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Abstract
In this paper, a method for broadband polarization-dependent coding metasurface design is proposed. Single-polarized unit cells are employed due to their single-polarized phase manipulation with little effect on cross-polarized phase in broadband. The equivalent circuit of these unit cells is developed to analyze the mechanism. Because of single-polarized phase manipulation, coding metasurfaces for different polarizations can be designed separately. The polarization-dependent coding metasurface can be obtained by simply combining them into a sharing aperture. Simulated and measured results prove that our method offers a simple and effective strategy for broadband polarization-dependent metasurface design.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces composed of subwavelength structures have obtained great popularity in recent years due to their powerful manipulation of electromagnetic (EM) waves [1–3]. A number of functions have been realized by utilizing metasurfaces, such as absorbing [4–8], polarization conversion [9–11] and anomalous refraction/reflection [12–14]. Many of the previous metasurface designs are implemented by phase manipulation [15–17]. Based on the generalized Snell’s law, the propagation direction of EM waves can be manipulated by introducing abrupt phase changes on the interface. The group delay can be tuned in broadband by modifying the implemented resonances [18]. In addition, some metasurfaces are devised and analyzed according to antenna array theory [19]. During the design, metasurface is divided into a number of lattices that each contains several uniform unit cells. Every lattice is regarded as an array element. Through converting the phase response of per lattice, the scattering patterns are able to be controlled. Therefore, plenty of scattering patterns can be implemented by utilizing various phase distribution, such as beam forming and diffusion [20–24].
More recently, the concepts of coding metamaterials, digital metamaterials, and programmable metamaterials present a new perspective for EM wave manipulation, and offer a novel method of designing metasurfaces [25,26]. The discrete phase response of the unit cell is encoded with binary codes ‘0’ and ‘1’, and the metasurface can be interpreted as a coding sequence. In this way, by designing the coding sequences elements “0” and “1”, the function of the metasurface is able to be managed. For more flexibility, multi-bit coding metasurfaces have been investigated. [27–29]. Furthermore, polarization-dependent coding metasurfaces have been proposed, which has distinct coding behavior for diverse polarizations [30–34]. Thus, dual functions are achievable by simply altering the polarization state in a single metasurface. Nevertheless, most previous polarization-dependent metasurfaces are devised using dual-polarized unit cells. The structure of the unit is integral and the reflection phases for the x- and y- polarizations are not independent. Because phase responses for two polarizations will change with the structure at the same time, phase responses of each unit cell for disparate polarized incidences should be considered simultaneously, resulting in relatively high complexity. Besides, it is difficult to realize broadband design.
In this paper, we propose a broadband polarization-dependent coding metasurface. Instead of employing dual-polarized unit cells, four types of single-polarized unit cells are developed as the fundamental element. These unit cells can reflect the normal incidence with 0° (state ‘00’), 90° (state ‘01’), 180° (state ‘10’) and 270° (state ‘11’) for one linear polarization, with little effect on the reflection phase for cross-polarization. Based on these unit cells, two metasurfaces for different polarizations are designed, and the polarization-dependent coding metasurface can be acquired by simply integrating them into a sharing aperture. For demonstration purposes, we fulfill diffusion for x- polarization incidence and anomalous reflection for y-polarization. Hence, another polarization-dependent coding metasurface with unlike operating frequencies for x- and y-polarizations is designed. Compared with other works, our design is broadband, easy to design and analyzed by equivalent circuit. Both simulated and measured results certify the effectiveness of certain approach for broadband polarization-dependent coding metasurface design.
2. Design method and the single-polarized unit cell
It is known that the metasurface manipulates EM wave by introducing resonance mode into the structure. Because we want change the phase for one polarization only, single-polarized unit cells are designed based on metallic line structures. Metallic line structures can only be excited by the linear polarization parallel to them, which indicate that, they have no resonance mode for the polarization vertical to them.
As shown in Fig. 1(a), single-polarized unit cells of the metasurface contain a metallic patterned sheet, a dielectric substrate and a full metallic ground. The top view of these unit cells are shown in Fig. 1(b). The substrate is F4B with a dielectric constant of 2.65 and loss tangent of 0.001. The metallic patterned sheet and metallic ground are all copper with conductivity of 5.8×107S/m and the thickness is 0.036mm. The period of the unit cells is 7mm and the thickness of substrate is 3mm. Other geometrical parameters designed for broadband are as shown in Table 1.
