Spin-Controlled Multiple Pencil Beams and Vortex Beams with

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Spin-Controlled Multiple Pencil Beams and Vortex Beams with Different Polarizations Generated by Pancharatnam-Berry Coding Metasurfaces Lei Zhang, Shuo Liu, Lian Lin Li, and Tie Jun Cui ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b12468 • Publication Date (Web): 25 Sep 2017 Downloaded from http://pubs.acs.org on September 27, 2017

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ACS Applied Materials & Interfaces

Spin-Controlled Multiple Pencil Beams and Vortex Beams with Different Polarizations Generated by Pancharatnam-Berry Coding Metasurfaces Lei Zhang1,2, Shuo Liu1,2, Lian Lin Li4, and Tie Jun Cui1,3,* 1 2

State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China Synergetic Innovation Center of Wireless Communication Technology, Southeast University, Nanjing

210096, China Cooperative Innovation Centre of Terahertz Science, No.4, Section 2, North Jianshe Road, Chengdu 610054, China 4 School of Electronic Engineering and Computer Sciences, Peking University, Beijing 100871, China 3

*

Corresponding author. E-mail: [email protected].

ABSTRACT We propose to design coding metasurfaces based on Pancharatnam-Berry (PB) phase. The proposed PB coding metasurface could control circularly polarized components of incident waves, by encoding geometric phase into the orientation angle of coding particles to generate 1-bit and multi-bit phase responses. We perform digital convolution operations on scattering patterns of the PB coding metasurface to reach flexible controls of the circularly-polarized waves, forming spin-controlled multiple beams with different polarizations in free space, such as pencil beams and vortex beams carrying orbital angular momentum. Both numerical and experimental results demonstrate the excellent performance of the PB coding metasurface, which opens a pathway to novel types of multi-beam generations and provides an effective way to expand the beam coverage for wireless communication applications. Keywords: Coding metasurface; Pancharatnam-Berry phase; anisotropy; vortex beam; circularly polarized waves; multiple beams

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INTRODUCTION In the past 20 years, metamaterials have experienced a rapid development due to their unique electromagnetic (EM) properties that are not available in nature. Traditionally, metamaterials are artificial structures that are described by the effective medium theory, and have been widely used to manipulate EM waves, producing many exciting phenomena.1 Metasurfaces, as the two-dimensional (2D) equivalence of metamaterials, have recently attracted great interests from researches in both science and engineering communities owning to their superior abilities to provide abrupt phase shift, amplitude modulation, and polarization conversion of EM waves.2,3 Compared with three-dimensional (3D) bulk metamaterials, metasurfaces have a negligible thickness with respect to the working wavelength, thus occupying much less physical space and with lower insertion loss. In comparison with various types of metasurfaces that tailor the phase discontinuities through structure-parameter variation of meta-atoms, Pancharatnam-Berry (PB) metasurfaces with controllable geometric phase through the orientation variation of constituent meta-atoms have shown great potential in manipulating EM waves.4-18 They were developed from the concept of PB phase19,20 and composed of an array of identical anisotropic subwavelength scatterers with different orientations. When the orientation angles of scatterers vary, a specific phase will be generated for circularly polarized stimulations, resulting in a space-variant phase-front modification. Based on the convenient local phase control, PB metasurfaces have been successfully employed to generate photonic spin Hall effect,16 directional surface plasmon polaritions,7,8 holograms,17,18 reflect/transmit arrays,6,13-15 random diffusions,11,12 and vortex beams,4,15 etc. More recently, the concept of coding metasurface was proposed to digitally control EM waves by designing two distinct coding particles with opposite reflection phases 0 and 180° as the digital bits of ‘0’ and ‘1’ (1-bit coding).21 The concept of coding metasurfaces can be extended from 1-bit to multi-bit. For example, 2-bit coding metasurfaces are constructed by a sequence of four coding particles “00”, “01”, “10”, and “11”, which have 0, 90°, 180°, and


