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Abstract
Conical beams have recently attracted much attention due to their excellent performances and potential applications in wireless and satellite-based communication technology. Here, reflective metasurfaces composed of Pancharatnam-Berry (PB) phase elements are demonstrated to have the ability to be flexible and to fully control the conical beam generation with desirable orbital angular momentum (OAM) modes. The theoretical model is developed to analyze the behavior of the conical beam radiation from the reflective metasurface and especially to predict the cone angle, one of the most important factors in the conical beam design. Analysis shows that arbitrary combinations of the cone angle and the OAM mode can be obtained by synthesizing the spatial phase distribution of the metasurface. Finally, two prototypes of microwave metasurfaces, with working bands from 14 GHz to 17 GHz, are fabricated and measured, and the results agree well with the theoretical predictions and simulations. This work demonstrates that metasurfaces can be used for controlling the conical beam generation with desirable OAM modes to potentially enable high capacity data communication, paving the way for novel devices with an appealing low-profile in wireless communication applications.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The rapid development of wireless and satellite-based communication technology, both in civil and military fields, have required terminal devices with stable performance in order to account for the link budget and ensure rapid moving cars, ships or airplanes have access to satellite signals [1–6]. To solve the problem, modern antenna technology offers several routes to meet the increasing demands. For instance, phased-array antenna can be applied to track the satellite signal, but with high manufacturing cost and complex feeding network. The omni-directional antenna can receive satellite signals in arbitrary direction but limited by its low gain. Conical beam antenna is proposed to be a good candidate for the applications, which has an omni-directional radiation pattern in azimuth plane while the main-lobe direction is tilted to a specific angle in the elevation plane. Many works have been demonstrated to generate conical beams in microwave frequency region, such as periodic microstrip radial array antenna [2], circular-polarized patch antenna [3] and planar switched parasitic array antenna [4], etc. Besides, multi-ring array antennas have also been proposed to efficiently generate conical beams recently [5,6], where a careful design of their parameters, such as the number of rings and ring radius, allows a flexible control over the conical beam radiation. However, the relative high profile and the complex feeding network of such antennas might still hinder their applications especially in where the space is limited or expensive, eg., in integrated systems.
Recently, as the two-dimensional engineered structures, metasurfaces have been applied into many aspects of electromagnetic (EM) wave manipulation due to their unique properties of flat-profile and sub-wavelength thickness [7–12]. With the great abilities to manipulate the amplitude, phase and polarization state of EM waves, metasurfaces offer a new platform for arbitrarily tailoring EM wave in a desirable way, and numerous physical phenomena or applications have been demonstrated, such as anomalous reflection [13–17] and refraction [18–20], flat lensing [21–23], invisibility cloaking [24–26], etc. Besides, geometric phase metasurfaces or termed Pancharatnam-Berry (PB) phase metasurfaces [27–30] are capable of realizing continuous phase change for circularly polarized (CP) EM wave, which have been successfully implemented into new devices with diverse features, for example, handedness-switchable holographic imaging [31]. The PB phase metasurfaces can provide great flexibility in the wavefront control just by using an array of identical anisotropic resonant inclusions with different geometric orientations, thus reducing the design complexity.
Orbital angular momentum (OAM) vortex waves have attracted much attention due to their excellent performances and potential applications from extremely low radio frequencies [32–34] to terahertz bands [35,36] and optical regions [37–39]. OAM can offer a new degree of freedom for tremendously enhancing the data capacity of communication systems, which is of great importance in nowadays as the wireless data link budgets become increasingly huge [40–42]. In this paper, we propose an approach to design a reflective PB phase metasurface for generating and fully controlling conical beam carrying OAM. Since the cone angle, which means the direction of the main radiation lobe, is of great importance in the conical beam radiation for practical applications, we develop a general theoretical framework to analyze the far-field radiation properties of conical beam generated by the reflective metasurface and especially to predict the cone angle of the conical beam. Furthermore, the cone angle and the OAM mode can be controlled independently by synthesizing the spatial phase distribution of reflective metasurface guided by the theoretical analysis, thus achieving a full control over the conical beam generation. This passive reflective metasurface has the advantages of low-profile and light-weight, with element phase response and the spatial phase distribution easy to be tailored. Several different examples are designed in microwave frequency region using full-wave simulation conducted by commercial software. Two of these examples are fabricated for experimental verification, and good agreements are observed between simulations and experiments, validating the good performances of the proposals.
