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Abstract
We design a coding metasurface based on Pancharatnam-Berry (PB) phase to manipulate terahertz waves, which is simple and flexible. Compared with the previous design of the coding metasurface, the present coding particles can be obtained by using a same size meta-particle with various orientations instead of designing multiple structures or changing specific size parameters. The PB coding metasurfaces composed of U-shaped particles with pre-designed coding sequences can generate multi-bit coding in the terahertz frequencies and control the reflected terahertz waves to the various directions. Both simulation and theoretical calculation scattering patterns of the designed PB coding metasurfaces demonstrate the expected manipulations. Additionally, the bandwidth of radar cross section (RCS) reduction of approaching −15 dB is 1.05THz (range from 0.9THz to 1.95THz). We believe that the proposed design provides a more flexible way for the manipulation of reflected terahertz waves.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, due to its thin thickness, small loss, and strong manipulation ability in the phase shift, polarization modes, and amplitude of electromagnetic wave, metasurface has attracted great attention [1–3]. It provides a platform for diversified requirements in practical application, such as high-efficiency polarization conversion [4–5], anomalous reflection and refraction [6–7], focus impinge waves [8], vortex beam [9], quarter-wave plate [10–11], highly efficient beam steering [12] and hologram [13]. In 2014, the concept of coding metasurface [14] has been reported to manipulate the microwave from 8.1 GHz to 12.7 GHz by elaborately designing the coding sequences. Based on this coding metasurface concept, various functionalities such as beam steering and random electromagnetic-wave scattering [8,15] have been achieved by simply implementing the predesigned coding sequences. Similarly, the traditional coding metasurfaces are designed to reduce the RCS at terahertz frequency bands [8,16–17]. Now the question raised that whether we can control reflected terahertz wave to multiple directions and achieve RCS reduction by rotating the coding particle with different orientation angles, rather than changing its size.
To address this question, in this work, we propose a wavefront manipulation method working in terahertz region using Pancharatnam Berry coding metasurface for RCS reduction. Different from the previous design of the coding metasurface which control electromagnetic wave by designing multiple structures or changing specific size parameters, the highlight of Pancharatnam-Berry coding metasurface is to flexibly control terahertz wave by elaborately arranging the rotating metal patterns and coding sequences. The phase change is caused by the different angle orientation of a single basic coding particle. We utilize 6×6 U-shaped coding particles as a coding element and achieve multiple directions scattering. By elaborately designing the rotating angle of the coding particle and coding sequences, six far-field beams splitting can be achieved. The multiple directions scattering coding metasurfaces composed of the coding particles which generated based on the Pancharatnam-Berry phase are realized under left-handed circularly polarized plane (LCP), right-handed circularly polarized plane (RCP) and linearly polarized (LP) waves incidence. The RCS reduction is improved with increasing numbers of the scattering beam. Finally, 1-bit, 2-bit and 3-bit random PB coding metasurfaces are designed to control reflected terahertz wave directions and achieve RCS reduction.