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270° phase responses, respectively. Coding metasurfaces could simplify the design and optimization procedures owing to the digitalization of unit cells. By arranging coding particles on a 2D plane with pre-designed coding sequences, the coding metasurfaces can be used to manipulate the EM waves in a simpler and more efficient way, leading to many exotic phenomena such as anomalous reflections, refractions, and random diffusions.11,12,21-29 It is worth noting that the application scope of the coding metasurfaces is not only limited to microwave frequencies, but also can be extended to the terahertz waves,22-25,32 and acoustic waves.27 Most importantly, coding metasurfaces have become a bridge linking the physical metamaterial particles and digital codes, making it possible for us to revisit metamaterials from the perspective of information science.30,31 For instance, the digital convolution operation was applied to coding metasurfaces to realize scattering pattern shift, which could rotate a radiation beam to arbitrarily desired directions with little distortion in the whole upper half space.32,33 In this paper, we propose a PB-phase-based reflection-type coding metasurface, which consists of an array of rod antennas with spatially varying orientations. We perform convolution operation on scattering patterns to realize flexible control of circularly-polarized EM waves. The combination of the encoded PB phase with the principle of scattering-pattern shift helps the PB coding metasurface generate spin-controlled multiple beams in free space, which provides another degree of freedom in designing novel multi-beam antennas for wireless communication systems. RESULTS AND DISCUSSIONS Design of the PB coding particles. Polarization is one of the basic properties of EM waves, and spin-controlled metasurface could provide more degrees of freedom in many practical applications.7,8,17,18 Here, we combine the concept of PB phase with the design of coding metasurface. As illustrated in Figure 1a, straight rod antennas with different orientation angles are used to build the coding metasurface, which shows distinct scattering behaviors for lefthanded circularly polarized (LCP) and right-handed circularly polarized (RCP) incident



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waves. For instance, when the proposed PB coding metasurface is normally illuminated by linearly polarized (LP) plane wave, it will generate four symmetric beams simultaneously in the upper-half space, which contain two RCP beams toward the –x direction and two LCP beams toward the +x direction, as shown in Figure 1a. Specifically, if illuminated by RCP plane wave, it only creates two RCP beams toward the -x direction; while illuminated by LCP plane wave, it only creates two LCP beams toward the +x direction. This phenomenon shows the spin-dependent property of the PB coding metasurface. In most metasurface designs, abrupt phase changes are engineered by varying structural parameters of meta-atoms.2,3 But for PB metasurfaces, the phase responses are simply achieved by rotating an identical meta-atom with different orientation angles.4-18 In our design of PB coding metasurface, a straight rod antenna printed on a grounded FR4 substrate is used as the basic coding particle, as shown in Figure 1b. The substrate has a thickness of h=2mm with relative permittivity of 4.4 and loss tangent of 0.02. The rod antenna and ground plane are made of copper with the thickness of t=0.018mm. Such a coding particle can be considered as an anisotropic scatterer, which gives rise to a polarization dependent response. The full-wave simulations are carried out by using a commercial software, CST Microwave Studio 2014, in which the unit-cell boundaries are applied to the x and y directions, and two Floquet ports are applied to the +z and -z directions. The electric field is applied to the x and y directions to obtain the reflection coefficients of the coding particle under the illumination of linearly x- and y-polarized waves, respectively. By optimizing the geometric parameters of the coding particle, a nearly constant 180° reflection phase difference between the x- and ylinearly polarized incidences can be achieved in a wide frequency band (reaching exactly 180° at 15GHz), as shown in Figure 2a, which indicates that the coding particles can form a perfect reflection-type half-wave plate.16 Meanwhile, the reflection amplitudes of the coding particle under the x- and y-polarized incidences are kept almost unity. The period of the coding particle is p=6mm, with the other parameters optimized as w=1.5mm and d=4.8mm for opposite phase responses.


