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Abstract
Multi-functional metasurfaces have exhibited powerful abilities of manipulating electromagnetic (EM) wave in predetermined manners, largely improving their information capacities. However, most works are implemented with EM functions controlled by one of the intrinsic properties of EM wave, such as polarization, frequency, etc. Herein, we propose a coding scheme to design a broadband and high-efficient multi-functional metasurface independently controlled by both frequency and polarization. To achieve this goal, we design anisotropic coding particles to realize independent phase functions and polarization-selectivity in the microwave region. Meta-atoms are finally optimized to exhibit 2-bit phase responses insensitive to incident polarization in the X-band while showing a 1-bit phase shift sensitive to incident polarization in the Ku-band. As a proof of concept, a metasurface is configured as an isotropic lens in the X-band, whereas the metasurface is designed as an anisotropic beam deflector in the Ku-band with or without polarization-conversion functionality dependent on the input polarization. The measured results, which agree well with the simulated ones, show excellent performances in the designed dual bands. Such a multi-functional coding metasurface may provide a flexible and robust approach to manipulate EM wave of multiple frequencies, as well as to integrate diverse functionalities into a single flat device.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials, a kind of artificially engineered electromagnetic (EM) materials composed of subwavelength-scaled structures, have experienced an unprecedented development in the past decades. Their powerful capabilities of manipulating EM waves can lead to many abnormal phenomena and novel devices [1,2]. As the two-dimensional version of metamaterials, the recently developed metasurfaces (MSs) have attracted tremendous attention due to their simple fabrication, thin electrical thickness and low insertion losses [3–6]. With upsurge of researches on MSs, a number of meta-devices have been successfully implemented from microwave [7,8] to terahertz [9], and to optical frequencies [10,11], such as meta-lens [12–14], polarizers [15–17], holographic imaging [18–20] and orbit angular momentum generations [21–23], etc.
As a special category of MSs, multi-functional MSs can integrate diverse EM functionalities into a single passive prototype, performing concurrent multi-tasks [24–29]. They play a crucial role in the development of advanced devices, because they can largely improve the information capacities of the meta-devices, which may be a key to solve the increasing demands on the speed of EM devices. The possibilities to achieve multi-functions mainly resorts to the intrinsic properties of the EM wave such as polarization [24–26], helicity [27,28] or frequency [8,18,29], etc. By applying active or nonlinear components, MSs can also vary from a certain function to another according to the external stimulations. Compared with active MSs to realize multiple functions, the passive multi-functional counterparts exhibit higher efficiency and simple structural configuration. Despite numerous advantages of multi-functional MSs, there are still some challenges ahead for further developments. For example, when functions of MSs are controlled by the polarization state, the operating frequency band is usually limited [24–26]. In addition, difficulties still exist in suppressing the polarization cross-talk for such kind of multi-functional MSs, which in fact is a key point to achieve independent functions for orthogonal polarizations. As for multi-functional MSs controlled by frequency, it’s also difficult to realize enough band separation in multi-spectra manner to avoid the crosstalk and therefore to keep independent phase tuning for different frequencies [18,29]. To address these problems, the recently developed digital coding MSs [30–33] may be an effective alternative, because finite phasing elements to control the wavefront will be conducive to suppressing the crosstalk between different EM functionalities. The concept of coding MS introduces digital code to traditional MSs, for example, by designing “0” and “1” digital bits to represent two MS elements with reflection phases of 0° and 180°, respectively. And in this way, meta-devices are easier to be realized since full phase coverage of 360° is not strictly required. Besides, physical particles are linked to the digital codes, possibly extending it to the applications like digital signal processing and information theory [30,31]. Furthermore, most reported multi-functional MSs so far are controlled by a single property of EM wave, e.g, either polarization or frequency, leaving much potentials unexploited. In general, more degrees of freedom can be obtained, although challenging, if multiple intrinsic properties are simultaneously utilized.