2. Theoretical analysis and element design
The proposed schematic of generating conical beam by PB phase metasurface is shown in Fig. 1(a). When illuminated by CP EM wave, the reflective metasurface can reshape the incidence into conical beam carrying OAM mode, obtained by the pre-designed spatial distribution of metasurface elements with varying orientations. Since each reflective metasurface element can be regarded as an EM radiator, the elements should be elaborately designed to have near unity reflection amplitude but with varying phase responses, ensuring a high-efficient wavefront shaping. To this end, we design the basic element (shown in Fig. 1(b)) based on the concept of PB phase [14,27–29,31], of which the phase response for CP wave can be continuously adjusted by changing its geometric orientation when reflection coefficients for the two orthogonal linear polarized waves meet certain requirements. In details, the complex reflection coefficient of an arbitrary reflective element for left circularly polarized (LCP) wave and right circularly polarized (RCP) wave excitations can be obtained by [43]:
where, the first and second subscripts of the reflection coefficient r indicate the polarization of the reflected and incident EM wave, and the subscript l, r, x, and y represent LCP, RCP, linear x- and y-polarization, respectively. Parameter α is the self-rotational angle of the element with respect to x-axis, as depicted in Fig. 1(b). Therefore, if an element structure is optimized to have unity amplitude response () for two orthogonal linearly polarized incidence but with a 180° phase difference, the cross-polarized reflection coefficients can be well suppressed to zero (), leading to a unity reflection amplitude for CP incidence (). Furthermore, an additional phase shift of ϕ = ± 2α can be imparted on the reflected EM wave when the element is rotated by an angle of α, and the sign “+” and “-” corresponds to RCP and LCP incident waves, respectively. The PB phase metasurface provides a simple approach to fully control the phase responses, which is different from the most conventional metasurfaces [19,44], where phase discontinuity is achieved by varying structural parameters.
Fig. 1 (a) Schematic of a reflective metasurface for generating conical beam carrying OAM. The black angled arrow indicates the direction with elevation angle θ and azimuth angle φmn in the spherical coordinate. (b) Schematic of the PB phase element.
Next, we give the theoretical framework on how to produce the conical beam with pre-defined cone angle by using reflective metasurface with spatially varying phase distribution. For the reflective metasurface, under the normal illumination of a plane wave, the far-field behavior is the collective result of the secondary scattered radiations from each elements [22,45]. Hence, the element can be approximately treated as an EM radiator with certain initial phase, determined by the rotational angle, and the scattering pattern of the reflective metasurface can be calculated similar to the process of phased-array antenna theory [22,45]. As shown in Fig. 1(a), we consider a concentric ring array of metasurface elements, and in the spherical coordinate, the elevation angle and azimuth angle are represented by θ and φ, and the parameters rm and φmn represent the radial coordinate and azimuth angle of the n-th element in m-th concentric ring array (denoted as the mn-th element), respectively. In this scenario, we assume Nm (integer) elements are arranged in the m-th concentric ring array. If OAM with l mode is imparted onto the conical beam, the elements of the ring array can be designed with equal phase intervals (2πl/Nm) in the azimuthal direction. To provide further control flexibility over the cone angle of radiating beam, we introduce a constant phase gradient along the radial direction, namely, a phase difference of δ = Δan between two adjacent elements along the radial direction. Then, the reflection phase response of each element for a desired frequency f0 (corresponding wavelength λ0) can be calculated and designed as:
where amn is the phase of the mn-th element, Δam is the phase difference between two adjacent elements along the circumferential direction. Here, the parameter l is termed as OAM mode, intuitionally interpreted as periodic number of 2π phase coverage in the azimuthal direction [32,33]. Based on the above assumption, the E-field radiation pattern of reflective metasurface can be calculated according to the interference theory [34], and given by:where, J represents the Bessel function, k is the phase constant in free space, and Imn is the excitation amplitude (or the reflection amplitude) of the mn-th element, which is nearly unity for all elements and could be approximately set as I. The parameter M represents the total number of the concentric ring arrays. The above theoretical analysis gives a general function of the metasurface parameters on the scattering pattern of the conical beam, and this model is relatively accurate as long as the inhomogeneity of the surface is not too steep with respect to the wavelength. Since the cone angle is very important for many practical applications [5,6], we further use this model to analyze how these parameters affects the cone angle, and to predict its exact numerical value.For a metasurface with given physical dimensions, for example with fixed number of array rings (M) and a constant radial periodicity of the elements (p), Eq. (4) can be further reduced, which only depends on the parameters l and δ. In other words, the cone angle can be controlled by both the OAM mode and the radial phase gradient. Figure 2 shows the calculated dependence of cone angle θ on these two parameters. When both of the two parameters equal to zero, the cone angle vanishes to zero with a planar wavefront, indicating the reflection wave being plane wave. When the radial phase gradient is fixed to zero, the cone angle can gradually increase from 0° to about 19° as the absolute value of OAM mode l increases from 0 to 15. Though the OAM mode can affect the cone angle, it lays a severe restriction on accessible cone angle range for a given metasurface dimension, even with large mode l. However, by introducing radial phase gradient, the accessible cone angle range will be greatly improved, reaching to about 80° as the phase difference δ increases to 0.54π. Thus, a wide range of cone angles can be achieved by the proposed method, which could cover the angle range, typically from θ = 10° to 70°, needed for satellite communication [2–6]. A larger phase gradient will further increase the cone angle, but its value may somehow deviate from the theoretical prediction attributed to the larger inhomogeneity with respect to the wavelength occurred in the radial direction. Arbitrary combinations of cone angle and OAM modes within the accessible range can be obtained by searching the design chart shown in Fig. 2. In a word, by modifying the spatial distribution of the rotational angle of PB phase elements, interpreted as the reflection phase for circular-polarized incidence, the cone angle can be flexibly and easily designed with high-efficiency, while keeping the OAM modes independently controllable.