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The coding particles based on PB phase can achieve 360° phase shift by simply rotating

the rod antenna with an orientation angle of with respect to the y-axis, as illustrated in

Figure 1c. Particularly, for a rod antenna with a local orientation angle denoted by , a

circularly polarized incident wave will maintain its helicity in the reflected direction with an abrupt geometric phase change of ±2.11,16 Here, the polarization sign “+” and “-” denote the

RCP and LCP incident waves, respectively. Moreover, the spatial variation of the phase has a simply linear relationship to the rotation angle of the rod antennas, as demonstrated in Figure

2b. Practically, for the 3-bit case, the step size of rotation angle for each coding particle

becomes 22.5° and the entire reflection phase coverage of 360° is discretized into eight levels, namely 0°, ±45°, ±90°, ±135°, ±180°, ±225°, ±270° and ±315°, to mimic the digital bits

of “000”, “001”, “010”, “011”, “100”, “101”, “110”, and “111”, respectively. For simplicity,

the number “0” to “7” stand for the digits “000” to “111”. Each coding particle is represented by the same rod antenna with a specific rotation angle. Hence this type of PB-phase-based coding metasurface could simplify the design processes, and provide more degree of freedom to manipulate the reflected beams by their spin-dependent phase responses. To evaluate the reflection property of the eight coding particles in broad frequency band, we further provide broadband phase responses of the 3-bit coding particles under the RCP and LCP incident waves. It is observed from Figures 2c and d that the phase difference between adjacent coding particles remains around 45° from 10GHz to 20GHz, which ensures that the PB coding metasurface can work over a wide frequency range and exhibit a nondispersive phase profile. In the following discussions, we will give several examples to demonstrate the spin-controlled behaviors of the PB coding metasurface by using the principle of scattering pattern shift. Design scheme of PB phase codes combined with convolution operation. To further elaborate the physical mechanism of convolution operation, we would like to make an analogy to the mixing process (modulation) in signal processing. As we know, a carrier wave with single frequency can be viewed as a Dirac function in the frequency domain. Once a baseband signal is multiplied with the carrier wave in the time domain, its frequency spectrum



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will be shifted to the central frequency of the carrier wave without distortion, which can be simply achieved by performing a convolution operation to the spectrum of the carrier wave (Dirac function) and the original signal in the frequency domain. Since there is a Fourier transform relation between the coding pattern and its far-field radiation pattern, the convolution theorem (or more specifically, the frequency shift theorem) can also be applied to design the coding metasurfaces. The schematic of our design is illustrated in Figure 3. For the first case, we take a 3-bit PB coding metasurface as proof of principle to show the polarization-dependent behaviors in the multi-beam manipulations. The proposed metasurface consists of 40 × 40 particles with a

certain coding patterns. Figure 3 shows three different coding patterns (Figures 3a-c) and their corresponding 3D scattering patterns at 15GHz under the RCP (Figure 3d-f), LCP (Figures 3g-i), and linearly-polarized (LP, Figures 3j-l) illuminations, respectively. In this illustration, the coding metasurfaces are normally illuminated by plane waves. From Figures 3d, g and j, it can been seen that all RCP, LCP and LP incident waves are equally split into two symmetrical pencil beams in the yoz-plane with the coding sequence of “0 0 0 0 4 4 4 4…” varying along the y direction. Figures 3e and h show that the RCP and LCP incident waves are independently reflected to mirror-symmetric directions in the xoz-plane, respectively, with the coding sequence of “0 1 2 3 4 5 6 7…” varying along the x direction. This is mainly due to the fact that the spatially varying phase distribution on the coding metasurface exhibits opposite phase gradient between the RCP and LCP illuminations. As expected, the metasurface generates two mirror-symmetric beams simultaneously in the xoz-plane under the illumination of LP incident wave, which can be decomposed into two circularly polarized waves (RCP and LCP) with equal amplitude, as shown in Figure 3k. The deviation angle with respect to the z-axis is exactly equal to the anomalous reflected angle determined by the generalized Snell’s law,2 = (/),


(1)

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in which and represent the free-space wavelength and the period of the gradient coding sequence, respectively. Substituting = 20 (15GHz) and = 48 into Eq. (1), the

deviation angle with respect to the z-axis can be calculated as 24.6°, which is in excellent agreement with the numerical simulations.