In this paper, we propose a reflective multi-functional coding MS providing both frequency- and polarization-controlled EM functionalities in microwave region. As a proof of concept, phase response of the meta-atoms are designed for 2 bit digital configuration in X-band while 1 bit configuration in Ku-band. Specifically, the elements can provide additional polarization-conversion effects in Ku-band, which operate either in cross- or co-polarized mode, determined by the incident polarization state. Meanwhile, phase response of the elements in X-band can always work in co-polarized operations immune to the change of incident polarization. Based on the designed meta-atoms, a multi-functional meta-device is finally optimized to realize isotropic focusing and anisotropic beam deflection in X- and Ku-band, respectively. As a result, the proposed MS can perform as a reflective meta-lens or anomalous beam deflector, controlled by the incident frequency. At the same time, the MS possesses polarization-selective performances that works as co- or cross-polarized anomalous beam deflector in Ku-band. Finally, we fabricate a prototype of the proposed MS and carry out the experimental measurements to further validate our design.
2. Design and analysis of the meta-atom
2.1 Concept and meta-atom design
Figure 1 schematically depicts the concrete functions controlled by frequency and polarization state of incident wave, where the MS performs as a meta-lens in X-band but acts as a beam deflector in Ku-band. The meta-lens in X-band operates in co-polarized status, insensitive to the incident polarization, whereas the anomalous deflector in Ku-band changes from cross- to co-polarization operation when incident polarization angle (defined as the angle between E-field vector and + x direction) jumps from 0° to 45°. The key step to realize the abovementioned multiple functions is to deliberately design meta-atoms capable of achieving frequency-dependent phase functions with simultaneous polarization-conversion effects in Ku-band. In addition, the phase shifts in the two bands of interest should be independent, avoiding mutual coupling that may spoil the overall performances. To this end, we tend to use a well-known cross-shaped structure [34] to introduce phase change in X-band, whereas employ a quasi-I-shaped metallic pattern in our previous works [35,36] to generate phase change in
Fig. 1 Functions of the designed MS varied with frequency and incident polarization. (a) and (b) depict the function of isotropic meta-lens immune to incident polarization in X-band. (c) Simultaneous beam deflection and polarization-conversion in Ku-band when the metasurface is illuminated by x(y)-polarized incidence. (d) Anomalous beam deflection in co-polarized operation when the metasurface is illuminated by ± 45°-polarized incidence in Ku-band. Here, ± 45°-polarization means the polarized direction is ± 45° deviated from x-axis in xoz plane.
Ku-band. The finally optimized meta-atom is schematically shown in Fig. 2(a), where a substrate (FR4) with relative permittivity εr = 4.3 and tan δ = 0.003 is sandwiched between two metallic layers. Figure 2(b) shows the top metallic layer that consists of four arc quasi-I-shaped structures separated by a cross-shaped structure. Besides, the substrate is grounded by a bottom metallic layer to totally block the transmission, ensuring the element working in reflection geometry. Other physical parameters of the element are denoted by h = 2.5 mm, p = 11 mm, r = 1.75 mm, θ = 60°, φ = 45°.
Fig. 2 Designed meta-atom and its surface current distribution. (a) Top view and (b) perspective view of the designed element. (c) and (d) depict the surface current intensity at 9 GHz and 15 GHz under y-polarized incidence.
To illustrate the independent controls of EM wave in X and Ku-band, the surface currents at 9 GHz and 15 GHz are investigated by the commercial software of CST Microwave Studio, as shown in Figs. 2(c) and 2(d). Obviously, strong current flowing on the cross-shaped structure is only observed at 9 GHz, indicating that this structure resonates at 9 GHz but hardly couples with the incidence at 15GHz. On the contrary, the quasi-I-shaped metallic structure resonates at 15 GHz but hardly operates at 9 GHz, as evidenced by the current flow being only observed at 15 GHz. The above results provide possibilities to realize independent phase or polarization manipulation in two operating bands by controlling these two parts of the meta-atom separately. To verify our prediction, we conduct a simulation of the proposed meta-atom by applying periodic boundary condition along x- and y-directions and a normal Flouquet port excitation.