Fig. 2 The cone angle of conical beam as functions of two parameters l and δ. Other parameters are set as M = 30 and p = 0.31λ0.
As examples of the proposed PB phase metasurface at microwave frequencies, we design the metasurface with the central frequency around 15.5 GHz. As shown in Fig. 1(b). The optimized metasurface element is composed of three layers: two orthogonal I-shaped metallic patterns are printed on a back-grounded dielectric F4B substrate. The dielectric substrate has a thickness of 2 mm, with a relative permittivity and loss tangent of 2.65 and 0.001, respectively. The radial distance between two PB phase elements p is set as 6 mm (about 0.31 free space wavelength λ0). The physical dimensions of the metasurface element are s = 1.8 mm, lx = 2.73 mm, ly = 4 mm and w = 0.2 mm. The top metallic structures and ground plane are made of copper film with a thickness of t = 0.018 mm. The frequency-domain solver of a commercial full wave simulation tool (CST Microwave StudioTM) is applied to calculate the EM response of the element, with unit-cell boundary conditions along both x and y directions while open for the z direction in free space. As illustrated in Fig. 3(a), the phase difference of the co-polarized reflection of the PB phase element between linearly x-polarized and y-polarized incidence is nearly 180° from 14 GHz to 17 GHz, with perfectly reaching 180° at 15.5 GHz. Meanwhile, the reflection amplitude is nearly unity, indicating a good PB metasurface element with working frequency from 14 GHz to 17 GHz. Therefore, the amplitude of reflection coefficients rll for different rotational angle α can be obtained as shown in Fig. 3(b), which is larger than 0.9 within the working band. Figure 3(c) shows the corresponding results of the reflection phase responses, which decrease with an interval of 45° as the rotational angle gradually increases from 0° to 157.5° with an interval of 22.5°. For the RCP incident case, the phase variation is exactly the opposite, and the reflection phase response increases twice of the rotational angle, as illustrated in Fig. 3(d). Based on these PB phase elements, the conical beam can be conveniently designed by the reflective metasurface.
Fig. 3 (a) Simulated reflection spectrum of the metasurface element for different polarization incidences. (b) Simulated reflection amplitude of the metasurface element with different rotational angels for LCP incidence. Simulated reflection phase responses of the element with different rotational angels for (c) LCP and (d) RCP incidences.
3. Metasurface design and simulation results
In order to verify the feasibility of the theoretical model and interpret the design process, we show the conical beam evolutions when “encoding” the metasurface with both radial phase gradient and the OAM successively, as demonstrated in Fig. 4. All the phase distributions and radiation results are under the normal illumination of a LCP plane wave, except for the ones in the rightmost panel [Figs. 4(d), 4(h) and 4(l)] which are illuminated by RCP plane wave. Figure 4(a) shows the ideal phase distributions for conical beam generation with only radial phase gradient (δ = π/5), while Fig. 4(b) shows the one with only OAM mode of l = −7 (with only circumferential gradient), and these two phase distributions are superposed together in Fig. 4(c). To generate the phase distribution with reflective metasurface, these continuously distributed phase profile are then discretized into pixels and realized by the real PB phase elements. The metasurface performance is then evaluated by both the theoretical analysis and full-wave simulation. As illustrated in Fig. 4(e), the normalized three-dimensional (3D) scattering pattern at 15.5 GHz shows that a conical beam with the cone angle of 18° can be realized by the reflective metasurface when the parameter δ set as π/5 and l as zero. Figure 4(i) shows the corresponding two-dimensional (2D) theoretical and simulated scattering pattern in the plane of φ = 0°, where excellent agreements are found. However, it is obvious that there is a large sidelobe at the zenith (θ = 0°) both in the theoretical and simulated results, which will affect the overall performance of the conical beam and should be drastically suppressed in the conical beam design and application. Actually, using only radial phase gradient will generate a peak sidelobe along the surface normal due to the in-phase radiation from the metasurface with sysmetric elements distribution. On the other hand, if only imparted by OAM with the parameters δ = 0 and l = −7, the reflective metasurface can generate conical beam with a cone angle of 10°. It should be noted that, for l ≠ 0, the phase front is not planar but helical, and the OAM mode will lead to a singular point in the propagation direction, even in the far-field region, which naturally acts as a good conical beam scattering but with slightly narrow cone angle. The 3D and 2D results are shown in Figs. 4(f) and (g), respectively. Simultaneously imparting the OAM mode and the radial phase gradient will allow an enhanced ability to control the scattering wave. As shown in Figs. 4(g) and (k), the metasurface with mixed phase distribution will generate a conical beam with increased cone angle of 23° under LCP incidence