The coding metasurfaces with PB phase can be specially designed to create the desired multiple beams by simply adding several coding patterns. It is worth noting that the convolution of scattering patterns can be easily implemented by calculating the modulus of different coding patterns,32 which allows the PB coding metasurface to manipulate the circularly polarized beams flexibly with significantly reduced computational complexity. The mixed coding pattern M1 illustrated in Figure 3c is obtained by adding the periodic sequence “0 0 0 0 4 4 4 4…” along the y direction (Figure 3a) with the gradient sequence “0 1 2 3 4 5 6 7…” along the x direction (Figure 3b). The far-field patterns of M1 under the RCP (Figure 3f), LCP (Figure 3i) and LP (Figure 3l) incidences show that the original far-field patterns with two symmetric beams in the yoz-plane (Figures 3d, g and j) are deflected to the ±x direction, after being conducted by the convolution operations with the scattering patterns in Figures 3e,

h and k, respectively. Finally, under the illumination of the LP incident wave, the metasurface will generate four symmetrical pencil beams in the upper-half space, which contains two RCP beams toward the -x direction and two LCP beams toward the +x direction. The elevation

angle and azimuth angle of the four beams can be calculated by the following

equations,32

= ! + ! ! # = $% &'( )* # &'( )

,

(2)

+

in which and ! are the deviation angles corresponding to the two coding sequences

varying along the x and y directions, respectively. In this case, and ! calculated by Eq. (1)

are both 24.6°, and thus is calculated as 36.1°. The azimuthal angle of four beams are 45°,

135°, 225°, and 315°, respectively, which are in good agreements with the numerical simulations.



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To demonstrate flexible controls of multiple beams via the PB coding metasurfaces, we present some other mixed coding patterns. Figure 4c shows a mixed coding pattern M2 formed by the modulus of a periodic coding sequence “0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4…” (Figure 4a) and a gradient coding sequence “0 1 2 3 4 5 6 7…” (Figure 4b), both of which vary along the x direction. Referring to the analysis process of the mixed coding pattern M1 in Figure 3, the mixed coding pattern M2 generates four pencil beams in the xoz-plane, which contains two RCP beams towards the –x direction and two LCP beams towards the +x direction symmetrically, as displayed in Figure 4d. The elevation angles of the two RCP/LCP beams can be calculated as,32 = ( ! ± ),

(3)

in which and ! are the anomalous scattering angles corresponding to the two coding

sequences varying along the x direction, respectively. In this case, and ! are theoretically calculated by Eq. (1) as 12° and 24.6°, respectively, and thus the deviation angle can be

calculated by Eq. (3) as 12° and 38.7° for the two RCP/LCP beams, which have good agreements with the numerical simulations. Generation of multiple vortex beams. More interestingly, we can use the proposed method to generate multiple vortex beams with helicoidal equal-phase wavefronts. The beams have an azimuthal phase dependence exp (i0) and carry orbital angular momentum (OAM).2,4 A simple method for creating the vortex beam is to introduce a spiral-like phase shift via metasurfaces, and the phase distribution of the metasurface can be expressed as, Φ(2, 4) = 0 × = 0 × %56$% (4/2),

(4)

where l is the topological charge, and is the azimuth angle. Note that the coding pattern in

Figure 5a consists of eight sectors and the successive phase step from a sector to another is ±45°. This rotated phase distribution can generate a vortex beam with OAM mode l=1. Here,

we add the rotated OAM coding pattern with a gradient coding sequence “0 1 2 3 4 5 6 7” varying along the x direction (Figure 5b). The mixed coding pattern M3 in Figure 5c generates


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two symmetrical vortex beams in the xoz-plane and the deviation angle of the two beams are calculated as 24.6° by Eq. (1).