2. Theory analysis
A coding metasurface generally consists of N×N array of coding elements. Each element is made of M×M array of coding particles. Since the coding metasurface is composed of equivalent homogeneous structures, it can be considered as a passive array antenna and the coding element as a sub-array antenna. When the PB particle is illuminated by a commonly incident terahertz wave, the far-field function $F({\theta ,\varphi } )$can be given by [14]
where θ and φ are the elevation and azimuth angles of the reflected terahertz waves, ${f_{m,n}}({\theta ,\varphi } )$are the main modes representing far-field polarization and directional mode vector characteristics. ${S_a}({\theta ,\varphi } )$is a scalar array pattern. At circular polarization (CP) wave incidence, the relation of the array pattern ${S_a}({\theta ,\varphi } )$ of coding phase gradient metasurface, incident elevation angle θi and azimuth angle φi can be calculated byThe main lobe direction of the main mode $({{\theta_a},{\varphi_a}} )$ can be derived from the generalized law of reflection transformation
In this work, under the normal incidence of plane wave, the far-field pattern function of the coding metasurfaces can be described as
3. Coding particle design
In this paper, the U-shaped metallic pattern was designed as the basic coding particle which was printed on a grounded Polyimide (PI) dielectric substrate, as depicted in Fig. 1(a). The period of the unit cell is P = 55μm. The PI dielectric substrate has a thickness of h = 25μm with relative permittivity of ɛ=3.0 and loss tangent tanδ=0.03. And both the metallic pattern and metal ground plate are made of copper with a conductivity of 5.96×107S/m and a thickness of 0.2μm. By using the simulation software CST, the coding particles are obtained by optimizing the dimensions: L = 35μm, w = 5μm and t = 25μm. As shown in Figs. 1(b) and 1(c), the reflection amplitude of the co-polarization and cross-polarization of the unit cell in the frequency from 0.6THz to 2.2 THz under vertical incidence of left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) waves. From the figures, it can be found that the reflection amplitude of the cross-polarization is less than −1 dB ranging from 1.0 THz to 1.8THz. This is due to the metal ground plate reflects the circularly polarized (CP) normal incidence wave and inverts the polarization state of incident CP wave. Furthermore, there are three resonance frequencies at 1.07THz, 1.37THz and 1.71THz under normal incidence of the LCP, RCP and LP waves. As illustrated in Fig. 1(d), it can be noted that a π reflection phase difference and over 0.8 reflection amplitude values between the x- and y- polarized waves achieves in the frequency range from 1.0 THz to 1.8THz. By combining PB metasurfaces with different predesigned coding sequences, we designed PB coding metasurfaces to control the terahertz wave.
Fig. 1. Design of the basic coding particle. (a) Schematic diagram of the basic coding particle. Reflection magnitude of the basic coding particle under normal incidence of LCP (b) and RCP (c) waves. Here, RLL(RRR) and RRL(RLR) are the reflection magnitude with co-polarization and cross-polarization under normally incident LCP (RCP) waves, respectively. (d) Reflection phase and amplitude values under normal incidence of x- and y linearly polarized waves, respectively.
As shown in Fig. 2(a), we can achieve eight coding particles by rotating the top metallic pattern with different orientation angle of α. The coding particle can realize the reflection phase shift of ± 2α (Here, the sign “+” and “−” denote the RCP and LCP waves, respectively.). Moreover, the spatial variation of the phase has a simply linear relationship to the rotation angle of the U-shaped metallic pattern, as demonstrated in Fig. 2(b). In fact, the designed PB coding metasurfaces can be extended from 1-bit to mulit-bit. For 1-bit coding metasurfaces, two coding particles with opposite reflection phase 0 and 180° are required. Similarly, for 2-bit coding metasurfaces, four coding particles are required and the phase difference between adjacent coding particles is close to 90° (i.e. 0, 90°, 180°, 270° phase responses). Actually, for 3-bit coding metasurfaces, eight coding particles with a fixed reflection phase difference of 45° are employed to imitate the digital bits of “000”, “001”, “010”, “011”, “100”, “101”, “110” and “111”. Figure 2(c) depicted the reflection magnitude (located in the upper half of the area with a black ring around the part) and phase (located in the lower half of the area and surrounded by a green ring) of cross-polarization with different rotation angle α of the top metallic pattern under normal incidence of the LCP wave. Practically, in order to obtain eight coding particles, the rotation angle α varies from 0° to 157.5° with the step width of 22.5°. The corresponding phase response is as follows: 0°, 45°, 90°, 135°, 180°, 225°, 270° and 315° (i.e. “000”, “001”, “010”, “011”, “100”, “101”, “110”, and “111”, respectively.). Then, each coding particle is represented by the U-shaped metallic pattern with a specific rotation angle α. Figure 2(d) gives the corresponding relationship between the eight coding particles and the 1-bit, 2-bit and 3-bit coding PB phase metasurfaces, as well as the supercoding particles. Here, we used 5×5 coding particles as the supercoding particles in order to minimize the couple effect of the adjacent particles.
Fig. 2. Spectrum information of the coding particle versus different rotation angle α under normal incidence of LCP and RCP waves. (a) Description of the rotation angle α. (b) Curves of the phase responses and rotation angle of U-shaped coding particle under normally incident RCP and LCP waves. (c) Reflection magnitude and phase versus different rotation angle α. (d) Eight coding particles for coding metasurfaces.
