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Abstract
In this paper, a concept of dual-circular polarized coding metasurface is proposed. Different from previous coding metasurfaces, it has independent and broadband coding behaviors for two circular polarized incidences. By encoding the unit cells with designed coding matrices (both 1-bit and 2-bit matrices), anomalous reflection or diffusion can be realized for two circular polarizations independently. The simulated and measured results demonstrate the independently functional performance of the coding metasurface. By adjusting sizes of unit cells, this concept can also be applied in terahertz and optical frequency regimes.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterial is an artificially periodic or aperiodic structure material with the sub-wavelength unit structure, and it has been of great interest owning to its novel property in the past decades [1–3]. Recently, metasurfaces were proposed as an alternative approach to realize full controls of the electromagnetic waves [4–5]. As the planar two-dimensional metamaterials, metasurfaces are easier for fabrication. Metasurfaces inspire several interesting functions including polarization conversion [6–10], anomalous reflection/ refraction [11–13], perfect absorbing [14–16] and spoof surface plasmon polaritons [17–18], which have been demonstrated recently.
Most of metasurfaces are composed of sub-wavelength unit cells which have various amplitude and phase responses. Amplitude manipulation is traditionally based on absorption using perfect absorbers [19]. And many efforts were made to increase the absorption bandwidth, such as multilayer structure, resistor-loaded, resistive surface and graphene [20–21]. Another way of amplitude manipulation is convert energies into cross-polarization [22]. On the other hand, Phase manipulation is utilized widely during metasurfaces design. The transmission and reflection can be manipulated by introducing gradient phase shift to the interface [23–25]. The propagation direction can be manipulated based on the generalized Snell’s law. To realize phase manipulation, various unit cells of metasurfaces were designed using different geometries [26–28]. Most of them are isotropic which lead to the same phase responses for different polarizations. Previously, some metasurfaces were proposed considering polarization [29–30]. Anisotropic units were utilized to design metasurfaces. The reflected phase for two orthogonal, linear polarizations could be independently controlled by the anisotropic metasurfaces. Meanwhile, some metasurfaces realize equal and opposite phase profiles for two circular polarizations by rotating geometries of unit cells [31]. The phases of these unit cells are opposite and correlative for two circular polarizations.
Recently, the concepts of coding metasurfaces has been proposed as an alternative approach to realize electromagnetic wave manipulation by using the binary codes ‘0’ and ‘1’, which denote the discretized reflection phase [32]. Hence the scattering can be manipulated by designing the distribution of “0” and “1” coding matrices. Based on this idea, various functionalities have been achieved such as steering, bending, focusing and diffused scattering [33–36]. Most of proposed coding metasurfaces have the similar behavior for different polarizations. In [37], an anisotropic coding metasurface was proposed, which has distinct coding behaviors for two orthogonal, linear polarizations. As we know, no coding metasurface with distinct behaviors two circular polarizations has been proposed.
In this paper, we propose several broadband coding metasurfaces with distinct behaviors for two circular polarizations. Four types of unit cells are designed, which can independently reflect the normal incidence with either 0° (state ‘0’) or 180° (state ‘1’) reflection phase under two circular polarizations. Utilizing these unit cells, 1-bit coding metasurfaces are built up to demonstrate the independent control ability and distinct behaviors for two circular polarizations. Moreover, 2-bit broadband coding metasurfaces were proposed utilizing sixteen types units, in which the four different digital states ‘00’ (0°), ‘01’ (90°), ‘10’ (180°) and ‘11’ (270°) were independently realized under different circular polarizations. For demonstration, we realize anomalous reflection in y-z plane for left-hand circular polarizaion (LCP) and anomalous reflection in x-z plane for right-hand circular polarizaion (RCP), as shown in Fig. 1. Both simulations and measurements prove that our method offers an effective strategy for coding metasurface design.
Fig. 1. An illustration of the dual-circular polarized coding metasurface, which can manipulate two circular polarizations independently.
2. Designs and methods
2.1 Design concept and unit cells
Supposing an incidence to a given interface, the reflection coefficients of the electromagnetic wave can be represented by the Jones matrix in a linear base. The reflection coefficients for circular polarizations are related to the linear Jones matrix through:
We start with the 1-bit case to demonstrate the ability of phase manipulation independently for LCP and RCP. In 1-bit case, “0l0r”, “0l1r”, “1l1r”, “1l0r” is required, where the subscripts l and r denote the polarization state of waves, corresponding to LCP and RCP, respectively. Meanwhile, α and β are set as “0°,0°”, “90°,-45°”, “180°,0°”,“90°,45°”,correspondingly. It is noteworthy that α are not absolute phase values here, but relative values which have been normalized for simplicity.
