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Abstract
In order to extend to 3-bit encoding, we propose notched-wheel structures as polarization insensitive coding metasurfaces to control terahertz wave reflection and suppress backward scattering. By using a coding sequence of “00110011…” along x-axis direction and 16 × 16 random coding sequence, we investigate the polarization insensitive properties of the coding metasurfaces. By designing the coding sequences of the basic coding elements, the terahertz wave reflection can be flexibly manipulated. Additionally, radar cross section (RCS) reduction in the backward direction is less than −10dB in a wide band. The present approach can offer application for novel terahertz manipulation devices.
© 2017 Optical Society of America
1. Introduction
Terahertz technology offers a variety of applications including imaging, spectroscopy, and high-speed wireless communications. With the rapid development of terahertz wave technology, it becomes very significant and urgent to control the terahertz wave transmittance efficiently. Recently, much effort has been devoted to developing some typical terahertz wave manipulation devices such as power dividers [1], switches [2], de-multiplexers [3], absorbers [4], polarizers [5], modulators [6], and filters [7]. However, these devices mainly control terahertz wave transmission, and little attention has been paid to manipulate terahertz wave reflection. In recent years, researchers have discovered metasurfaces having ability to manipulate electromagnetic wave propagation at the wavelength scale and negligible layer thickness [8–10]. With the advent of generalized snell's laws, the anomalous reflection, refraction and transmission have been achieved on the various metasurfaces [11–15]. Especially in the microwave and light-wave bands, metasurfaces have already been applied in some fields, such as phase modulation [16], polarization converter [17–20], optical lenses [21], holography [22]. These shows the metasurface's superior characteristics in achieving simultaneous phase and amplitude manipulation [23,24] and the focusing of sub-wavelength [25,26]. More recently, a concept of coding metasurfaces has been reported at the microwave frequency band [27]. Some coding metasufaces-based devices are designed to reduce the radar cross section (RCS) at microwave and terahertz frequency bands [28–30]. In 2015, L. Liang proposed 1-bit THz coding metasurface [31]. Although some progress has been made in the research on terahertz wave manipulation, it is still lagging behind for flexible controlling terahertz wave reflection.
In this paper, we present a notched wheel structures as coding particle to create 1-bit, 2-bit and 3-bit coding metasurfaces to achieve manipulating terahertz wave reflection and suppressing backward scattering. It can flexible manipulate terahertz waves reflection to arbitrary directions by the predesigned metasurfaces with different coding sequences. Additionally, in our case, the coding metasurfaces are polarization insensitive. It offers a new approach to study terahertz wave manipulation and has enormous potential application for future terahertz system.
2. Coding metasurfaces design and theoretical analysis
To build up the coding metasurface, we propose a notched-wheel structure as the basic coding particle unit to change the peak backward scattering of terahertz waves to diffusion. Each notched wheel has four gaps with an excellent self-similar property. As illustrated in Fig. 1(a), the coding particle unit, which consists of notched-wheel metallic film, is patterned on polyimide film (thickness of 35μm) with a loss tangent of 0.03 and a dielectric constant of 3.0. The bottom layer is metal plate with thickness of t = 0.2μm. The schematic of a random coding metasurface in the upper half-space is sketched in Fig. 1(b). Here, we presented digital metasurfaces including 1-bit, 2-bit and 3-bit coding metasurfaces (i.e.“0”, “1”, “00”,“01”, “10”, “11”, “000”, “001”, “010”, “011”, “100”, “101”, “110”, and “111” digital elements). To design coding particles using the notched wheel structures, we optimize the coding sequences of the “0”, “1”, “00”,“01”, “10”, “11”, “000”, “001”, “010”, “011”, “100”, “101”, “110”, and “111” by CST Microwave studio with period boundary condition along x- and y- axis direction. The lattice constant of the digital element, the gap and the width of the metal microstrip line are D = 110μm, L = 20μm, and W = 6μm, respectively. From Fig. 1(c), one can see that the reflection phases is at 0, ± 45°, ± 90°, ± 135°, ± 180°, ± 225°, ± 270°, and ± 315° as R = 27μm, 29μm, 30.7μm, 33.4μm, 38.5μm, 47μm, 51.5μm, and 55μm, respectively. Hence, the notched-wheel with scales R = 27μm and 38.5μm can be employed as the 1-bit coding particles “0” and “1”, 2-bit coding particles “00” and “10”, and 3-bit coding particles “000” and “100”. The notched-wheels with scales R = 30.7μm and 51.5μm can be employed as 2-bit coding particles “01” and “11”, and 3-bit coding particles “010” and “110”. At last, the notched-wheels with scales R = 29μm, 33.4μm, 47μm, and 55μm can be employed as 3-bit coding particles “001”, “011”, “101”, and “111”.
Fig. 1 (a) Side-view and (b) top-view schematic of the digital elements, (c) Random coding metasurfaces, (d) The designed 1-, 2-, and 3-bit coding particles using different-scale notched-wheels.