We first investigate the dependence of the reflection properties on the parameter l, namely the arm-length of cross-shaped structure, under normal illumination of x-polarized incidence. As shown in Fig. 3(a), the element achieves a high co-polarized reflectivity in 8 −10 GHz but a much lower co-polarized reflection in 13.2 - 16.8 GHz. Since the dielectric substrate is assumed with small loss tangent, negligible energy absorption occurs for most cases. Therefore, the low co-polarized reflection leads to a high cross-polarized reflection in 13.2 - 16.8 GHz. Then, we investigate the co-polarized reflection phase in X-band and cross-polarized counterpart in Ku-band, both with l changed from 10.5 mm to 6.5 mm, as shown in Figs. 3(b) and 3(c), respectively. Clearly, 2-bit phase shifts (phase difference of 90° between adjacent particles) are obtained near 9 GHz for co-polarized reflection. At the same time, the phase shifts of cross-polarized components remain almost unchanged in 13.5 - 17.1 GHz. It concludes that the designed element can provide 2-bit phase shifts in X-band by changing the parameter l while convert the incidence into cross-polarized reflection with uniform phase shift in Ku-band.
Fig. 3 Reflectivity and phase response of the proposed element varied with l and φ. (a) Co-polarized reflection coefficient, (b) co-polarized reflection phase and (c) cross-polarized reflection phase with φ fixed for 45° but l altered from 6.5 mm to 10.5 mm. (d) Co-polarized reflection coefficient, (e) co-polarized reflection phase and (f) cross-polarized reflection phase with l fixed for 6.5mm and 10.5 mm but φ jumped from 45° to −45°.
Then, we construct a 1-bit digital element in Ku-band by rotating the orientation angle of the quasi-I-shaped structure (denoted by φ), in addition to the 2-bit coding scheme in low frequency band. Figure 3(d) illustrates the influence of the orientation angle on the reflectivity of the element. Obviously, the reflectivity keeps unchanged across the whole band when l is fixed but φ jumps from 45° to −45°. Figures 3(e) and 3(f) show the variation of co- and cross-polarized reflection phases as functions of φ in X and Ku-band, respectively. The phase curves in low frequency band keeps unchanged while those in Ku-band achieve an additional 180° phase shifts by setting φ from 45° to −45°. Therefore, we can obtain a 1-bit coding elements (phase difference of 180° between adjacent particles) in Ku-band, without affecting the co-polarized reflection properties including phase and amplitude in X-band. It should be noted that, even though the conclusions we have drawn are all under the illumination of x-polarization, the same results can be achieved under y-polarized incidence due to the rotational symmetry of the meta-atom.
2.2 Analysis of the anisotropic meta-atom
The phase shifts of the meta-atom in X-band can be regarded as a result of the change of structural resonances by parametric variation for the cross-shaped structure. However, for Ku-band, it is worthwhile to point out the mechanism of polarization-conversion effect as well as the phase change for cross-polarized component. By applying a 45° rotational operation to the xoy coordinate, we have constructed the relative uov coordinate, as shown in Fig. 4(a). Since the element always has a diagonal symmetry (or mirror symmetry with respect to u and v axis), the polarization cross-talk will be well suppressed when incident wave is polarized along u or v axis ( ± 45°-polarized direction in xoy coordinate). In this case, the reflection coefficients of the element can be described as ruv = rvu = 0, ruu = ejΦu and rvv = ejΦv. If the incident wave is polarized along x-axis, the relationship between output and input waves can be detailed as [37]
Here, Ex and Ey represent the reflected electric field that are polarized along x and y axis, respectively. And ΔΦ is the phase difference between Φu and Φv. The cross-polarized conversion coefficient under xoy coordinate, denoted by ryx, can be derived from Eq. (1) as [37]: . Therefore, the polarization-conversion efficiency will approach unity when ΔΦ is equal to 180°. In other words, the co-polarized reflection coefficient (rxx) will be reduced to zero. To verify this, we show the reflectivity of rxx and phase difference of ΔΦ versus frequency in Fig. 4(b) by setting (l, φ) as (8.9 mm, 45°). Consistent with theoretical prediction, the minimum value of rxx lies in where ΔΦ is equal to 180°. Then, we show the reason for the phase change of cross-polarized component when parameter φ varies from 45° to −45°. Writing the x-polarized incidence as the reflection wave can be written as Then, if expressed in xoy coordinate system, the reflection wave will beOn this basis, the cross-polarized coefficient ryx becomesWhen φ is set for −45°, the particle is seen to be rotated for 90° with respect to the element under the condition of φ = 45°. In such a scheme, the reflection Jones matrix of the element will be varied from to and the cross-polarized coefficient ryx will change toComparing Eqs. (3) and (4), we can precisely achieve a reverse phase response for cross-polarized reflection components by setting φ = 45° and φ = −45°. Therefore, by using thepolarization-conversion effects, we can obtain 1-bit phase shifts for cross-polarized reflection mode when the element is rotated with or without 90°.Fig. 4 Element topology and phase response in Ku-band. (a) Element topology for the analysis of polarization-conversion effect. (b) Reflectivity of rxx and phase difference of ΔΦ with parameters (l, φ) set as (8.9mm, 45°).
