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Abstract
Vortex beams have witnessed tremendous development in the past decade by exhibiting profound implications for both fundamental physics and a multitude of novel engineering applications. In this work, broadband high-efficiency multiple vortex beams with independent topological modes and inclination angles are generated leveraging an interleaved geometric-phase multifunctional metasurface operating in a very broadband frequency range. A set of meta-atoms are elaborately engineered to offer broadband high-efficiency complete phase control covering the entire 2π range. Multiple geometric-phase sub-arrays implemented by the designed meta-atoms are synthesized into one metasurface via a shared-aperture interleaved manner, in which each sub-array can be individually manipulated and serves as an independent channel for launching a vortex beam. According to the established design methodology, two vortex beams with topological modes of −1 and +2 and distinct inclination angles are generated by one metasurface. Experimental results are provided to corroborate the proposed mechanism for multiple vortex beams generation, which exhibit broadband and high-efficiency features. The presented multifunctional metasurface paves the way for the generation of broadband high-efficiency multiple vortex beams in the microwave, millimeter-wave and terahertz regions. This work is of significance for high-capacity wireless communication applications, high-efficiency manipulation of electromagnetic waves, and novel design of radar and imaging systems.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Electromagnetic vortex beams, featured by a helical wavefront, have drawn extensive attention and triggered unprecedented development due to their unique characteristics and wide range of fascinating applications [1]. As the carrier of orbital angular momentum (OAM), helical phase structure of the vortex can be represented in the form of exp(ilφ), where l represents the topological mode (TM) and φ is the azimuthal angle [2]. Electromagnetic vortex beams have found diversified unprecedented applications, such as particle manipulation [3], high-resolution imaging [4], detection of rotational motion [5] and communications [6]. Especially with the exponentially growing demand of capacity and spectral efficiency in communications, a plethora of electromagnetic vortex generators have been investigated and the compelling potential of vortex beams in boosting data capacity of communications has been reported in various scenarios [7–10].
A flexible and powerful manner to generate vortex beams is using metasurfaces [11–15], which are ultrathin two-dimensional artificial structures capable of tailoring electromagnetic waves in diversified ways [16,17]. Nowadays, multifunctional metasurfaces open up alternative frontiers for wave engineering, which generate multiple beams or channels with different functions, for example, multiple foci [18], multi-color holograms [19], and multiple vortex beams [20]. Two approaches, namely polarization-controlled and frequency-controlled, have been most extensively explored for realizing multifunction by metasurfaces [21,22]. However, these two methods are hampered by several deficiencies limiting the applications and potentials of the multifunctional metasurfaces. First, some features of the generated beams, such as propagation direction and TM (for vortex generators), cannot be individually tailored at will. Second, the bandwidth is narrow for most of the reported multifunctional metasurfaces. Third, the efficiency of the proposed multifunctional metasurfaces is generally low. Another technique based on an anisotropic metasurface has been proposed specifically for the generation of two vortex beams [23]. Nevertheless, besides its intrinsic narrow bandwidth, the propagation direction and TM of the two beams are intrinsically coupled and not independent of each other, prohibiting individual control of each beam for this anisotropic technique. Therefore, a more flexible strategy to individually manipulate the multiple beams and maintain high efficiency of the metasurface in a broad frequency range is desired.
Shared-aperture technology with interleaved design is a good candidate to address the problems of the conventional multifunctional metasurfaces. It was initially used in phased array radar antennas [24,25] and diversified multifunctional optical metasurfaces based on the shared-aperture method have been recently demonstrated for various interesting applications [26–28]. Subsequently, shared-aperture metasurfaces have also been investigated to manipulate and focus microwave beams in multi-channel independently [29,30]. However, to the best of the authors’ knowledge, no reported work focuses on using the shared-aperture metasurfaces to achieve broadband high-efficiency individually addressable multifunctional beams. In this work, we design three-layer metallic meta-atoms based on a gapped ring to realize broadband and high-efficiency multifunction, which renders a broadband tunable transmission phase shift ranging from 0 to 2π and high transmission efficiency from 40 to 80 GHz, yielding a fractional bandwidth of 66.7%. Then a geometric-phase (GP) metasurface is engineered in an interleaved manner to launch two vortex beams as a proof-of-concept demonstration. TM and propagation direction of the two vortex beams are completely independent of each other and can be flexibly designed at will. The two vortex beams are also specifically designed to exhibit non-diffraction feature to enhance their propagation distances. According to the obtained experimental results, two millimeter-wave vortex beams can be reliably generated in the design bandwidth presenting a measured operation efficiency over 70% and polarization conversion efficiency over 89%, which validates the effectiveness of the proposed approach. Detailed analysis of the operation efficiency regarding the specific designed vortex modes is also provided. Although only two vortex beams are generated as a proof-of-concept example, it is possible to launch more beams via the proposed shared-aperture interleaved metasurface. This work may advance various applications like wave manipulation, vortex-beam-based communications, imaging and sensing. The proposed design methodology for multiple vortex beam generation embraces three distinct advantages compared to previous works. First, it allows flexible adjustment of the TM and inclination angles of the generated vortices. Second, the shared-aperture interleaved protocol can be further improved to engender more than two vortex beams via sparser or even randomly distributed GP profiles. Third, the obtained bandwidth and measured efficiency are superior to reported related works.