while at the same time the sidelobe at the zenith direction of the scattering pattern can be suppressed into very low level. The underlying mechanism can be understood theoretically from Eq. (4). For Bessel function of the first kind, if l ≠ 0, the value of Bessel function Jl(krmsinθ) equals zero at θ = 0. Hence, the value of F(0, φ) is always zero immune from the change of parameter δ, leading to a suppressed sidelobe at the zenith of the field pattern. Compared with the metasurface with only radial phase gradient or circumferential phase gradient, the one with mixed phase distribution can increase the accessible range of the cone angle while simultaneously suppressing the sidelobe along the surface normal. As shown in Fig. 4(d), the spatial phase distribution for RCP incident wave is exactly opposite to that of LCP incidence. The cone angle of the radiation pattern is still 23°, which means the cone angle of the proposed metasurface is identical for LCP and RCP incident case. So we only consider cases operated with LCP incidence in the rest part of the paper. All the corresponding 2D scattering patterns at the plane of φ = 0° are shown in Figs. 4(i)-4(l), where good coincidence are observed between theoretical and simulated results, indicating that the theoretical model can work well.
Fig. 4 Ideal phase distributions of the metasurface for LCP incidence, with (a) δ = π/5 and l = 0, (b) δ = 0 and l = −7, and (c) the superposition of (a) and (b). (d) Phase distribution with δ = π/5 and l = −7 for RCP incidence. (e - h) The corresponding normalized 3D scattering patterns of the metasurface at 15.5 GHz, and (j - l) the theoretical and simulated normalized 2D scattering patterns of the metasurface at 15.5 GHz in the plane of φ = 0°.
To further investigate the OAM behavior carried by the conical beam from the proposed metasurface, we present the theoretical and simulated E-field phase distribution as shown in Fig. 5, where the observation plane is set as 100 mm, approximately 5λ0 away from the metasurface. The OAM with mode number −7 (or parameter l = −7) can be clearly observed, indicating that the conical beam (shown in Fig. 4(g)) can act as a vortex wave carrying OAM under LCP incident wave. Comparing with the ideal phase distribution for the metasurface design [Fig. 4(c)], the phase distributions in Fig. 5 show a similar variation trend. These results also demonstrate that the phase gradient along the radial direction can offer a new degree of freedom to manipulate the conical beam, but without much extra influence on the OAM behavior of the scattered wave. By the proposed metasurface, we can flexibly adjust the cone angle of the conical beam carrying OAM. The theoretical and simulated results are in good coincidence as shown in Fig. 5, further demonstrating the feasibility of the theoretical model.
Fig. 5 (a) The theoretical and (b) simulated phase distribution of the metasurface in Fig. 4c at 15.5GHz. The observation plane is set as 100 mm away from the metasurface.
As aforementioned, the reflective metasurface can allow a flexible and independent control over the cone angle and the OAM mode of the scattered conical beam by synthesizing the two parameters l and δ, namely the radial phase gradient and the circumferential phase gradient (or OAM mode), respectively. As the exemplary demonstrations, we show several metasurface designs that can achieve fixed OAM mode but with diverse cone angles, or fixed cone angle but with diverse OAM modes. For the first scenario, OAM mode number is fixed to l = 2 but with the cone angles ranging from 18°, 24° to 33°. Correspondingly, the phase distribution along radial direction should be designed with δ equals 0.19π, 0.25π and 0.33π. The ideal phase distributions and the 3D normalized scattering patterns for LCP incident wave are shown in Fig. 6. The far-field results in Figs. 6(a)-6(c) show that the main lobe of the conical beams for the LCP incidence are deviated from the surface normal with angles of 18°, 24° and 33°, when the metasurface are designed with a discretization of the ideal phase distribution show in Figs. 6(e)- 6(f). The corresponding 2D scattering patterns at the plane of φ = 0° are shown in Figs. 6(g)-6(i). Meanwhile, all the reflected conical beams are uniformly carrying the OAM mode l = 2. In the second scenario, the conical beams are designed with a fixed cone angle but carrying different OAM modes. From the design chart shown in Fig. 3, we can easily conclude that diverse combinations of parameter l and δ can lead to a same cone angle. Therefore, as an example, this angle is fixed to 14° with three different OAM modes of l = 2, 4 and 10. On this basis, the metasurface should be designed with l = 2, δ = 0.16, l = 4, δ = 0.13π, and l = 10, δ = 0 (without radial phase gradient), respectively. Here, the 3D far-field results and corresponding 2D scattering patterns for these three different cases are illustrated in Fig. 7, where good conical beams with fixed main lobe direction with different OAM modes can be obtained. The metasurface designs are not limited to the above cases and can be extended into more general cases, where the cone angle and the OAM mode, within certain accessible range, can be arbitrarily desirable according to the practical requirement.