As mentioned above, the designed meta-atom featuring diagonal symmetry will not generate cross-talk, when the incident wave is polarized along ± 45° directions (or v- and u-polarized incidence). The simulated results are shown in Figs. 5(a) and 5(c), where the co-polarized reflectivity always stays at a high level across the working band for all coding cases when the elements are impinged by 45°-polarized wave. The reflectivity dropping at some frequency points near 18 GHz are mostly induced by the resonant loss. Figure 5(b) shows the co-polarized reflection phases varied with the size changes of the cross-structure. Apparently, phase responses keep unchanged within 13.5 GHz −17.2 GHz. At the same time, the phase responses in X-band cover a large range, providing the required 2-bit coding elements in low frequencies. Finally, the phase difference of the cross-reflection between the elements with φ = 45° and φ = −45° is depicted in Fig. 5(d). The phase difference fluctuates around 0° in 8 −10 GHz but around −180° in 13.5 GHz −17.2 GHz. That is to say, when the parameter φ jumps from 45° to −45°, co-polarized 1-bit phase shifts are generated in Ku-band, without affecting the phase response in X-band.
Fig. 5 Co-polarized reflectivity and phase response under 45°-polarized incidence. (a) Co-polarized reflectivity and (b) co-polarized phase shift with φ fixed for −45° but l varied from 10.5 mm to 6.5 mm. (c) Co-polarized reflectivity with l fixed for 10.5 mm and 6.5 mm but φ jumping from −45° to 45°. (d) Phase difference between φ = 45° and φ = −45° when l is fixed for 10.5 mm and 6.5 mm.
To give a brief design chart, we list the digital bytes of the coding elements in Table 1. It shows that we can achieve independent 2-bit co-polarized phases and 1-bit cross-polarized phases under x- or y-polarized excitation, while achieve independent 2-bit co-polarized phases and 1-bit co-polarized phases under u- or v-polarized (± 45°-polarized) excitation.
Table 1. Coding elements for multifunctional MS
3. Metasurface design and simulation results
3.1 Metasurface design
As a proof of concept to illustrate the multiple functionalities, we integrate focusing lens, anomalous deflector and polarization convertor into a single meta-device by the proposed metasurface. To this end, a hyperbolical and a constant gradient phase profile are discretized into 2-bit and 1-bit coding sequences for EM manipulation in X and Ku-band, respectively. Particularly, the hyperbolical phase distribution can be expressed as
where λ represents the wavelength at 9 GHz and F corresponds to the focal distance of 90 mm in this scenario. In Fig. 6(a), we show the discrete coding sequence of the hyperbolical phase profile. It should be noted that, despite such a meta-lens is actualized with 2-bit phase elements, focusing performances can still be predicted by formula (5). As for the gradient phase profile, only two kinds of meta-atoms with reverse phase response are necessary. The phase profile for anomalous reflection is finally configured into a sequence encoded by “010101…”, as shown in Fig. 6(b), and the deflection angle for such a metasurface can be predicted by the generalized Snell laws [3] given aswhere λ refers to the operating wavelength and L represents the periodic size of a supercell to realize 360° phase coverage. Here, each supercell contains 6 × 6 meta-atoms. Therefore, parameter L is designed as 66 mm, which results in a deflection angle of 17.6° at 15 GHz. Besides, it should be noted that a grating lobe will be generated in the opposite direction of −17.6°, which is also defined as the anomalous reflection with mode of −1. Based on the above phase profiles, the metasurface prototype is finally configured with a total size of 165165 mm2, as depicted in Fig. 6(c).Fig. 6 (a) Phase profile of the discrete hyperbolical phase profile in X-band. (b) Phase profile of the discrete gradient phase profile in Ku-band. (c) Configured metasurface.