2. Design of broadband high-efficiency meta-atoms
A transmission-type metasurface is applied in this work to construct the multifunctional metasurface. The proposed meta-atoms of the metasurface are composed of three layers with metallic structures separated by two layers of dielectric substrate (F4B with dielectric constant of 2.2 and loss tangent of 0.002) as shown in Fig. 1(a). The middle metallic layer is a gapped rectangular ring that performs the phase tuning function of the transmitted wave. The cross-sectional size of the meta-atoms is 1.5 mm × 1.5 mm, which is smaller than half of the wavelength at the upper limit of the design bandwidth 80 GHz and has been proved to be acceptable for microwave and millimeter-wave metasurfaces. Adjusting dimensions and rotation angle of the gapped metallic ring can efficiently achieve full phase control covering the range from 0 to 2π in the entire targeted bandwidth. To facilitate the design of the metasurface, eight different meta-atoms [shown in Fig. 1(b)] offering discrete phase shifts from 0 to 7π/4 with a step of π/4 are engineered and optimized by CST microwave studio to implement all the needed phase shifts from 0 to 2π. Because the middle gapped-metallic rings can induce electric dipoles in both the x and y directions, polarization conversion can be realized for transmitted waves. There are also some other reported methods to implement polarization conversion, such as mode asymmetry induced by bilayer dielectric slabs [31], synthesized twist polarizer based on circuit resonance [32] and built-in anisotropy in the applied materials [33]. Compared with these techniques that rely on complicated dielectric structures, the polarization conversion mechanism applied in this work is relatively easier to be designed and fabricated at the targeted band.
Fig. 1. (a) Configuration of the designed meta-atom. The dimension parameters are l = 1.5 mm, w1 = 0.15 mm, w2 = 0.1 mm, s = 1.2 mm, t = 1.5 mm. The side length a and b, as well as the rotation angle of the eight designed meta-atoms are given in Table 1. (b) Profiles of the eight meta-atoms to achieve broadband gradient phase variation from 0 to 2π with a step of π/4.
The top and bottom layers are metallic gratings, arranged to be perpendicular to each other due to the polarization conversion effect, that can greatly ameliorate the transmission efficiency of the metasurface [34]. The underlying physics is that the two grating layers effectively form a Fabry-Perot resonant cavity. An x-polarized incident wave [shown in Fig. 1(a)] can simply transmit the top grating layer without disturbance, which then interferes with the gapped ring and engenders multiple reflections in the resonant cavity. To be specific, both the waves transmitting or reflected by the gapped rings are largely transformed to y-polarized waves and partially maintain the original x polarization, which are denoted as Ety and Etx for the transmitting waves in the bottom substrate and Ery and Erx for the reflected waves in the top substrate. Ety can pass the bottom grating layer, while Etx is totally reflected, which then interferes again with the gapped ring in a similar manner. Thus, multiple reflections take place in the bottom substrate and properly choosing the thickness of the substrate can lead to constructive interference at the bottom grating layer that in turn maximizes the waves transmitting this layer. Similarly, multiple reflections also exist in the front substrate and it is possible to tune the thickness of the substrate to realize destructive interference of the multiple waves at the top grating layer to suppress the overall reflection. Accordingly, the entire meta-atom structure exhibits high transmission efficiency. The incident wave for simulating the meta-atom in CST software package is set to be x-polarized and the transmitted field with y polarization is recorded, as depicted in Fig. 1(a). The boundary condition for the boundaries of the meta-atom in the xz plane and yz plane are set to be “unit cell” in CST. Detailed parameters of the meta-atoms are list in Table 1, which are optimized by the parameter sweep function in CST simulations. Considering the fabrication technique utilized to realize the designed metasurface in this work has an error of ±0.02 mm in making the metallic lines, simulations are performed to evaluate the effects of such errors. It is found that by disturbing the width of the gapped metallic rings by 0.02 and −0.02 mm, the resulting phase and amplitude exhibit less than 1% and 2% variation, respectively. Therefore, the designed meta-atoms are largely immune to small fabrication defects. Selection of the 0° and 78° rotation angles of the gapped rings is a trade-off between the available bandwidth and phase/amplitude control. Although the metallic-gapped-ring structure and similar polarization conversion mechanism has been reported in [35], the designed meta-atoms in this work has higher efficiency and is the first of its kind presenting broadband feature in the millimeter-wave regime.