To verify this operating principle, we design four types of unit cells that approximate the reflection coefficients requirement. Structures of unit cells are schematically shown in Fig. 2. These unit cells are composed of metallic structure, a dielectric substrate and a full metallic ground. The dielectric constant of the dielectric substrate is 2.65 and the loss tangent is 0.001. The metallic structures and ground are copper with conductivity of 5.8×107 S/m and the thickness of 0.036 mm. The periodicity of unit cells is p = 7 mm and the thickness of substrate is t = 3 mm. Other geometrical parameters are as follows: l1 = 6.6 mm, l2=5 mm, l3 = 6.8 mm, w1 = 0.4 mm, w2 = 1 mm, w3 = 1.3 mm and wr = 0.15 mm. Geometries of “0l0r” and “0l1r” units are same as “1l1r” and “1l0r”units except for a rotated angle of 90°.
These unit cells are simulated by software CST Microwave Studio. Figure 3(a) shows the simulated reflection amplitudes of these units for normal incidence. For LCP and RCP incidences, co-polarized reflection amplitudes are above 0.97 from 12 GHz to 18 GHz, in contrast, cross- polarized reflection amplitudes are close to 0. It indicates a nearly total co-polarized reflection for LCP and RCP incidences. Co-polarized reflection phases for normal incidences of LCP and RCP are depicted in Fig. 3(b). The phase curves remains almost stable in a broadband with a nearly π phase difference between them. Therefore, four types of units provides coding states of “0l0r”, “0l1r”, “1l1r”, “1l0r” respectively.
Fig. 3. Simulated reflection amplitudes and phases of 1bit units for normal incidences. (a) Co-polarized reflection amplitudes for LCP and RCP. (b) Co-polarized reflection phases for LCP and RCP.
To examine how well the proposed metasurface approximates the condition of Eq. (2), unit cells shown in Fig. 4 are analyzed which have not been rotated with an angle of β. Simulated reflection amplitudes of these unit cells for x- and y-polarized incidences are shown in Fig. 4(a). It can be observed that rxx and ryy are close to 1, and ryx and rxy are close to 0. Because of the nearly total co-polarization reflection, we only depict co-polarized reflection phases for x- and y-polarized incidences, as shown in Fig. 4(b). Four stable phase states with nearly π/2 phase difference can be observed over the working frequency range. For a single unit, nearly π phase difference can be observed between φxx and φyy. And for the same polarization (φxx or φyy), there is π/2 phase difference between two units. We normalize these phase curves with respect to the third one (φxx of unit 1). Thus, α=0° and α=270° can be realized using unit 1 and unit 2, respectively. By rotating these units with 90°, additional α=90° and α=180° can be obtained. Hence, desired phase values of α for x-polarization and α-π for y-polarization can be obtained.
Fig. 4. Simulated reflection amplitudes and phases of units with no rotation for normal incidence of x and y polarizations. (a) Reflection amplitudes. (b) Reflection phases.
Unit 1 and unit 2 can be seen as the combination of orthogonal line resonators, as shown in Fig. 5. Co-polarization reflected phases of line resonators under normal incidence of parallel and vertical polarizations are shown in Fig. 5. It can be observed that variable reflection phases with nearly π/2 phase difference are generated in the parallel electric case, and similar reflected phases can be observed in the vertical electric case. It indicates that the line resonators can control the reflection phase in the parallel electric case and not change the reflection phase in the vertical electric case. Unit 1 and unit 2 are designed by combining these four geometries orthogonally.
Fig. 5. Co-polarization reflected phases of line resonators under normal incidence of parallel and vertical polarizations. (a) Parallel electric case. (b) Vertical electric case.
In other to get the required β, we rotate the metallic structures of unit 1 and unit 2. The co-polarization reflection phases of units with a rotated angle β under normal incidence are shown in Fig. 6. These unit cells follow the same principle: phase shifts of 2β for LCP and -2β for RCP emerge following the Eq. (5). In this way, desired reflection phases for LCP and RCP can be realized.
Fig. 6. Co-polarization reflection phases with different rotated angles. (a) Unit 1, left-hand circular polarized case. (b) Unit 1, right-hand circular polarized case. (c) Unit 2, left-hand circular polarized case. (d) Unit 2, right-hand circular polarized case.
2.2 1-bit dual-circular polarized coding metasurfaces
For a quantitative illustration of the coding metasurfaces, we encode two metasurfaces with coding matrices M1 and M2, as shown in Fig. 7. To satisfy the periodic boundary in the unit cell simulation, a lattice which contains 4 × 4 same unit cells is adopted. In this way, two 1-bit metasurafaces are built up, and structures of them are shown in Fig. 8.