3.2 Simulation results
We perform simulations by using a FDTD method in CST Microwave Studio with open boundary conditions in all directions. The power distribution on xoz plane is calculated and then exhibited in Fig. 7(a), under the normal illumination of an x-polarized excitation in X-band. Clearly, the energy is well accumulated in the central area to form a focal point. To measure the focal length, power distributions scanned along the line of (x = 0, y = 0) are shown in Fig. 7(b), where power peak is observed at z = 80 mm, which is slightly deviated from the designed focal length of 90 mm. This can be explained by that the designed focal point based on Eq. (5) is the phase focal point rather than the point where power peaks. As validated in [38], it is particularly true for a metasurface-based meta-lens that the phase focal length is slightly longer than the distance of power peak to the metasurface, due to the different space losses for different meta-atoms. In Fig. 7(c), normalized power distributions scanned along the line of (x = 0, y = 0) at different frequencies are synthesized to a 2D map to further show the focusing effect in the band of 8-10 GHz. The result shows that power flow is well focused from 8 GHz to 9.5 GHz, with a slight change of the focal distance. This is actually due to the dispersion nature of the metasurfaces that, for a broadband meta-lens, the frequency change will lead to a gradually increased focal length [39,40].
Fig. 7 (a) Power distribution on xoz plane at 9 GHz. (b) Normalized power distribution on the line of (x = 0, y = 0). (c) Normalized power distribution on the line of (x = 0, y = 0) in the frequency bandwidth of 8 - 10GHz. (d) Power distribution on the plane of z = 90 mm at 9 GHz. (b) Normalized power distribution on the line of (y = 0, z = 90 mm). (c) Normalized power distribution on the line of (y = 0, z = 90 mm) in the frequency bandwidth of 8 - 10GHz.
To further show the focusing effect, energy distribution on the plane of z = 90 mm at 9 GHz is then calculated and depicted in Fig. 7(d). With energy well converged to the central hot spot, the result further proves a good focusing effect of the meta-lens. The focusing efficiency of the meta-lens, defined by the ratio of the power measured at the focal spot to the incident beam, almost reaches 70.1% at 9 GHz [24]. To further illustrate the focusing performance, the normalized power distribution scanned along the line of (y = 0, z = 90 mm) is shown in Fig. 7(e). With focal width defined as the width over which the peak power drops by half (or termed full width at half maximum), it can be seen that the focal width reaches 19 mm (0.57λ at 9 GHz) which indeed approaches the diffraction limit of 0.5λ, further verifying the good focusing quality of the meta-lens in X-band. Finally, to illustrate the focusing effect within 8 - 10 GHz, power distributions at different frequencies scanned along the line of (y = 0, z = 90 mm) are synthesized to a 2D map, as depicted in Fig. 7(f). Apparently, good focusing performance can always be observed from 8.2 GHz to 9.4 GHz. Moreover, the same results can also be achieved under the excitation of y-polarization, because topologies of the meta-atoms are all characterized by the diagonal symmetry.