Table 1. Optimized parameters and characteristics of the meta-atoms.
The simulated phase shifts are given in Fig. 2(a), showing that the phase increment is well kept around π/4. The simulated amplitude results shown in Fig. 2(b) reveal that the polarization conversion efficiency is above 0.9 over most of the design bandwidth. The induced electric dipole by the currents on the metallic rings cause phase shifts between the incident and transmitted waves [36,37]. Owing to the complicated structure of the rings, the formed electric dipole is essentially a result of interference and superposition of all the induced currents on the metallic rings [38]. By tuning the parameters a, b and rotation angle of the ring, the electric dipole can be manipulated to offer different phase shifts.
Fig. 2. (a) Simulated phase and (b) amplitude of the cross-polarized transmission fields for the eight meta-atoms.
3. Shared-aperture interleaved metasurface design
A schematic configuration of the shared-aperture interleaved multifunctional metasurface is provided in Fig. 3. Although generation of vortex beams is shown here as an example, such multifunctional metasurface configuration can be designed to launch beams for other functions. An incident wave radiated by an antenna illuminates the metasurface incorporating multiple interleaved sub-arrays sharing the same aperture of the metasurface. Each sub-array carries a GP profile that can in turn excite one spatial channel for one vortex beam. In order to achieve a favorable performance, it is desired to arrange these sub-arrays in an interleaved manner, regularly or randomly [26], rather than gathering the meta-atoms of a sub-array in a local area. Generally, different sub-arrays contain roughly the same numbers of meta-atoms to maintain relatively equal energy in each channel. Two vortex beams are realized in this work by the very broadband high-efficiency interleaved metasurface as an example, with the first one carrying TM = −1 and tilted by +20° (with respect to the z axis given in Fig. 3) and the second one featured with TM = +2 and being tilted by −10°. For multiple beams generated utilizing the shared-aperture technique, tilting propagation angles of the beams is beneficial to practical applications. Meta-atoms of the two sub-arrays are arranged in a regular interleaved distribution as shown in Fig. 3. To be specific, the first sub-array is composed of meta-atoms featured by while $\bmod ({|{i - j} |,2} )= 0$ the second sub-array is constituted of meta-atoms described by $\bmod ({|{i - j} |,2} )= 1$, where $i = 1,2, \cdots ,N$ and $j = 1,2, \cdots ,N$ are the indices of the meta-atoms along the x and y direction, respectively, in the metasurface containing N × N meta-atoms. Because the two sub-arrays are completely independent from each other, it is able to flexibly and individually control the TM and tilted angles of the two resulting vortex beams, which is unattainable in similar previous works investigating multiple vortex beam generation [20–23]. Moreover, such independent manipulation capability is still possible even for the generation of more vortex beams by a shared-aperture interleaved metasurface, shown in the four insets of Fig. 3.
Fig. 3. A schematic illustration of the shared-aperture interleaved multifunctional metasurface for generating two vortex beams with different TM and inclination angles. The blue and red squares represent two types of meta-atoms forming two sub-arrays. The four small insets at the bottom are the schematic descriptions of the cases for applying a metasurface to generate vortex beams with different numbers of channels, in which different sub-arrays in the metasurface are represented by meta-atoms with different colors.
GP distributions of the two sub-arrays are essentially the superimposition of four phase profiles, as illustrated in Fig. 4. Each phase profile serves as a functionalized phase-manipulating lens [39,40]. The first one converts the quasi-spherical wavefront generated by the antenna to a planar wavefront that is desired for the generation of vortex beams. Its corresponding phase profile can be expressed as
Fig. 4. Design procedure of the GP distributions of the two sub-arrays. The final interleaved phase design is also shown.
