## Abstract

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 (*E _{x}* or

*E*) incident wave along

_{y}*z*axis, the wave vector can be written as

*k*represents the wave-vector along

_{xi}*x*direction,

*k*denotes the wave-vector along

_{yi}*y*direction,

*k*

_{0}is the propagation constant in free space.

Replace the conventional meta-surface with a GMS, the wave vector can be calculated as

*ξ*and

_{x}*ξ*denote the phase gradient along

_{y}*x*and

*y*directions introduced by the GMS, which can be further calculated as

*(*

_{x}*x*,

*y*) and φ

*(*

_{y}*x*,

*y*) represent the phase profiles at a position (

*x*,

*y*) along

*x*and

*y*directions, respectively. We can engineer φ

*(*

_{x}*x*,

*y*) and φ

*(*

_{y}*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 (φ

*(*

_{x}*x*,

*y*) = C

_{1}, φ

*(*

_{y}*x*,

*y*) = C

_{2}), shown in Figs. 1(a) and 1(b), mirror reflection occurs by normally illuminating the sample with

*E*and

_{x}*E*polarizations according to the Snell’s laws. For the GMS2 shown in Figs. 1(c) and 1(d), a parabolic phase profile along

_{y}*x*direction and a linear gradient phase distribution along

*y*direction are pre-arranged as

*F*denotes the focal length. Both focusing and anomalous deflection functions can be realized under

*E*and

_{x}*E*excitations, respectively.

_{y}To enlarge the operating bandwidth, we require similar slopes for the phase responses at different frequencies within a band. Therefore, we enforce the condition

*f*

_{1}and

*f*

_{2}are the lower and upper frequencies of the working band,

*f*denotes the frequency within the band. Our aim is to realize a large frequency interval (

_{j}*f*

_{2}-

*f*

_{1}), 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 (*ε _{r}* = 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.

For a special case with b_{1} = 4.5 mm, b_{2} = 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 *f*_{1} = 8.1 GHz and *f*_{2} = 13.4 GHz for the TMLR, which plays an essential role in extending the phase variation range [25]. The magnetic resonance *f*_{1} can be explained by the resonance between the middle bar and the ground plane, while the magnetic resonance *f*_{2} is mainly generated by the other two bars and the ground plane. Both resonances can be dictated by the geometrical parameters b_{1} and b_{2} of the structure. Since the incident wave polarized along *y* (or *x*) direction can only “see” the phase φ* _{y}* and φ

*, we can tune the reflection phases φ*

_{x}*and φ*

_{y}*independently and freely by varying the parameters b*

_{x}_{1}and b

_{2}, respectively, as shown in Fig. 3. Referring to Fig. 3(a), under excitation of

*E*, φ

_{y}*undergoes a desirable phase-shift range over 360° as b*

_{y}_{1}increases. However, φ

*keeps consistent under excitation of*

_{x}*E*as b

_{x}_{1}varies, as shown in Figs. 3(b) and 3(d), since φ

*is predominantly determined by other parameter b*

_{x}_{2}. 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

*f*

_{0}= 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.

The well-optimized TMLR can provide arbitrary phases φ* _{y}* and φ

*by carefully tuning b*

_{x}_{1}and b

_{2}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 ξ

*(*

_{y}*y*) = 0.5

*k*

_{0}are pre-designed at the center frequency

*f*

_{0}= 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 λ

_{0}× 6.03 λ

_{0}, where λ

_{0}is the wave length at the frequency of

*f*

_{0}. The related phase distributions for

*E*and

_{y}*E*polarizations are depicted in Figs. 4(b) and 4(c), respectively.

_{x}Then, we experimentally evaluate the focusing effect of the bifunctional meta-surface. Shining the sample by a wide horn antenna (2-18 GHz), the *E _{x}* field at

*yoz*plane with an area of 140 × 100 mm

^{2}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

*f*

_{0}= 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

*E*amplitude along

_{x}*z*axis as a function of frequency with the results shown in Fig. 6. With a perfect phase profile at

*f*

_{0}= 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

*E*field distribution at the focal plane of

_{x}*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.

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 *E _{y}*-field distribution in

*xoz*plane at frequency of

*f*

_{0}= 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 θ

_{r}= 29.7°, which coincides well with the theoretically calculated value (θ

_{r}= 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

*f*

_{0}= 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

*f*

_{0}= 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].

## 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 *E _{x}* 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

*f*

_{0}= 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

*f*

_{0}= 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*/

*D*

_{max}= G/(4π

*PQ*/λ

_{0}

^{2}) × 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

*f*

_{0}, 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.

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.

## 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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