4. Design and simulate coding metasurfaces
In order to verify different physical phenomena of scattering field modes are generated by arbitrary coding metasurfaces with unique coding sequences, the coding metasurface with pre-designed coding sequence (shown in Fig. 3) are used to achieve the desired scattering field pattern and broadband RCS reduction.
Fig. 3. Pre-designed regular coding sequences. (a) Pre-designed coding sequence with “000,000,100,100…” periodically distributed along x-axis (Denoted as 1-bit coding metasurface 1), (b) Pre-designed coding sequence with “100,000,100,000…” periodically distributed along y-axis direction (Denoted as 1-bit coding metasurface 2), (c) Pre-designed coding sequence with “000,010,100,110…” periodically distributed along y-axis direction (Denoted as 2-bit coding metasurface 1), (d) Pre-designed coding sequence with “110,100,110,100…/000,010,000,010…” periodically distributed along x-axis direction (Denoted as 2-bit coding metasurface 2), (e) Pre-designed coding sequence with “000,001,010,011,100,101,110,111…” periodically distributed along x-axis direction (Denoted as 3-bit coding metasurface 1), (f) Pre-designed coding sequence with “000,001,010,011,100,101,110,111/100,101,110,111,000,001,010,011…” periodically distributed along x-axis direction (Denoted as 3-bit coding metasurface 2), (g) Pre-designed coding sequence with “000,001,010,011,100,101,110,111/000,001,010,011,100,101,110,111/100,101,110,111,000,001,010,011…” periodically distributed along x-axis direction (Denoted as 3-bit coding metasurface 3).
4.1 1-bit regular coding metasurface
For 1-bit coding metasurface, the basic coding particles with the inverse reflection phase information are required such as 0 and ± 180°. Figure 4 show the simulated 3D far-field and 2D electric-field scattering patterns of the 1-bit coding metasurface 1 and 1-bit coding metasurface 2 under the LP wave normal incidence at 1.4THz. When the 1-bit coding metasurfaces with “00000…”coding sequence displayed in Fig. 3(a) are arranged along x-direction, the backward scattering wave is reflected into two symmetric main lobes direction with the angle of (θ1=arcsin(λ/Γ1) = 11.2°, φ=0° or φ=180°), Γ1=4×275 µm is the physical period length of the 1-bit coding metasurface 1, as shown in Figs. 4(a) and 4(c). Similarly, when the 1-bit coding metasurfaces with periodical distributing “001001…” coding sequences displayed in Fig. 3(b) are arranged along x-axis direction, the LP wave normal incidence is also reflected into two symmetric directions with the angle of (θ2=arcsin(λ/Γ2) = 22.9°, φ=90°or φ=270°), Γ2=2×275 µm is the physical period length of the 1-bit coding metasurface 2, as shown in Figs. 4(b) and 4(d).
Fig. 4. 3D far-field scattering patterns of 1-bit regular coding metasurface. (a) with Fig. 3(a) coding sequence under normal incidence of LP wave, (b) with Fig. 3(b) coding sequence under normal incidence of LP wave. 2D far-field scattering patterns of 1-bit regular coding metasurface. (c) with Fig. 3(a) coding sequence under normal incidence of LP wave, (d) with Fig. 3(b) coding sequence under normal incidence of LP wave.
4.2 2-bit regular coding metasurface
In order to verify the coding metasurfaces produce different scattering field mode physical phenomena, we designed two kinds of 2-bit regular coding metasurfaces based on four coding particles which have a fixed phase difference of 90°. The designed coding metasurfaces are arranged according to a pre-designed coding sequence shown in Figs. 3(c) and 3(d). Here, Fig. 3(c) is denoted as 2-bit coding metasurface 1 and Fig. 3(d) is denoted as 2-bit coding metasurface 2. Figure 5 shows the simulated 3D and 2D far-field scattering patterns for 2-bit coding metasurface 1 and 2-bit coding metasurface 2 direction under normal incidence of the LP wave at 1.4THz, respectively. As can be clearly seen from Figs. 5(a) and 5(c), the LP wave normal incidence is reflected into two symmetric main lobes direction with the angle of θ1=arcsin(λ/Γ1) = 11.2°, φ=90°or φ=270°), Γ1=4×275 µm is the physical period length of the 2-bit coding metasurface 1. Figures 5(b) and (d) show that the normal incidence LP wave is reflected into four symmetric directions with the angle of (θ2=arcsin(λ/Γ2) = 22.9°, φ=0°, φ=90°, φ=180° or φ=270°), Γ2=2×275 µm is the physical period length of the 2-bit coding metasurface 2.