The second phase profile is featured with the spiral distribution to excite a vortex beam according to its TM (−1 for the first beam and +2 for the second beam) and given in Eq. (2).
The third one exhibits a linearly varying gradient phase profile that is capable of tuning the transmission direction or inclination angle of the vortex beam. It is expressed in Eq. (3) with γ representing the inclination angle (γ1 = +20° for the first beam and γ2 = −10° for the second beam). Gradient phase variation in the x direction is adopted in this work.Since vortex beams gradually spread as they propagate, especially for high-order vortex beams [41], it is desired to compensate for the spreading effect to some extent to facilitate the practical receiving and identification of vortex beams in communications applications. The last lens serving as an Axicon can effectively converge the vortex beams, which essentially generates a quasi-non-diffraction Bessel beam. Phase profile of the Axicon is provided in Eq. (4) with tanθ is a parameter to be adjusted to control the distance of non-diffraction propagation.
The resultant total superimposed phase profiles for the two designed vortex beams, denoted as ${\Phi _1}({x,y} )$ and ${\Phi _2}({x,y} )$, are expressed in Eq. (5) and plotted in Fig. 4 in a pixelized manner. Finally, pixels defined by $\bmod ({|{i - j} |,2} )= 0$ in ${\Phi _1}({x,y} )$ form the first sub-array and pixels defined by $\bmod ({|{i - j} |,2} )= 1$ in ${\Phi _2}({x,y} )$ forms the second sub-array, which effectively makes up the final phase profile of the interleaved metasurface to be implemented by the designed broadband meta-atoms.
It is found that φ1, φ3 and φ4 are all inherently frequency dependent. Fixing λ = 5 mm at 60 GHz for all the lenses inevitably incurs some discrepancies among the generated vortex beams at different frequencies in terms of spiral phase profiles (related to φ1), inclination angles (related to φ3), and non-diffraction propagation distances (related to φ4). For example, the inclination angle of the first beam γ1 is exactly +20° at 60 GHz, while deviated to +30°, +24°, +17.14° and +15° for 40, 50, 70 and 80 GHz, respectively. In a similar manner, γ2 is exactly −10° at 60 GHz, while changed to −15°, −12°, −8.57° and −7.5° for 40, 50, 70 and 80 GHz, respectively. The non-diffraction propagation distances realized by λ = 5 mm tend to be shorter for 40 and 50 GHz and longer for 70 and 80 GHz. It is worth mentioning that such drawbacks do not compromise the major contribution of this work, which is launching multiple vortex beams with individually controllable TM and inclination angles in a broadband millimeter-wave regime via a shared-aperture interleaved metasurface. It is also shown in the results that the generated vortex beam can still be measured with acceptable quality even on a plane not exactly perpendicular to its direction of propagation.
4. Experiment and results
Schematic setup and photo of the experiment are given in Figs. 5(a) and 5(b), respectively. The proposed metasurface containing 150 × 150 elements interpreting a dimension of 225 mm × 225 mm is fabricated on printed circuit boards (0.6-mm-thick F4B plate covered by 35-μm-thick copper) using the photoetching technique. Two boards are applied, with the top and middle layer fabricated on the first board and the bottom layer fabricated on the second board. Then the two boards are pressed into a whole structure. In higher frequency bands like the terahertz region and infrared regime, such metallic structures can be respectively manufactured by photolithography in conjunction with metallization and electron-beam lithography. In the visible band, dielectric metasurfaces are easier to be realized using diversified fabrication techniques [42–44]. For the realization of multi-layer or 3-D structures, combination of different fabrication approaches can facilitate the procedure and improve the quality. Performance of the metasurface at five frequency points, from 40 to 80 GHz with a step of 10 GHz, are recorded by three different pairs of antennas, including a WR-28 rectangular waveguide antenna testing 40 GHz, a WR-15 rectangular horn antenna measuring 50 and 60 GHz, and a WR-10 rectangular antenna handling 70 and 80 GHz. The transmitting antenna normally radiates the vertically placed metasurface by y-polarized TE10 mode from 100 mm away. Short side of the rectangular waveguide antenna and the metallic strips of the first grating layer [shown in Fig. 1(a)] are both arranged along the y axis. The receiving antenna is scanned by a motorized stage with a step of 1 mm on three cut planes of 380 mm × 580 mm, 80 mm × 80 mm and 80 mm × 80 mm, respectively. Because of the polarization conversion, the receiving antenna is set to be x-polarized. The two antennas are connected to a vector network analyzer (Keysight technologies, N5227B), which implements the measurement of scattering matrix indicative of the amplitude and phase information of the generated vortex beams.