As for the functions in Ku-band, simulations are performed by illuminating the surface with x-polarized plane wave. In Fig. 8(a), the 3D scattering pattern of the metasurface sample at 15 GHz shows that the incident plane wave is split into two symmetric beams in xoz plane, verifying the anomalous reflections in Ku-band. Figure 8(b) shows the 2D scattering pattern on xoz plane. For convenience and clear view of the far-field characteristics, scattering patterns are normalized to their maximal intensity of the cross-polarized components. The incident wave are not only split into two symmetric directions with θ = ± 18° but also converted into the cross-polarized mode, agreeing well with the theoretical predictions. To assess its operating bandwidth, the co-polarized scattering patterns as well as the cross-polarized counterparts on xoz plane within the frequency range of 12 - 18 GHz are calculated and plotted in Figs. 8(c) and 8(d). For clear comparisons, all the results are normalized to the co-polarized maximum scattering results of the same-sized metallic plate. As expected, anomalous beam deflection and simultaneously polarization-conversion effect across the entire band of 13 - 18 GHz are observed.
Fig. 8 (a) Simulated 3D scattering pattern with x-polarized excitation at 15 GHz. (b) Normalized scattering pattern on xoz plane at 15 GHz. (c) Scattering patterns of co-polarized component on xoz plane within 12 - 18 GHz. (d) Scattering patterns of cross-polarized component on xoz plane within 12 - 18 GHz.
It should be noted that the above coincident results in Ku-band are carried out with x-polarized excitation. As predicted in the section of element design, the lens in X-band and the beam deflector in Ku-band will operate at co-polarized states when the surface is impinged by ± 45°-polarized wave (v- or u-polarized wave). Hence, we plot in Fig. 9 the simulated results under the normal illumination of a 45°-polarized incidence. Metasurface with identical element distributions are used in Fig. 9 and Fig. 8. As expected, the good focusing effect shown in Figs. 9(a) and 9(c) verify the polarization-insensitive property of the meta-lens in X-band. On the contrary, the deflection effects in Figs. 9(b) and 9(d) have strong co-polarized components in Ku-band, demonstrating the polarization-controlled property of the anomalous deflector. These simulated results clearly show the ability of the proposed multi-functional metasurfaces in controlling the waves in a frequency-selective and polarization-selective manner.
Fig. 9 Simulated results of the metasurface under 45°-polarized excitation. (a) Normalized power distribution on the line of (x = 0, y = 0) at 9 GHz. (b) Scattering pattern of the metasurface on xoz plane at 15 GHz. (c) Synthesized power distribution on the line of (x = 0, y = 0) versus frequency. (d) Scattering patterns of co-polarized mode on xoz plane versus frequency.
4. Experimental validation and discussion
According to the principle of reversibility of light path, the incident wave will be reconstructed when a point source is fixed at the focal point. Hence, we alternatively exhibit a practical lens antenna application based on the proposed meta-lens as a reliable validation of the lensing effects in X-band. In this way, the performance of the meta-lens can be evaluated from near-field distribution where spherical wave will be transformed into plane wave, or from far-field region that exhibits a pencil-beam-like radiation, induced from the near-field planar wavefront. As depicted in Fig. 10(a), a Vivaldi antenna, whose structural parameters can be found in [41], is adopted to emit spherical wave, and its phase center at 9 GHz is exactly located at the focal point of the meta-lens. The simulated near field performance on xoz plane, which refers to the real part of Ex, is shown in Fig. 10(b). The secondary plane wave transformed from the primary feed of spherical wave well validate focusing ability of the meta-lens. The far-field results in Fig. 10(c) shows a pencil beam radiation, further proving the near-field result in Fig. 10(b).
Fig. 10 Application and validation of the meta-lens in X-band. (a) Designed metasurface assembled with a Vivaldi antenna. (b) Simulated results of Re(Ex) on xoz plane. (c) far-field characteristic of the meta-lens illuminated by the Vivaldi point source.