Fig. 5. 3D far-field scattering patterns of 2-bit regular coding metasurface. (a) With Fig. 3(c) coding sequence under normal incidence of LP wave, (b) With Fig. 3(d) under normal incidence of the LP wave. 2D far-field scattering patterns of 2-bit regular coding metasurface.(c) 2D far-field scattering patterns of 2-bit coding metasurface with Fig. 3(c) coding sequence under normal incidence of LP waves, (d) 2D far-field scattering patterns of 2-bit coding metasurface with Fig. 3(d) under normal incidence of the LP wave.
4.3 3-bit regular coding metasurface
Figures 6(a)∼(c) and Figs. 7(a)∼(c) show the 3D and 2D far-field scattering patterns for the 3-bit coding metasurfaces with “000, 001, 010, 011, 100, 101, 110, 111…” coding sequence periodically distributed along y-axis direction (i.e. Fig. 3(e)) under LCP, RCP, and LP waves incidence at 1.4THz. Figures 6(d)∼(f) and Figs. 7(d)∼(f) depict the 3D and 2D far-field scattering patterns for the 3-bit coded metasurfaces with “000, 001, 010, 011, 100, 101, 110, 111/100, 101, 110, 111, 000, 001, 010, 011…”encoding sequence periodically distributed in the y-axis direction (i.e. Fig. 3(f)). Figures 6(g)∼(i) and Figs. 7(g)∼(i) give the 3D and 2D far-field scattering patterns for the 3-bit coded metasurfaces with “000, 001, 010, 011, 100, 101, 110, 111/000, 001, 010, 011, 100, 101, 110, 111/100, 101, 110, 111, 000, 001, 010, 011…” encoding sequence periodically distributed in the y-axis direction (i.e. Fig. 3(g)). Figures 6(a)∼(c), 6(d)∼(f) and 6(g)∼(i) show the results of 3D far field scattering patterns for the 3-bit coding metasurface 1, 3-bit coding metasurface 2 and 3-bit coding metasurface 3 direction under normal incidence of the LCP, RCP, and LP waves at 1.4THz, respectively.
Similarly, Figs. 7(a)∼(c), 7(d)∼(f) and 7(g)∼(i) depict the results of 2D far field scattering patterns for the 3-bit coding metasurface 1, 3-bit coding metasurface 2 and 3-bit coding metasurface 3 direction under normal incidence of the LCP, RCP, and LP waves at 1.4THz, respectively. In Fig. 6(a) and Fig. 7(a), it is observed that the LCP wave normal incidence is reflected into the main lobe direction of the primary pattern with (θ1=5.6°, φ=0°). However, when the normal incidence wave is the RCP wave, the azimuth angle φ increases from 0° to 180° while the elevation angle is still θ1=5.6°, as depicted in Fig. 6(b) and Fig. 7(b). As shown in Fig. 6(c) and Fig. 7(c), under the LP wave normal incidence, the reflected waves in two symmetrical directions appear with the angle of (θ1=arcsin(λ/Γ1) = 5.6°, φ=0° or φ=180°, Γ1=8×275 µm). As illustrated in Fig. 6(d) and Fig. 7(d), for 3-bit coding metasurface 2, the LCP wave normal incidence is reflected into two symmetrical orientations with the angle of (θ2=22.9°, φ=76°) and (θ2=22.9°, φ=284°), where θ2=arcsin(λ/Γ2), and Γ2=2×275 µm. For the RCP wave normal incidence, the angles of the two symmetrical orientations reflected waves become (θ2=22.9°, φ=104°) and (θ2=22.9°, φ=256°), as depicted in Figs. 6(e) and 7(e). In addition, it is observed that the LP wave normal incidence is reflected into four symmetrical waves with the orientation angle of (θ2=22.9°, φ=76°), (θ2=22.9°, φ=104°), (θ2=22.9°, φ=256°) and (θ2=22.9°, φ=284°), as shown in Figs. 6(f) and 7(f). For the 3-bit coding