The measurements are performed on three cut planes as depicted in Fig. 5(a). The first cut plane is in the xoz plane with a dimension of 135 mm × 200 mm. It should be noted that the second and third cut planes have different inclination angles at different frequencies. The second and third cut planes (40 mm × 40 mm) are perpendicular to the actual directions of propagation of the two beams, respectively, as depicted in Fig. 5(a) and the centers of these two cut planes are 200 mm away from the metasurface. The actual inclination angles of the two beams are γ1 = +30° and γ2 = −15° at 40 GHz, γ1 = +24° and γ2 = −12° at 50 GHz, γ1 = +20° and γ2 = −10° at 60 GHz, γ1 = +17.14° and γ2 = −8.57° at 70 GHz, γ1 = +15° and γ2 = −7.5° at 80 GHz.
The measured results are shown in Fig. 6. The biggest inset of each subfigure presents the results on the first cut plane, from which the two beams with inclined directions of propagation are apparently observed at all the simulated frequencies. On the second and third cut planes, it is clearly perceived that spiral phase profiles with one arm and two arms are recorded for the first (TM = −1) and second (TM = +2) beam, respectively. In addition, the amplitude profiles are featured with apparent doughnut-shaped distributions, associated with all vortex beams. Such results undoubtedly corroborate the effectiveness of the designed metasurface for the generation of two vortex beams with inclined directions of propagation and different TM in a broad frequency range. At higher frequencies, the two beams can maintain highly concentrated amplitude profiles in a longer propagation distance or suffer from less diffraction, which is because of a larger electrical size of the metasurface or the lenses. For instance, in Fig. 6(d), both vortex beams can reliably propagate more than 580 mm or 135 wavelengths at 70 GHz, proving the validity of the Axicon lens and great potential to transmit multiple message-encrypted vortex beams to long distances. It is straightforward to find that the spiral phase profiles are generally better at a higher frequency, which is also attributed to the less diffracted vortex beams. This phenomenon suggests the necessity of using Bessel beams as the carrier of vortex beams in the millimeter-wave region. Validity of the shared-aperture interleaved metasurface design methodology is thus corroborated. Although the amplitude profiles at 40 and 80 GHz are marred by some deficiencies, the calculated mode purity [13] at all the measured frequencies are all above 75% as given in Figs. 7(c), 7(d), unambiguously demonstrating the high quality of the produced two vortex beams. Measurements are then performed again at all frequencies by making the second and third cut planes always perpendicular to the two beams excited at 60 GHz (γ1 = +20° and γ2 = −10°). It is straightforward to see that the corresponding obtained mode purity results shown in Figs. 7(c), 7(d) are degraded, but are still above 55%. This finding implies that the generated multiple vortex beams by the proposed technique are highly robust and can still largely exhibit acceptable quality even if characterized from an angle deviated by −10° from the direction of propagation (for example, the first beam at 40 GHz), which is highly meaningful for practical applications in communications. Furthermore, the methods to identify misaligned vortex beams and correct spectrum dispersion can also be used to extract information in the future application scenarios of millimeter-wave communication [45,46].
Fig. 6. Measured electric field results on different cut planes at different frequencies. (a) is for 40 GHz; (b) is for 50 GHz; (c) is for 60 GHz; (d) is for 70 GHz; (e) is for 80 GHz. The biggest inset in each subfigure is the amplitude distribution in the first cut plane, with a dimension of 380 mm × 580 mm. The upper two small insets in each subfigure respectively represent the phase profile and amplitude distribution in the second cut plane detecting the first beam, with a dimension of 80 mm × 80 mm for the experimental results. The bottom two small insets respectively depict the phase profile and amplitude distribution in the third cut plane perceiving the second beam, with the same dimension as the second cut plane.
Fig. 7. Mode spectrum at 60 GHz of (a) the first beam with TM = −1 and (b) the second beam with TM = +2. Broadband mode purity of (c) the first beam and (d) the second beam. The red lines represent results obtained on cut planes perpendicular to the actual directions of propagation of the two beams, while the black lines represent results obtained on cut planes perpendicular to the two beams excited at 60 GHz with γ1 = +20° and γ2 = −10°, respectively. (e) Broadband operation efficiency and (f) polarization conversion efficiency of the metasurface. Broadband operation efficiency of (g) the TM = −1 mode in the first beam and (h) the TM = +2 mode in the second beam.