We clearly observe that the center of each beam is a deep null region and is about 15dB lower than the annular high-intensity region, as displayed in Figure 5d, which is consistent with the characteristic beam profile of vortex beams: a typical ring-shaped intensity profiles with a hollow in the center. Figures 5e and f display the simulated near-field distributions of the coding pattern M3, and the normalized intensity and phase distribution of the Ey

component are examined on the cross section perpendicular to the beam direction of = 0°,

= 24.6°. Due to the limilation of the computer resources, the observation plane is only set

as 273mm ( 13.65) away from the center of the metasurface with an area of 240mm ×

240mm . Both the ring-shaped intensity distribution and the spiral phase distribution

demonstrate that the beam is a vortex beam and carries OAM (l=1).

Figure 6a shows another coding pattern composed of 16 sectors and the successive phase

step from a sector to another is ±45°. This rotated phase distribution can generate a vortex

beam with OAM mode l=2. Specifically, if the rotated OAM coding is added with a periodic

coding sequence “0 0 0 0 4 4 4 4…” varying along the y direction (Figure 6b) and a gradient coding sequence “0 1 2 3 4 5 6 7…” varying along the x direction (Figure 6c), the mixed coding pattern M4 shown in Figure 6d will generate four vortex beams symmetrically in the upper half space, which contain two RCP vortex beams toward the –x direction and two LCP vortex beams toward the +x direction, as displayed in Figure 6e. In this case, the deep null region of the four beams is about 20dB lower than the annular high-intensity region, and the

elevation angle and azimuth angle of the beams are the same as those in the coding

pattern M1: =36.1°, and =45°, 135°, 225°, and 315°, respectively. Figures 6f and g

present the simulated near-field distributions of the coding pattern shown in Figure 6a, in which the normalized intensity and phase distribution of the Ey component are examined on the cross section perpendicular to the z-axis. Here, the observation plane is set at only 200mm

(10) above the metasurface with an area of 240mm × 240mm. The main feature of the



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spiral phase distribution obtained in Figure 6g clearly indicates that the vortex beam has the OAM mode of l=2. The above numerical simulation results demonstrate that the multiple vortex beams can be effectively generated by the proposed PB coding metasurface. Overall, OAM is a new degree of freedom in EM waves and is promising for channel multiplexing in the communication systems. The spin-controlled vortex beams carrying OAMs with different modes can be used to encode information and increase the communication capacity without increasing the bandwidth. In addition, many other coding patterns have been simulated for verifying the proposed method, which are not presented here for brevity. Experimental verification. To experimentally validate the proposed concepts and designs, we fabricated three samples of the PB coding metasurfaces. The structures of such coding metasurfaces are very simple and can be easily fabricated using the printed circuit board (PCB) technique. Figures 7a, b, and c show photographs of the fabricated PB coding metasurfaces with coding patterns M1, M2, and M3, respectively. All samples are composed of 40 × 40

particles and have the same size of 240mm × 240mm (12 × 12). As illustrated in Figure

8, the measured 2D scattering patterns of the coding metasurfaces at 15 GHz with coding

patterns M1, M2, and M3 are in very good agreements with the simulated results. Particularly, the comparison of simulated and measured xoz-plane scattering patterns of sample M3 is shown in Figure 8c, in which it is clearly observed that there are two hollows at the elevation angles of ±24.6°. In general, the deviation angles of all scattering beams are in excellent

match to theoretical predictions, validating the effectiveness of the proposed method in generating spin-dependent multiple beams with different polarizations by combining the PB

phase and the principle of scattering pattern shift. Besides, the near-field planar scanning technique was performed to measure the OAM vortex wavefront of the coding pattern M3. Here, the near-field distributions of the coding pattern M3 are given at the frequencies of 14.5 GHz (Figures 9a and b), 15.0 GHz (Figures 9c and d), and 15.5 GHz (Figures 9e and f), respectively. The near-field intensity distribution presents doughnut-shaped profiles and the spiral phase distribution shows clearly the beam carrying OAMs with mode of l=1. Those