metasurface 3, as described in Figs. 6(g) and 7(g), the LCP wave normal incidence is reflected to three orientations with angles of (θ1=5.6°, φ=0°), (θ3=15.1°, φ=69.4°) and (θ3=15.1°, φ=290.6°). Likewise, the reflected angles of the RCP wave normal incidence become (θ1=5.6°, φ=180°), (θ3=15.1°, φ=110.6°) and (θ3=15.1°, φ=249.4°), where θ3=arcsin(λ/Γ3) and Γ3=3×275 µm, as depicted in Figs. 6(h) and 7(h). As shown in Figs. 6(i) and 7(i), the LP wave normal incidence is reflected into six symmetrical orientations with the angle of (θ1=5.6°, φ=0°), (θ3=15.1°, φ=69.4°), (θ3=15.1°, φ=290.6°), (θ1=5.6°, φ=180°), (θ3=15.1°, φ=110.6°) and (θ3=15.1°, φ=249.4°), respectively.
Fig. 6. 3D far-field scattering patterns of 3-bit coding metasurface with Fig. 3(e) coding sequence under normal incidence of LCP (a), RCP (b), LP (c) waves. With Fig. 3(f) coding sequence under normal incidence of LCP (d), RCP (e), LP (f). With Fig. 3(g) coding sequence under normal incidence of LCP (g), RCP (h), LP (i).
Fig. 7. 2D far-field scattering patterns of 3-bit coding metasurface with Fig. 3(e) coding sequence under normal incidence of LCP (a), RCP (b), LP (c) waves. With Fig. 3(f) coding sequence under normal incidence of LCP (d), RCP (e), LP (f). With Fig. 3(g) coding sequence under normal incidence of LCP (g), RCP (h), LP (i).
4.4 Random PB coding metasurface
The random coding sequences of the 1-bit, 2-bit and 3-bit coding metasurfaces composed of 8×8 array of coding particles produced by MATLAB [18] are given as shown in Figs. 8(a)∼(c). According to these random coding sequences, Figs. 8(d)∼(f) show the 1bit, 2-bit and 3-bit random PB coding metasurfaces, respectively. Figure 9 illustrates the RCS versus frequency ranging from 0.6THz to 2.2THz of both same size bare metallic plate and coding metasurfaces under terahertz waves normal incidence. Compared with bare metallic plate, the RCS of the PB coding metasurfaces is reduced more than 15 dB from 0.9THz to 1.95THz. This proves that the PB phase coding metasurfaces have a good property in reducing RCS.
Fig. 8. (a)∼(c) are the random coding sequences of 1-bit, 2-bit and 3-bit coding metasurfaces composed of 8×8 array of coding particles produced by MATLAB, respectively. (d)∼(f) are 1-bit, 2-bit and 3-bit coding metasurfaces with random coding sequence, respectively.
5. Conclusion
In summary, we designed Pancharatnam-Berry coding metasurfaces to control the reflected terahertz wave beam and achieve RCS reduction. Regular and random 1-bit, 2-bit, 3-bit coding metasurfaces, which are combined the PB phase with the pre-designed different coding sequences, are used to reveal the different dual functionalities. It can redirect the normal incidence plane wave to numerous directions and the RCS is reduced to −10 dB in a wide frequency band ranging from 0.9THz to 1.95THz. The simulation results of the proposed coding Pancharatnam-Berry metasurfaces are highly consistent with the theoretical analysis results. Moreover, we believe that the proposed design provides a more flexible way for the manipulation of reflected terahertz waves.
Funding
National Natural Science Foundation of China (NSFC) (61831012, 61871355); Natural Science Foundation of Zhejiang Province (LY18F010016).
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