The operation efficiency ${\eta _o}$ and polarization conversion efficiency ${\eta _c}$ are calculated based on measurements obtained in a 250 mm × 250 mm region parallel to and 30 mm away from the metasurface plate. The operation efficiency is expressed as
where ${E_{t\_y}}$ is the measured y-polarized electric field traversing the metasurface and ${E_{o\_x}}$ is measured x-polarized electric field with the metasurface absent. The polarization conversion efficiency is defined asThe amplitude distributions in Fig. 6 at 40 and 80 GHz are a little degraded compared with those at 50, 60, and 70 GHz. There are two possible reasons for this imperfection. First, the designed meta-atoms have relatively worse performance around the lower and upper limits of the targeted band. Second, the designed phase profiles in (1), (3) and (4) are dependent on the wavelength, but it is fixed at the wavelength at 60 GHz. This causes some degradation in the measured beam quality at 40 and 80 GHz. Since the two beams are generated by two sub-arrays with the same number of elements, they are launched with equal power theoretically. But the experimental results show that the second vortex beam carries a little stronger power than the first beam. The power ratio of the second beam to the first beam is 1.47, 1.43, 1.32, 1.39 and 1.23 at 40, 50, 60, 70 and 80 GHz, respectively. The reason for this unequal power distribution is probably because the first vortex beam has a bigger inclination angle than the second one, which reduces the power in the first beam. This phenomenon is analogous to the effect in the beam steering of a phased array antenna, in which a high-gain beam formed at a large angle has lower power than a beam formed at the boresight since the former has more power distributed in the sidelobes. To adjust the power ratio between the two beams, one possible way is adjusting the number of meta-atom elements in the two sub-arrays.
Because some power in the transmitted wave do not contribute to the two designed modes, as implied by Figs. 7(a) and 7(b), Figs. 7(g) and 7(h) are provided to better illustrate the operation efficiency specifically for the generation of the two vortex beams. It can be perceived from Fig. 7(h) that the designed TM = +2 mode in the second beam maintains an operation efficiency around 40% across the entire band, which is close to its theoretical limit of 50%. For the designed TM = −1 mode in the first beam [Fig. 7(g)], the operation efficiency is about 28%. Compared with Fig. 7(h), the degradation in the efficiency in Fig. 7(g) is mainly caused by the lower mode purity and total power in the beam. It is worth noting that the shared-aperture mechanism for multifunctional beams has a limit in the operation efficiency for each beam, e.g., 50% for two functions and 33% for three functions. This drawback may be addressed by combining a newly developed technique merging multiple phase-shift methods [47–49].
5. Conclusion
This work reports the generation of broadband high-efficiency multiple vortex beams with individually controllable TM and inclination angles applying a shared-aperture interleaved multifunctional metasurface. The operating bandwidth of the multifunctional metasurface spans over a very broad millimeter-wave region from 40 to 80 GHz. Eight meta-atoms are designed to render high transmission efficiency and approximately linearly varying phase modulation in the entire design bandwidth. A metasurface is designed by the meta-atoms to launch two vortex beams with TM of −1 and +2 and inclination angles of +20° and −10°, respectively, as a proof-of-concept example of the multifunctional metasurface. Meta-atoms of two sub-arrays for generating the two vortex beams are integrated into one metasurface following the shared-aperture interleaved manner and the GP distribution of each sub-array is formed by the superposition of four functional phase profiles. Successful generation of the two tilted vortex beams by the proposed technique is demonstrated by experiments, despite that the inclination angles vary with the frequency. Moreover, high-quality phase and amplitude profiles of the two vortex beams, as well as high mode purity are secured in the broad millimeter-wave range. The measured high efficiency of the metasurface in the entire designed frequency band also proves the validity and usefulness of the metasurface. This work validates the effectiveness of generating millimeter-wave multiple vortex beams by one shared-aperture interleaved metasurface and establishes a novel paradigm for possible applications like high-capacity wireless communications, high-efficiency manipulation of millimeter waves, and imaging systems.
Funding
National Natural Science Foundation of China (61701305, 61874073, 61971287); State Key Laboratory of Millimeter Waves (K201931).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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