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measured results experimentally demonstrate that vortex beam with OAM mode l=1 can be successfully realized in a broadband. CONCLUSIONS In summary, we have proposed a method to design 3-bit coding metasurfaces which could generate spin-dependent multiple beams with the aid of PB-phase coding particles and the digital convolution operations on the coding metasurface. The PB coding metasurfaces with the mixed coding patterns can generate the desired scattering patterns based on the principle of scattering pattern shift. The flexible controls of circularly-polarized waves and their simple designs have been numerically demonstrated and experimentally verified by several samples fabricated in the microwave frequency. The measured results show very good agreement with the simulated ones, indicating the excellent performance of the proposed PB coding metasurface for realizing the spin-controlled multiple beams, such as four symmetrical pencil beams, and multiple vortex beams with different OAM modes. The proposed PB coding metasurfaces provide another degree of freedom in designing new multi-beam antennas that may have potential applications in radio and microwave wireless communications. Owing to the simple structural design and easy fabrication, the proposed method can be extended to the terahertz, optical and even acoustics regimes, and further exploited to control transmitted waves. METHODS Experimental setup. The experiments were carried out in the microwave anechoic chamber and the experimental setup of far-field measurement is illustrated in Figure 7d. An LP horn antenna working from 12 to 18GHz served as transmitter to generate normal illumination to the coding metasurface. The distance between the metasurface and transmitter was set as about 2m to provide the quasi-plane-wave illumination. Both metasurface and transmitter were mounted on an antenna turntable, which could automatically rotate 360° in the

horizontal plane. Besides, two opposite circularly polarized (RCP and LCP) horn antennas served as receivers to measure the RCP and LCP components of the scattering fields. The



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transmitting and receiving antennas were connected to two ports of an Agilent N5245A vector network analyzer (VNA). As shown in Figure 7e, the near-field experimental system is composed of a fixed platform and a position-controllable probe connected to one port of the Agilent VNA. The standard measurement probe located in front of the sampe M3 at a distance of 900 mm (45) serves as the detector. During measurements, the sample M3 is illuminated by normally incident waves emitted form the LP horn antenna placed at 1 m away, and the probe moves along the x and y directions with step of 5 mm. The scanning plane is perpendicular to the radiation beam with an area of 500×500 mm2, covering the main radiation region. The intensity and phase of the near electric field can be obtained from the measured tansmission scattering parameters at each sampled point. Then the intensity and phase distribution of the Ey component are plotted with the aid of MATLAB. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (61631007, 61571117, 61302018, 61401089, 61401091, 61501112 and 61501117), and the 111 Project (111-2-05) REFERENCES (1) Cui, T. J.; Smith, D.; Liu, R., Metamaterials: Theory, Design, and Applications. Springer, New York: 2009. (2) Yu, N. F.; Genevet, P.; Kats, M. A.; Aieta, F.; Tetienne, J. P.; Capasso, F.; Gaburro, Z. Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction. Science 2011, 334, 333-337.


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Figure 1. Illustration of PB coding metasurface and its constituent particles. (a) An example to demonstrate the spin-dependent generation of circularly polarized beams. For the RCP incidence, two RCP beams are generated toward the –x direction; for the LCP incidence, two LCP beams are generated toward the +x direction; for the LP incidence, two RCP and two LCP beams are generated. (b) The structure of the anisotropic coding particle. (c) The coding particle when the rod antenna is rotated at an orientation angle

with respect to the y-axis.



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Figure 2. The reflection performance of coding particles. (a) Simulated reflection coefficients of the coding particle shown in Figure 1b under the normal illumination of linearly x- and y-polarized plane waves. (b) The relationship between the phase responses and rotation angle of the rod antenna for RCP and LCP incident waves. (c, d) The phase responses of the 3-bit coding particles as the frequency varies from 10 to 20GHz under RCP and LCP incidences, respectively.