Fig. 6 Ideal phase distributions for the metasurfaces with l = 2 and (a) δ = 0.19π, (b) δ = 0.25π, (c) δ = 0.33π. (d-f) Corresponding simulations of the normalized 3D scattering patterns for the LCP incidence at 15.5 GHz. (g-i) The corresponding theoretical and simulated normalized 2D scattering patterns of the metasurface at 15.5 GHz in the plane of φ = 0°.
Fig. 7 Ideal phase distributions for the metasurfaces with (a) l = 2 and δ = 0.16π, (b) l = 4 and δ = 0.13π, (c) l = 10 and δ = 0. (d-f) Corresponding simulations of normalized 3D scattering patterns of the metasurfaces for the LCP incidence at 15.5 GHz. (g-i) The corresponding theoretical and simulated normalized 2D scattering patterns of the metasurface at 15.5 GHz in the plane of φ = 0°.
4. Experimental verification
To experimentally validate the design principle and the proposed metasurfaces, two samples of the PB phase metasurfaces are fabricated by standard print circuit board (PCB) technique and tested in microwave range. The photograph of the fabricated metasurface with l = 10, δ = 0 is shown in Fig. 8(a), where the inset shows the enlarged view of the metasurface elements. The corresponding simulated 3D radiation pattern is shown in Fig. 7(f). The scattering patterns of the sample are measured in a standard microwave chamber and all the scattering patterns are calibrated to a same-sized copper slab. The measured frequency-dependent 2D far-field normalized scattering pattern at the plane of φ = 0° for LCP incidence is shown in Fig. 8(b), where the blue asterisks represent the cone angles at different frequencies obtained by simulations. Good agreements are observed between the measured and simulated results. It verifies that the proposed metasurface can work well in a certain frequency band from 14 GHz to 17 GHz, while the cone angle of the conical beam changes from 15° to 12°, correspondingly. The simulated and measured 2D normalized scattering pattern at the plane of φ = 0° and 90° at 15.5 GHz are compared in Figs. 8(c) and 8(d), respectively. It is obviously that the measured results of both orthogonal planes denote reflection peaks around ± 14° and reflection nulls at θ = 0°, which roughly agree with the full-wave simulated results by taking consideration of the imperfect fabrication (dielectric substrate with fabrication tolerance of ± 0.05 in relative permittivity and ± 0.05 mm in thickness, and wire width with fabrication tolerance of ± 0.02 mm) and measurement tolerance. This reflective metasurface, with cone angle of 14°, only has a phase gradient along circumferential direction. Without loss of generality, we also fabricate a metasurface with both phase change along the circumferential and radial direction that has parameters of l = 2 and δ = 0.25π, as shown in Fig. 9, of which the corresponding simulated 3D radiation pattern is shown in Fig. 6(e). The simulated and measured 2D normalized scattering pattern indicate that the reflection peaks change from ± 27° to ± 22° as the working frequency increases from 14 GHz to 17 GHz. The measured cone angle reaches 24° at 15.5 GHz for LCP incidence both in the planes of φ = 0° and 90°.
Fig. 8 (a) Fabricated PB phase metasurface sample with l = 10, δ = 0. (b) The simulated and measured normalized scattering pattern (in the plane of φ = 0°) of the metasurface under the LCP incidence. The blue asterisks represent the cone angles obtained from simulations. (c), (d) Simulated and measured normalized scattering patterns in the planes of φ = 0° and 90° at 15.5 GHz, respectively.
Fig. 9 (a) Fabricated PB phase metasurface sample with l = 2, δ = 0.25π. (b) The simulated and measured normalized scattering pattern (in the plane of φ = 0°) of the metasurface under the LCP incidence. The blue asterisks represent the cone angles obtained from simulations. (c), (d) Simulated and measured normalized scattering patterns in the planes of φ = 0° and 90° at 15.5 GHz, respectively.
