.
Fig. 8 Characterizations of the reflectarray antenna. (a) Topology of the designed reflectarray antenna; (b) numerical and experimental results of radiation gain for the referenced Vivaldi antenna and the proposed reflectarray antenna; (c) FDTD simulated 3-D radiation patterns at f0 = 13 GHz; (d) Simulated and measured 2-D far field patterns in E-plane at f0 = 13 GHz.
Under excitation of a y-polarized plane wave emitted by a horn antenna, the system can work as a beam steering antenna. The numerical and experimental 2-D far-field patterns at 11, 13 and 15 GHz are depicted in Fig. 9, respectively. Obvious beam steering effects is unambiguously observed in simulation and measurement as expected. The beam is deflected to 35.6° (35°), 29.7° (30°), and 25.6° (25°) at 11, 13 and 15 GHz, respectively in simulated (measured) results, which is again consistent with the theoretical prediction according to Eq. (6). The wider beam in the measured cases is attributed to the deteriorated wavefront of the horn antenna than that of the ideal plane wave. The good performances of the beam steering antenna indicate a potential application in the wireless communication systems.
Fig. 9 Characterizations of the beam steering antenna. 2-D far field patterns at yoz plane for (a) simulated and (b) measured results at three representative frequencies.
5. Conclusion
In summary, we have designed, fabricated and validated a high-performance bifunctional meta-surface in reflection geometry, which integrates a focusing lens and a beam deflector together. We enhance the working bandwidth by carefully designing a dual-resonant TMLR element which provides an almost consistent phase response within a large frequency interval. For potential applications, a bifunctional antenna with high-gain pencil beam and a steering beam has been implemented using the designed meta-surface. Both near field and far field measurement results show that the antenna system advances in many aspects such as bifunctional radiation patterns, broad operation bandwidth of more than 5 GHz (10-15 GHz), and elegant antenna performances. The findings here pave a way for many exciting applications with bifunctionality in communication systems.
Funding
National Natural Science Foundation China (Nos. 61372034, 61501499); Natural Science Foundation of Shaanxi Province (Nos. 2016JM6063, 2016JQ6001).
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