Table 1. Geometrical parameters of these four unit cells
These unit cells are simulated by the commercial software CST Microwave Studio. Simulated co-polarized reflection amplitudes of these unit cells under normal incidence are shown in Fig. 2(a) and Fig. 2(b). These unit cells are perfectly reflective for incident waves of both polarizations and a nearly total reflection of co-polarization can be observed. Because of little cross-polarization reflection, we only show the co-polarized reflection phases of these unit cells under normal incidence in Fig. 2(c) and Fig. 2(d). For x-polarized incidence, reflection phases remain stable with nearly π/2 phase difference in a wide frequency band. However, reflection phases are almost the same for y-polarized incidence. Therefore, four types of unit cells can provide coding states of “00”, “01”, “10” and “11” for x-polarization without any behavior for y-polarization. Rotated with 90°, these unit cells can provide coding states for y-polarization.
Fig. 2. Simulated reflection amplitudes and phases of these unit cells under normal incidence. (a) Co-polarized reflection amplitude for x-polarization. (b) Co-polarized reflection amplitude for y-polarization. (c) Co-polarized reflection phase for x-polarization. (d) Co-polarized reflection phase for y-polarization.
To further understand the reflection response of these unit cells, we monitored the surface current distribution on the metallic line structures. As shown in Fig. 3, metallic line structures can generate resonance for x-polarized incidence, while they keep almost unexcited for y-polarized incidence. Therefore, these unit cells have phase shift for x-polarization while they have no behavior for y-polarization. Hence, discrepant resonance can be observed on each structure for x-polarization which results in various phase shifts.
Fig. 3. The surface current distribution on the metallic line structures for x- and y-polarization at 15GHz
The resonant behavior can be explained by the equivalent LC circuit, whose effective inductance L and effective capacitance C are relevant to the pattern geometry [35]. Then, we will study the reflection coefficient of the metasurface using the equivalent circuit model.
The metasurface is modeled as an equivalent circuit, as shown in Fig. 4. The metallic ground is regarded as a short circuit line, and the substrate is treated as lossless transmission line with impedance of the wave impedance in the dielectric. The impedance of the substrate with metallic ground Z1 can be calculated as:
in which, Zm is the wave impedance in the dielectric, $\beta$ is the propagation constant and h is the thickness of the substrate. The metallic patterned sheet is regarded as lossless sheet regardless of its thickness, and its impedance can be explained by an equivalent LC circuit. Therefore, the input impedance Zin can be calculated as follows: The reflection amplitude r and the reflection phase φ can be expressed as:For the “00” unit cell, the equivalent circuit can be simplified without LC and the Zin will be equal to Z1. In the above equations, the reflection phase can be calculated with L and C. Values of L and C can be computed by matching the reflection response obtained from numerical simulations. The calculated reflection phase and corresponding values of L and C are shown in Fig. 5. The simulated results are also shown in Fig. 5 with the frequency domain solver in CST Microwave Studio. A good agreement between calculations based on equivalent circuit model and simulations can be observed which clearly indicates that our equivalent circuit model can analyze reflection responses of these unit cells. In this way, stable broadband phase difference can be obtained by adjusting the L and C which are relevant to the metallic pattern geometry. The equivalent circuit has a limitation, which L and C couldn’t be associated with the geometrical parameters when the structural parameters are changed within a large range. For example, the wire is wider and shorter in “11” unit cell, but the L is larger. However, when changing the length or width within a small range, L and C can be associated with the geometrical parameters, such as “01” and “10” designs.
Fig. 5. Calculated and simulated reflection phases of these unit cells. (a) Reflection phases of “00” unit cell (no L and C). (b) Reflection phases of “01” unit cell (C=4.7×10−2pF, L=7.4nH). (c) Reflection phases of “10” unit cell (C=2.78×10−2pF, L=4.2nH). (d) Reflection phases of “11” unit cell (C=1.4×10-2pF, L=4.4nH).