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Figure 3. Controls of multiple scattering beams and polarizations by convolution operations on the PB coding metasurfaces. (a-c) Coding patterns of a periodic coding sequence ‘0 0 0 0 4 4 4 4…’ varying along the y direction, a gradient coding sequence “0 1 2 3 4 5 6 7…” varying along the x direction, and their modulus M1, respectively. (d-f) Simulated 3D scattering patterns of the coding patterns in Figures 3a-c for the RCP incidence at 15GHz. (g-i) Simulated 3D scattering patterns of the coding patterns in Figures 3a-c for the LCP incidence at 15GHz. (j-l) Simulated 3D scattering patterns of the coding patterns in Figures 3ac for the LP incidence at 15GHz.



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Figure 4. Coding patterns of PB coding metasurfaces to control pencil beams and simulated 3D scattering patterns at 15GHz. (a) The coding pattern with periodic coding sequence ‘0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4…’ varying along the x direction. (b) The coding pattern with gradient coding sequence “0 1 2 3 4 5 6 7…” varying along the x direction. (c) The mixed coding pattern M2 formed by the modulus of coding patterns in Figures 4a and b. (d) The scattering pattern of M2 with four pencil beams in the xoz-plane.


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Figure 5. Coding patterns of PB coding metasurfaces to control votex beams with OAM mode l=1 and simulated 3D scattering patterns at 15GHz. (a) The coding pattern with OAM mode l=1. (b) The coding pattern with gradient coding sequence “0 1 2 3 4 5 6 7…” varying along the x direction. (c) The mixed coding pattern M3 formed by the modulus of coding patterns in Figures 5a and b. (d) The scattering pattern of M3 with two symmetrical vortex beams (OAM mode l=1) in the xoz-plane. (e, f) Simulated near-field

distributions of coding pattern M3 on the cross section perpendicular to the propagation direction = 0°, = 24.6°: The normalized intensity distribution of the Ey component (e), and the phase distribution of the

Ey component (f).



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Figure 6. Coding patterns of PB coding metasurfaces to control vortex beams with OAM mode l=2 and simulated 3D scattering patterns at 15GHz. (a) The coding pattern with OAM mode l=2. (b) The coding pattern with periodic coding sequence ‘0 0 0 0 4 4 4 4…’ varying along the y direction. (c) The coding pattern with gradient coding sequence “0 1 2 3 4 5 6 7…” varying along the x direction. (d) The mixed coding pattern M4 formed by the modulus of coding patterns in Figures 6a-c. (e) The scattering pattern of M4 with four symmetrical vortex beams (OAM mode l=2) in the upper-half space. (f, g) Simulated nearfield distributions of the coding pattern in Figure 6a: The normalized intensity distribution of the Ey component (f), and the phase distribution of the Ey component (g).


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Figure 7. The fabricated samples of PB coding metasurfaces and the experimental setups. (a-c) Photographs of the fabricated samples with the coding patterns M1, M2, and M3, respectively. (d) The farfield measurement system in the microwave anechoic chamber. (e) The experimental configuration of the near-field scanning.



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Figure 8. Comparisons of measured and simulated results of 2D scattering patterns at 15GHz. (a) The 2D

scattering pattern of coding pattern M1 at the azimuth angle = 45°. (b) The 2D scattering pattern of

coding pattern M2 at the azimuth angle = 0°. (c) The 2D scattering pattern of coding pattern M3 at the azimuth angle = 0°.


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Figure 9. Measured near-field distributions of the coding pattern M3 at different frequencies. (a, b) The intensity and phase distributions at 14.5 GHz. (c, d) The intensity and phase distributions at 15.0 GHz. (e, f) The intensity and phase distributions at 15.5 GHz.



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Table of Contents (TOC)


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Spin-Controlled Multiple Pencil Beams and Vortex Beams with

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