To investigate its OAM behavior experimentally, we have measured the emerging wavefront reflected from the metasurface (with l = 2, δ = 0.25π) at a distance of 100 mm (approximately 5λ0) apart from the metasurface placed in xoy-plane. The reflected fields from the metasurface are mapped by a 3D EM field-scanning system, which has a dipole probe to automatically detect the electric field pixel by pixel in a pre-designed plane with a step of 2 mm. As shown in Figs. 10(a) and 10(b), the OAM spatial phase distribution can be clearly observed, with the mode number of l = 2. The E-field intensity has a toroidal-shaped distribution in both simulation [Fig. 10(c)] and experiment [Fig. 10(d)], which further demonstrates the OAM performance carried by the conical beam. The measured results have experimentally verified that the proposed method can be applied to flexibly and independently control the cone angle and OAM mode by combining the radial and the circumferential phase gradient in the metasurface design.
Fig. 10 Simulated (left panel) and measured (right panel) E-field reflection phase ((a), (b)), and intensity ((c), (d)) distributions of the metasurface in Fig. 9 at 15.5 GHz.
5. Conclusion
In conclusion, we have proposed reflective metasurfaces based on PB phase concept to synthesize the conical beam carrying desired OAM mode in the microwave frequency range, under the normal illumination of CP incidence. Theoretical model is used to fully analyze the conical beam radiation, and especially to relate the cone angle with phase gradients of the reflective metasurface. Theory has predicted that a free and independent realization of the cone angle and OAM mode can be achieved by the reflective PB phase metasurface, which greatly simplifies the design process of conical beam generation. The proposed designs are then verified by both the full wave EM simulations and microwave experiments, and good agreements are found between them. The proposed method would be beneficial to design low-profile metasurfaces, probably even in conformal fashions [46], for generating conical beams that can carry desirable OAM to potentially improve their communication capacities. The proposed metasurface offers a new path to generate and control the conical beam in microwave region, and can be readily scaled to higher frequency bands, such as terahertz band, or even optical region.
Funding
National Key Research and Development Program of China (Grant NO. 2017YFA0700201); National Natural Science Foundation of China (NSFC) (61731010, 61671231, 61571218, 61571216); China Postdoctoral Science Foundation (2017M620202); and Natural Science Foundation of Jiangsu Province, China (Grant No. BK20151393).
Acknowledgments
This work is partially supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), the Fundamental Research Funds for the Central Universities and Jiangsu Provincial Key Laboratory of Advanced Manipulating Technique of Electromagnetic Wave.
References and links
1. J. Huang, “Circularly polarized conical patterns from circular microstrip antennas,” IEEE Trans. Antenn. Propag. 32(9), 991–994 (1984). [CrossRef]
2. K.-C. Chen, Y. Qian, C.-K. Tzuang, and T. Itoh, “A periodic microstrip radial antenna array with a conical beam,” IEEE Trans. Antenn. Propag. 51(4), 756–765 (2003). [CrossRef]
3. K. Lau and K. Luk, “A wideband circularly polarized conical-beam patch antenna,” IEEE Trans. Antenn. Propag. 54(5), 1591–1594 (2006). [CrossRef]
4. W. Chen, J. Sun, X. Wang, Z. Feng, F. Chen, Y. Furuya, and A. Kuramoto, “A novel planar switched parasitic array antenna with steered conical pattern,” IEEE Trans. Antenn. Propag. 55(6), 1883–1887 (2007). [CrossRef]
5. S.-H. Son, S.-I. Jeon, C.-J. Kim, and W. Hwang, “GA-based design of multi-ring arrays with omnidirectional conical beam pattern,” IEEE Trans. Antenn. Propag. 58(5), 1527–1535 (2010). [CrossRef]
6. L. Cui, S.-S. Qi, W. Wu, and D.-G. Fang, “High gain conical beam antenna array exploiting grating lobes,” IEEE Trans. Antenn. Propag. 63(2), 848–853 (2015). [CrossRef]
7. W. Wan, J. Gao, and X. Yang, “Full-color plasmonic metasurface holograms,” ACS Nano 10(12), 10671–10680 (2016). [CrossRef] [PubMed]
8. J. Liu, Z. Li, W. Liu, H. Cheng, S. Chen, and J. Tian, “High-Efficiency Mutual Dual-Band Asymmetric Transmission of Circularly Polarized Waves with Few-Layer Anisotropic Metasurfaces,” Adv. Opt. Mater. 4(12), 2028–2034 (2016). [CrossRef]
9. F. Lu, B. Liu, and S. Shen, “Infrared wavefront control based on graphene metasurfaces,” Adv. Opt. Mater. 2(8), 794–799 (2014). [CrossRef]
10. Y. Li, J. Zhang, S. Qu, J. Wang, H. Chen, Z. Xu, and A. Zhang, “Wideband radar cross section reduction using two-dimensional phase gradient metasurfaces,” Appl. Phys. Lett. 104(22), 221110 (2014). [CrossRef]
11. S. Liu and T. J. Cui, “Flexible controls of terahertz waves using coding and programmable metasurfaces,” IEEE J. Sel. Top. Quant. 23, 1–12 (2017).