In M1 case, a discontinuous phase shift on the metasurface is introduced along y axis for LCP and along x axis for RCP. According to the generalized Snell’s law, the anomalous reflection angle for normal incidence can be calculated as [4]:
where c is the velocity of light and $\varDelta$φ/dx is the phase gradient on the surface. In order to validate this, the metasurfaces is simulated using the open boundary condition and plane wave excitation in CST Microwave Studio. Figure 9 shows the 3D far-field scattering patterns of the metasurfaces under the normal incidences of LCP and RCP at 15 GHz. It can be observed that anomalous reflection occurs in the y-z plane for LCP waves and in the x-z plane for the LCP waves. Simulated scattering field spectrums versus frequency and reflection angle for LCP in y-z plane and for RCP incidence in x-z plane are shown in Fig. 10. Meanwhile, the θr calculated by Eq. (6) is plotted in Fig. 10 using black asterisk. Anomalous reflection in y-z plane for LCP and in x-z plane for RCP can be observed from 12 GHz to 18 GHz. And, good agreement can be observed between simulated results and calculated ones.Fig. 9. 3D far-field scattering patterns of the M1 metasurface under normal incidences at 15 GHz. (a) For LCP incidence. (b) For RCP incidence.
Fig. 10. Simulated scattering field spectrums versus frequency and reflection angle under normal incidences. (a) For LCP incidence in y-z plane. (b) For RCP incidence in x-z plane.
In M2 case, the metasurface is designed to exhibit diffusion for LCP and anomalous reflection for RCP. Because of the same behavior for RCP, the codes with the subscript of r in M2 are same as the ones in M1. To obtain a diffusion pattern for LCP, the codes with the subscript of l are optimized by the simulated annealing algorithm presented in [34]. The metasurface is simulated and the results are shown in Fig. 11. It can be observed that, for LCP incidence, the scattered energy is distributed to different directions in the upper half space. And the RCP incidence is reflected as two beams pointing to two symmetrical directions, which is similar as M1 case. To characterize the scattering reduction performance, the monostatic radar cross section (RCS) of the metasurface under normal incidence of LCP is shown in Fig. 12(a). The result of a metallic plane with same size is also presented for comparison. The RCS can be reduced by at least -10 dB in the frequency range from 12 GHz to 18 GHz. Simulated scattering field spectrums versus frequency and reflection angle for RCP incidence in x-z plane are shown in Fig. 12(b). Meanwhile, the θr calculated by Eq. (6) is plotted in Fig. 12(b) using black asterisk. Anomalous reflection can be observed and agrees well with calculated result from 12 GHz to 18 GHz.
Fig. 11. 3D far-field scattering patterns of the M2 metasurface under normal incidences at 15 GHz. (a) For LCP incidence. (b) For RCP incidence.
Fig. 12. Simulated results of M2 metasurface. (a) Monostatic RCS under normal incidence of LCP compared with that of metallic plate. (b) Scattering field spectrums versus frequency and reflection angle for RCP in x-z plane.
2.3 2-bit dual-circular polarized coding metasurfaces
Based on the design method of the 1-bit dual-circular polarized coding metasurfaces, a 2-bit dual-circular polarized coding metasurface is proposed, which can provide more flexibility in manipulating electromagnetic wave. Because the unit cells are designed to independently exhibit ‘00’ (0°), ‘01’ (90°), ‘10’ (180°) and ‘11’ (270°) for LCP and RCP, 16 types of unit cells are required. Structures of these unit cells are similar to those in 1-bit designs except for upper metallic structures. The top view of these unit cells are shown in Fig. 13. To demonstrate the flexibility of the 2-bit polarization-independent coding metasurfaces in manipulating electromagnetic waves, we encode a metasurface with coding matrices M3, as shown in Fig. 14. The size of lattice is also 4 × 4, and the final 2-bit coding layout is shown in Fig. 14.
The simulated 3D far-field scattering patterns of the M3 metasurface at 15 GHz are shown in Fig. 15. For the normal LCP, the incident beam is reflected as a beam with an anomalous reflection angle in the y-z plane, whereas for RCP, the incident wave is anomalous reflected in the x-z plane. Simulated scattering field spectrums versus frequency and reflection angle for LCP in y-z plane and for RCP incidence in x-z plane are shown in Fig. 16. The θr calculated by Eq. (6) is plotted in Fig. 16 using black asterisk. It can be observed that the normally incident beam is mostly deflected to a direction within the frequency band from about 12 GHz to 18 GHz. In addition, the deflection angle is strongly correlated with the generalized Snell’s law.
Fig. 15. 3D far-field scattering patterns of the M3 metasurface under normal incidences at 15 GHz. (a) For LCP incidence. (b) For RCP incidence.