3. Polarization-dependent coding metasurface design
3.1 Polarization-dependent coding metasurface composed of two single-polarized metasurfaces
First, we design two metasurfaces, using the above designed single-polarized unit cells that are encoded with coding matrices M1 and M2 for x and y polarization. The random coding matrices M1 is generated to realize diffusion for x-polarization whereas the gradient coding matrices M2 creation is for achieving the anomalous reflection for y-polarization, as follows:
To satisfy the periodic boundary in the unit cell simulation, each coding lattice contains 4 × 4 single-polarized unit cells. As a result, displayed in Fig. 6, Meta1 and Meta2 metasurface have been built up.
Fig. 6. Structures of the metasurfaces metasurface and 3D far-field scattering patterns of it under normal incidences at 15GHz. (a) Meta1 case; diffusion for x-polarization, normal reflection for y-polarization. (b) Meta2 case; normal reflection for x-polarization, deflection with φ=0°, θ=10.2° for y-polarization. (c) Meta3 case; diffusion for x-polarization, deflection with φ=0°, θ=10.2°for y-polarization.
These metasurfaces are simulated using CST Microwave Studio. In Fig. 6(a) and Fig. 6(b), far-field scattering patterns under x-polarized and y-polarized normal incidence are shown. As expected, in Meta1 case, diffusion for x-polarization and specular reflection for y-polarization can be observed. In Meta2 case, specular reflection for x-polarization and anomalous reflection can be observed. Note that each metasurface only change the scattering pattern for one polarization, which is attributed to the character of single-polarized unit cells.
Then the final polarization-dependent coding metasurface Meta3 is designed as a combination of Meta1 and Meta2 metasurface, as shown in Fig. 6(c). The simulated far-field scattering patterns of the metasurface under x-polarized and y-polarized normal incidence are also shown in Fig. 6(c). We found that, for x-polarized incidence, the scattered energy is distributed to diverse directions. And the y-polarized beam is anomalously reflected in the x–z plane. Functions of Meta1 and Meta2 metasurfaces are realized in a single metasurface Meta3. In addition, to characterize the broadband operation performance, we simulate the monostatic radar cross section (RCS) of the metasurface under normal incidence of x-polarized, as shown in Fig. 7(a). Compared with metallic plate, the RCS of the metasurface can be significantly reduced more than 10 dB from 11.2GHz to 18GHz for x-polarization. Because the scattering energy is steered to a lot of directions, the monostatic RCS is reduced. The lowest monostatic RCS at 13GHz is a result of lower normal reflection which caused by unit characteristics, coupling effect and arrangement. Figure 7(b) shows the simulated scattering field spectrum versus frequency and reflection angle for y-polarization in x-z plane. The theoretical anomalous reflection angle can be calculated as [1]:
where c is the velocity of light and Δφ/dx represent the phase gradient on the surface. The calculated result is also plotted in Fig. 7(b) using black asterisk. It is observed that the scattered beam deviates from the z axis to an anomalous reflection angle in broadband, which agrees with calculated results.Fig. 7. Simulated results of the polarization-dependent coding metasurface. (a) Monostatic RCS under normal incidence of x-polarization compared with that of metallic plate. (b) Scattering field spectrums versus frequency and reflection angle for y-polarization in x-z plane.
3.2 Polarization-dependent coding metasurface operating at different frequencies
For a further illustration of the design method, another polarization-dependent coding metasurface is designed, which can operate at different frequencies for x- and y-polarizations. The coding matrix and the structure of the metasurface for x-polarization are same as ones in Meta1 case. Because the metasurface is expected to operate at other frequencies for y-polarization, four single-polarized unit cells are employed, as shown in Fig. 8. Simulated reflection phases of these unit cells are shown in Fig. 8, which indicates they can provide coding states of “00”, “01”, “10” and “11” near 8 GHz. Based on these unit cells, Meta4 metasurface is built up for y-polarization, according to the coding matrix M2, as shown in Fig. 9(a). Simulated far-field scattering patterns under x-polarized and y-polarized normal incidence are shown in Fig. 9(a). It is observed that Meta4 metasurface only reflect the incidence anomalously for y-polarization at 8GHz.