12. Y. Li, J. Zhang, S. Qu, J. Wang, H. Chen, Z. Xu, and A. Zhang, “Wideband radar cross section reduction using two-dimensional phase gradient metasurfaces,” Appl. Phys. Lett. 104(22), 221110 (2014). [CrossRef]
13. C. Huang, W. Pan, X. Ma, and X. Luo, “Multi-spectral metasurface for different functional control of reflection waves,” Sci. Rep. 6(1), 23291 (2016). [CrossRef] [PubMed]
14. H.-X. Xu, G.-M. Wang, T. Cai, J. Xiao, and Y.-Q. Zhuang, “Tunable Pancharatnam-Berry metasurface for dynamical and high-efficiency anomalous reflection,” Opt. Express 24(24), 27836–27848 (2016). [CrossRef] [PubMed]
15. Y. Zhao, X. Cao, J. Gao, X. Liu, and S. Li, “Jigsaw puzzle metasurface for multiple functions: polarization conversion, anomalous reflection and diffusion,” Opt. Express 24(10), 11208–11217 (2016). [CrossRef] [PubMed]
16. Z. Li, E. Palacios, S. Butun, and K. Aydin, “Visible-frequency metasurfaces for broadband anomalous reflection and high-efficiency spectrum splitting,” Nano Lett. 15(3), 1615–1621 (2015). [CrossRef] [PubMed]
17. S. Sun, K.-Y. Yang, C.-M. Wang, T.-K. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W.-T. Kung, G.-Y. Guo, L. Zhou, and D. P. Tsai, “High-efficiency broadband anomalous reflection by gradient meta-surfaces,” Nano Lett. 12(12), 6223–6229 (2012). [CrossRef] [PubMed]
18. S. Liu, A. Noor, L. L. Du, L. Zhang, Q. Xu, K. Luan, T. Q. Wang, Z. Tian, W. X. Tang, J. G. Han, W. L. Zhang, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Anomalous refraction and nondiffractive bessel-beam generation of terahertz waves through transmission-type coding metasurfaces,” ACS Photonics 3(10), 1968–1977 (2016). [CrossRef]
19. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef] [PubMed]
20. H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3(12), 1744–1749 (2015). [CrossRef]
21. H.-X. Xu, S. Ma, W. Luo, T. Cai, S. Sun, Q. He, and L. Zhou, “Aberration-free and functionality-switchable meta-lenses based on tunable metasurfaces,” Appl. Phys. Lett. 109(19), 193506 (2016). [CrossRef]
22. K. Chen, Y. Feng, F. Monticone, J. Zhao, B. Zhu, T. Jiang, L. Zhang, Y. Kim, X. Ding, S. Zhang, A. Alù, and C. W. Qiu, “A reconfigurable active Huygens’ metalens,” Adv. Mater. 29(17), 1606422 (2017). [CrossRef] [PubMed]
23. Q. Wang, X. Zhang, Y. Xu, Z. Tian, J. Gu, W. Yue, S. Zhang, J. Han, and W. Zhang, “A broadband metasurface-based terahertz flat-lens array,” Adv. Opt. Mater. 3(6), 779–785 (2015). [CrossRef]
24. A. Alù, “Mantle cloak: Invisibility induced by a surface,” Phys. Rev. B 80(24), 245115 (2009). [CrossRef]
25. N. Xiang, Q. Cheng, H. B. Chen, J. Zhao, W. X. Jiang, H. F. Ma, and T. J. Cui, “Bifunctional metasurface for electromagnetic cloaking and illusion,” Appl. Phys. Express 8(9), 092601 (2015). [CrossRef]
26. X. Ni, Z. J. Wong, M. Mrejen, Y. Wang, and X. Zhang, “An ultrathin invisibility skin cloak for visible light,” Science 349(6254), 1310–1314 (2015). [CrossRef] [PubMed]
27. K. Chen, Y. Feng, Z. Yang, L. Cui, J. Zhao, B. Zhu, and T. Jiang, “Geometric phase coded metasurface: from polarization dependent directive electromagnetic wave scattering to diffusion-like scattering,” Sci. Rep. 6(1), 35968 (2016). [CrossRef] [PubMed]
28. L. Cong, N. Xu, J. Han, W. Zhang, and R. Singh, “A Tunable Dispersion-Free Terahertz Metadevice with Pancharatnam-Berry-Phase-Enabled Modulation and Polarization Control,” Adv. Mater. 27(42), 6630–6636 (2015). [CrossRef] [PubMed]