Fig. 16. Simulated scattering field spectrums versus frequency and reflection angle. (a) For LCP incidence in y-z plane. (b) For RCP incidence in x-z plane.
3. Fabrication and measurement
To experimentally validate the performance of the dual-circular polarized coding metasurface, two samples (M2 case and M3 case) are fabricated using printed circuit board processing technology, as shown in Fig. 17(a). F4B (ɛr = 2.65 and tanδ = 0.001) with thickness of 3 mm is selected as the dielectric substrate. These samples are measured in an anechoic chamber, and the experimental setup is presented in Fig. 17(b). Two wideband circular horn antennas are utilized for transmitting and receiving, respectively. The polarization of the antenna can be set as LCP or RCP by changing input port. A vector network analyzer (Agilent N5230C) is used to generate and detect the electromagnetic wave. The transmitting antenna is placed vertically to the sample to ensure normal incidence. In the M2 sample measurement, the receiving antenna is placed at the normal direction of the sample for LCP incidence, whereas it is placed at the angle of 20° and 30° with respect to the normal direction for RCP incidence, as shown in Fig. 18(b). In addition, a metallic board with same size is measured additionally to evaluate the RCS reduction of the sample for LCP incidence. In the M3 sample measurement, the receiving antenna is placed at the angle of 10° and 15° with respect to the normal direction, and the sample is rotated with 90° to detect the anomalous reflection in the x-z plane and y–z plane, respectively. The distance between the antennas and the samples under test satisfies the far-field condition.
Fig. 17. Fabricated metasurfaces and measurement setup. (a) Two samples of metasurfaces (M2 case and M3 case). (b) Measurement setup.
Fig. 18. Measured and simulated results of M2 metasurface under normal incidence. (a) RCS reductions for LCP. (b) Normalized reflection for RCP.
The measured results are shown in Fig. 18 and Fig. 19 along with their corresponding simulated curves. Figure 18(a) shows the RCS reduction of the M2 metasurface under normal incidence of LCP compared with the metallic board. Obvious reduction can be observed from 12 GHz∼18 GHz. Figure 18(b) shows the anomalous reflection performance of the M2 metasurface for RCP in x-z plane. Reflection peaks are observed at 16.7G Hz and 11.2 GHz for θ=20° and θ=30°, respectively. It implies that the incidence is anomalously reflected to observation directions at these frequencies. Figure 19(a) shows the reflection of the M3 metasurface for LCP in y-z plane. Reflection peaks are observed at 18 GHz and 12.1 GHz for θ=-10° and θ=-15° in y-z plane. Figure 19(b) shows the reflection of the M3 metasurface for RCP in x-z plane. Reflection peaks are observed at 17.9 GHz and 12.2 GHz for θ=10° and θ=15° in x-z plane. Well anomalous reflection performance can be observed and it agrees well with the simulated results. It is noteworthy that the reflection in Fig. 18(b), Fig. 19(a) and Fig. 19(b) has been normalized with respect to the maximum value.
Fig. 19. Measured and simulated results of M3 metasurface. (a) Normalized reflection for LCP. (b) Normalized reflection for RCP.
4. Conclusion
In summary, 1 bit and 2bit dual-circular polarized unit cells are proposed which can realize 2 or 4 phase states independently for LCP and RCP in broadband. The design concept is explained by Jones matrix. Then, 1-bit and 2-bit dual-circular polarized coding metasurfaces are proposed utilizing these units. For example, a 1-bit metasurface can anomalously reflected LCP incidence in y-z plane and RCP incidence in x-z plane; another 1-bit metasurface can exhibit diffusion for LCP and anomalously reflection for RCP. Furthermore, a 2-bit metasurface is designed which provide more flexibility in manipulating electromagnetic waves. Capabilities of these metasurfaces are demonstrated in simulation and measurement. Other dual functions for different circular polarizations can be further developed based on this idea. Our designs provide a method for independently manipulating different circular polarized waves. These metasurfaces allow us to encode two completely different coding matrices on a single metasurface. Therefore, dual functions of the manipulation for beam patterns can be realized under different circular polarized incidences. In addition, by adjusting the size of metasurface or utilizing other unit cells, this method could also be applied in other frequency ranges.
Funding
National Natural Science Foundation of China (61471389, 61671464, 61701523, 61801508); Postdoctoral Innovative Talents Support Program of China (BX20180375); China Postdoctoral Science Foundation (2019M650098); Natural Science Foundational Research Fund of Shaanxi Province (2017JM6025, 2018JM6040); Young Talent fund of University Association for Science and Technology in Shaanxi, China (20170107).
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