Fig. 9. Structures of the metasurfaces and 3D far-field scattering patterns of them under normal incidences. (a) Meta4 case; normal reflection for x-polarization at 8GHz, deflection with φ=0°, θ=19.4° for y-polarization at 8GHz. (b) Meta5 case; diffusion for x-polarization at 15GHz, deflection with φ=0°, θ=19.4° for y-polarization at 8GHz.
Then we combine metasurfaces Meta1 and Meta4 into a new polarization-dependent coding metasurface Meta5, as shown in Fig. 9(b). The simulated far-field scattering patterns of the metasurface under x-polarized and y-polarized normal incidence are shown in Fig. 9(b). It can be observed that, for x-polarized incidence, the scattered energy is distributed to different directions, which is same as the metasurface Meta3. And the y-polarized beam is anomalously reflected in the x–z plane at 8GHz.
4. Fabrication and measurement
To validate the performance of the polarization-dependent coding metasurface, a sample of the Meta3 metasurface has been fabricated with a total dimension of 234 mm × 234 mm, as shown in Fig. 10(a). The sample is manufactured using printed circuit board processing technology prototype. The F4B (ɛr = 2.65 and tanδ = 0.001) with thickness of 3mm is selected as the dielectric substrate. The sample is measured in an anechoic chamber and the measurement setup is shown in Fig. 10(b). Two wideband linear horn antennas are utilized to transmit and receive EM waves respectively. A vector network analyzer (Agilent N5230C) is connected to the transmitting and receiving antennas and the reflection performance of the sample can be evaluated by S21 parameter. The transmitting antenna is placed vertically to the sample to ensure normal incidence. For x-polarized incidence, the receiving antenna is placed at the normal direction of the sample. A metallic board with same size is measured to evaluate the RCS reduction of the metasurface. For y-polarized incidence, the receiving antenna is placed at the angle of 10° and 15° with respect to the normal direction of the sample to detect the anomalous reflection, as shown in Fig. 10(d). The polarizations of the transmitting and receiving antennas are always same and the distance between the sample and antennas meet the condition of far-field test. Due to limited experimental conditions, our equipment can only test up to 18GHz
Fig. 10. Measurement setup and measured results. (a) Fabricated Meta3 metasurface sample. (b) Measurement setup. (c) Measured and simulated RCS reductions of Meta3 metasurface for x-polarization under normal incidence. (d) Measured and simulated normalized reflection for y-polarization under normal incidence.
Figure 10(c) shows the RCS reduction under normal incidence of x-polarization. 10dB reduction is observed from 10.45 GHz∼18 GHz and the maximum value 21dB appears at 13.4 GHz. The peak value of the measured result is smaller, mainly affected by refraction and environment noise. The RCS reduction is the RCS of the metal plate minus the RCS of the metasurface. If the minimum of metasurface RCS is higher, then the RCS reduction peak will be lower. Figure 10(d) shows the anomalous reflection performance for y-polarization in x-z plane. The reflection in Fig. 10(d) has been normalized with respect to the maximum value. It can be seen that, reflection peaks appear at 16.55 GHz and 11.85GHz for θ=10° and θ=15°, respectively. It implies that the incidences are anomalously reflected to observation directions at these frequencies. Hence, the trend of measured results and simulated ones is consistent. The reason for the difference may be mainly due to the shift to high frequency caused by manufacturing errors.
5. Conclusion
In summary, polarization-dependent coding metasurfaces are proposed for independently manipulating different polarized waves in broadband. Four types of single-polarized unit cells are employed, which can realize four phase states for one polarization, independently. Surface current distribution and equivalent circuit are adopted to analyze the reflection character. As an example, two single-polarized metasurfaces are constructed utilizing these unit cells according to the coding matrices for x and y polarization, respectively. Then the polarization-dependent coding metasurface can be obtained by combining them simply. Our designs provide a simple method for broadband polarization-dependent coding metasurface design. This method could also be applied in other frequency ranges.
Funding
Natural Science Foundation of Shaanxi Province (2017JM6025, 2018JM6040); National Postdoctoral Program for Innovative Talents (BX20180375); National Natural Science Foundation of China (61471389, 61671464, 61701523, 61801508); China Postdoctoral Science Foundation (2019M650098); Young Talent fund of University Association for Science and Technology in Shaanxi (20170107).
Disclosures
The authors declare no conflicts of interest.
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