29. X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. de Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin Pancharatnam-Berry Metasurface with Maximal Cross-Polarization Efficiency,” Adv. Mater. 27(7), 1195–1200 (2015). [CrossRef] [PubMed]
30. Z. Q. Miao, Q. Wu, X. Li, Q. He, K. Ding, Z. H. An, Y. B. Zhang, and L. Zhou, “Widely Tunable Terahertz Phase Modulation with Gate-Controlled Graphene Metasurfaces,” Phys. Rev. X 5(4), 041027 (2015). [CrossRef]
31. L. Huang, H. Mühlenbernd, X. Li, X. Song, B. Bai, Y. Wang, and T. Zentgraf, “Broadband hybrid holographic multiplexing with geometric metasurfaces,” Adv. Mater. 27(41), 6444–6449 (2015). [CrossRef] [PubMed]
32. Q. Ma, C. B. Shi, G. D. Bai, T. Y. Chen, A. Noor, and T. J. Cui, “Beam-Editing Coding Metasurfaces Based on Polarization Bit and Orbital-Angular-Momentum-Mode Bit,” Adv. Opt. Mater. 5(23), 1700548 (2017). [CrossRef]
33. S. Yu, L. Li, G. Shi, C. Zhu, and Y. Shi, “Generating multiple orbital angular momentum vortex beams using a metasurface in radio frequency domain,” Appl. Phys. Lett. 108(24), 241901 (2016). [CrossRef]
34. S. M. Mohammadi, L. K. Daldorff, J. E. Bergman, R. L. Karlsson, B. Thidé, K. Forozesh, T. D. Carozzi, and B. Isham, “Orbital angular momentum in radio - a system study,” IEEE Trans. Antenn. Propag. 58(2), 565–572 (2010). [CrossRef]
35. H. Sobhani, H. Rooholamininejad, and A. Bahrampour, “Creation of twisted terahertz waves carrying orbital angular momentum via a plasma vortex,” J. Phys. D Appl. Phys. 49(29), 295107 (2016). [CrossRef]
36. H. Sobhani, “Creation of twisted terahertz carrying orbital angular momentum via stimulated Raman scattering in a plasma vortex,” Laser Phys. 27(9), 096001 (2017). [CrossRef]
37. R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017). [CrossRef] [PubMed]
38. E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014). [CrossRef]
39. Y. Guo, M. Pu, Z. Zhao, Y. Wang, J. Jin, P. Gao, X. Li, X. Ma, and X. Luo, “Merging geometric phase and plasmon retardation phase in continuously shaped metasurfaces for arbitrary orbital angular momentum generation,” ACS Photonics 3(11), 2022–2029 (2016). [CrossRef]
40. M. L. Chen, L. J. Jiang, and W. E. Sha, “Artificial perfect electric conductor-perfect magnetic conductor anisotropic metasurface for generating orbital angular momentum of microwave with nearly perfect conversion efficiency,” J. Appl. Phys. 119(6), 064506 (2016). [CrossRef]
41. F. Bouchard, I. De Leon, S. A. Schulz, J. Upham, E. Karimi, and R. W. Boyd, “Optical spin-to-orbital angular momentum conversion in ultra-thin metasurfaces with arbitrary topological charges,” Appl. Phys. Lett. 105(10), 101905 (2014). [CrossRef]
42. Y. Li, X. Li, L. Chen, M. Pu, J. Jin, M. Hong, and X. Luo, “Orbital angular momentum multiplexing and demultiplexing by a single metasurface,” Adv. Opt. Mater. 5(2), 1600502 (2017). [CrossRef]
43. L. Jing, Z. Wang, Y. Yang, B. Zheng, Y. Liu, and H. Chen, “Chiral metamirrors for broadband spin-selective absorption,” Appl. Phys. Lett. 110(23), 231103 (2017). [CrossRef]
44. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013). [CrossRef] [PubMed]
45. L.-H. Gao, Q. Cheng, J. Yang, S.-J. Ma, J. Zhao, S. Liu, H.-B. Chen, Q. He, W.-X. Jiang, H.-F. Ma, Q.-Y. Wen, L.-J. Liang, B.-B. Jin, W.-W. Liu, L. Zhou, J.-Q. Yao, P.-H. Wu, and T.-J. Cui, “Broadband diffusion of terahertz waves by multi-bit coding metasurfaces,” Light Sci. Appl. 4(9), e324 (2015). [CrossRef]
46. S. M. Kamali, A. Arbabi, E. Arbabi, Y. Horie, and A. Faraon, “Decoupling optical function and geometrical form using conformal flexible dielectric metasurfaces,” Nat. Commun. 7, 11618 (2016). [CrossRef] [PubMed]