We fabricate the metasurface prototype by adopting standard Printed Circuit Board (PCB) technology as shown in Fig. 11(a). Then, the measurement is performed in an anechoic chamber to avoid interference and unwanted reflections from surroundings. Particularly, in the far-field measurements, the prototype is placed on a turntable so that it can be freely rotated in both azimuth and elevation directions. For X-band validations, Fig. 11(b) show the measured setup in which a Vivaldi antenna is inserted in a microwave foam with a distance 90 mm away from the metasurface. By rotating the feed antenna, polarization angle of the incident spherical wave can be tailored easily. To validate polarization-controlled deflection of the prototype in Ku-band, quasi-plane wave emitted from a horn source is employed to mimic the plane wave incidence, as shown in Fig. 11(c). Different polarized-wave can be generated by rotating the horn antenna along its central axis. The measured co-polarized patterns on xoz plane under the spherical illumination of x- and 45°-polarized incidence in X-band is shown in Figs. 11(d) and11(e), respectively. Well matched with the simulated results, the measured ones further demonstrate that the designed meta-lens is immune to incident polarization in X-band. Gain performances of the lens antenna with x-polarized excitation in the frequency range of 8 - 10 GHz are depicted in Fig. 11(f). The high gain performance with low cross-talk within the band of 8.5 - 9.5 GHz validate the isotropic lensing functions of the proposed meta-lens.
Fig. 11 (a) Fabricated metasurface sample. (b) Measured setup of of the prototype in X-band. (c) Measured setup in Ku-band, where a horn source that is right ahead of the MS is employed to emit quasi-plane wave. Simulated (Sim.) and measured (Mea.) far-field patterns of co-polarization (Co-Pol.) and cross-polarization (X-Pol.) at 15 GHz on xoz plane under (d) x-polarized incidence and (e) 45°-polarized incidence. (f) Gain performances across the bandwidth of 8 - 10 GHz with x-polarized excitation.
In Fig. 12(a), we show the far-field radiation patterns on xoz plane at 15 GHz with the prototype shined by x-polarized excitation. For convenience, patterns are all calibrated to the maximum radiation of a same-sized metallic plate. Measured results are in good agreements with the simulated ones, both indicating twin beams working in cross-polarized operation with tilting angle of θ = ± 17.5°, which is slightly deviated from the theoretical prediction by Eq. (6), due to the quasi-plane wave used in the measurement. This imperfect incidence also leads to a wider beam width in the measurements compared to the simulation ones. Then we show the operating band of the beam deflector in Fig. 12(b) by mapping the cross-polarized radiation patterns on xoz plane at different frequencies. Considering the imperfect fabrication and assembly, as well as the measurement tolerance, the theoretically predicted, numerically simulated and experimentally measured results are in good agreements, demonstrating good deflection effect almost across the whole Ku-band. Notably, the above results are all operated in cross-polarized mode. In order to study the performances of the deflector varied with polarization, the fabricated prototype is also excited by 45°-polarized incidence by rotating the horn source. The results shown in Fig. 12(c) further prove the stable functionalities of the deflector in splitting incident waves equally into twin beams with directions of θ = ± 17.5°. Opposite to the case excited by x-polarized wave, the metasurface has a near-zero cross-polarized while high co-polarized scattering both in simulation and experiment under the 45°-polarized excitation. The co-polarized operation within 12 - 18 GHz are shown in Fig. 12(d), further validating the anomalous deflection functions in a broad frequency band.
Fig. 12 (a), (c) Normalized scattering pattern on xoz plane at 15 GHz under x- and 45°-polarized incidence. (b), (d) Scattering patterns of cross-polarized components on xoz plane within 12 - 18 GHz under x- and 45°-polarized incidence.
5. Conclusion
In conclusion, a multifunctional coding MS is proposed with functionalities controlled by both incident frequency and polarization. As a proof of concept, a prototype is designed as an isotropic meta-lens in X-band whereas an anisotropic beam deflector in Ku-band. Experiments have been carried out to demonstrate the design principle as well as the simulations. The proposed metasurface and the design method can be readily scaled to other frequencies, e.g., terahertz. Furthermore, the EM functionalities are not limited to what are discussed herein, but instead we may envision that diverse functionalities could be integrated in a frequency- and polarization-controlled manner, as long as these functionalities can be achieved by discrete coding sequences. This scheme may also provide practical uses in many real-world applications, such as multi-mode antennas in wireless communications, multi-functional scatterings in radar detection system, etc.
Funding
National Natural Science Foundation of China (NSFC) (61671231, 61871394); National Key Research and Development Program of China (2017YFA0700201); China Postdoctoral Science Foundation (2017M620202).
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