Under the normal incidence of plane wave, the far-field pattern function of the coding metasurfaces can be given by
where andare the length and width of the lattice which are occupied by the “0” or “1”, respectively, θ and φ are the elevation and azimuth angles of an arbitrary direction, respectively. The pattern function of a lattice is eliminated due to the destructive interference between digital elements. Then, the Eq. (1) can be rewritten aswhere and, . When the coding metasurfaces are encoded with periodic coding sequences along x- or y- axis direction, . In which Г is the physical length of a period of the coding sequence. From Eqs. (1) and (2), it can be find that we can change the lattice constant to realize the beam sweeping at the same frequency. Therefore, for the coding metasurface, it means to change the corresponding coding sequence to manipulate the beam sweeping at the same frequency.When terahertz wave is incident onto the coding metasurface, all coding particles are driven by random coding sequence. The reflected terahertz wave energy redistributes in all directions, thereby it can effectively control terahertz wave reflection. Figure 2(a) depicts the reflection responses amplitude of the eight basic coding particles. Figure 2(b) illustrated the reflection phase difference from the digital elements “0” and “1” which is used as the 1-bit coding metasurface. The phase difference ranges from 150° to 213° when the incidence terahertz wave frequency is from 0.76THz to 1.51THz. For the 2-bit coding metasurfaces, the phase difference of the four digital elements “00”, “01”, “10”, “11” is around 90° from 1.0THz to 1.57THz. Furthermore, the phase difference of the eight digital elements “000”, “001”, “010”, “011”, “100”, “101”, “110”, “111” is around 45° from 1.0THz to 1.55THz. According to the figure, one can see that the phase difference of the adjacent coding particle units are approximately 180°, 90° and 45° for the 1-bit, 2-bit and 3-bit digital coding elements, respectively.
2.1 1-bit coding metasurface
For 1-bit coding metasurface, the basic digital elements are “0” and “1” coding particles whose reflection phase difference is 0 and ± 180° with the same amplitude. Here, we design different coding sequences of the 1-bit coding metasurface. A commercial available finite-difference time-domain software, CST Microwave studio, is used to simulate a linearly polarized plane wave normal incidence onto the designed metasurface. The simulated three-dimensional (3D) far-field and two-dimensional (2D) electric-field scattering patterns are shown in Fig. 3. When the metasurfaces with “00000…”coding sequence are arranged along x-direction, the backward scattering wave is reflected according to the opposite direction of the incident terahertz wave, as shown in Figs. 3(a) and 3(b). The metasurface with “00110011…”coding sequences displayed in Fig. 3(c) along x-axis direction is utilized to generate two symmetrical directions reflected waves with the angles of θ = ± 34.6° for the linearly polarized plane wave incidence (see Fig. 3(d)). Similarly, Fig. 3(e) illustrates the coding elements with periodical distributing “001001…” coding sequences along x-axis direction. Figure 3(f) show the results for three pencil-like beams orientated with angles of θ = ± 49.3° and θ = 0° at the linearly polarized plane wave incidence. Then, we use a checkerboard to encode the 1-bit metasurface with the “010101…/101010…” coding sequence and each lattice consists of 3 × 3 arrays “0” or “1” coding particles, the vertical incident linearly polarized plane wave is reflected into four symmetrical main beams with the angle of (θ, φ) = (32.4°, 45°), (θ, φ) = (32.4°, 135°), (θ, φ) = (32.4°, 225°), and (θ, φ) = (32.4°, 315°) at 1.2THz (see Figs. 3(g) and 3(h)). Marvelously, when the each lattice becomes 3 × 6 arrays “0” or “1” coding particles, the four main lobes of the backward scattering waves will appear at the angles of (θ, φ) = (25.1°, 26.6°), (θ, φ) = (25.1°, 153.4°), (θ, φ) = (25.1°, 206.6°), and (θ, φ) = (25.1°, 333.4°), shown in Figs. 3(i) and 3(j).
Fig. 3 Simulated 3D- and 2D- scattering patterns of the coding metasurface with different coding sequences at 1.2THz. (3(a),3(c),3(e)) 3D far-field scattering patterns of the metasurface with the coding sequences “00000…, 00110011…, 001001…,” respectively. Corresponding 2D scattering patterns of the metasurface (3(b),3(d),3(f)); (3(g),3(i))3D far-field scattering patterns of the metasurface with the different lattice sizes of 3 × 3 arrays and 3 × 6 arrays in the chessboard distribution, respectively. (3(j),3(k)) Corresponding 2D scattering patterns with the θ = 32.4°and θ = 25.1°, respectively.
2.2 2-bit coding metasurface
For 2-bit coding metasurfaces, the basic digital elements are “00”, “01”, “10”, and “11” coding particles, whose reflection responses have the same amplitude and four phase states of 0, ± 90°, ± 180°, and ± 270°. Obviously, in order to achieve 2-bit coding metasurfaces, we choose the 90° phase difference of neighboring digital element for our design. The 3D far-field scattering patterns and 2D scattering electric-field patterns have been calculated by using CST Microwave studio with “open” boundary condition at 1.2THz. When a linearly polarized plane wave is vertical irradiated onto the coding metasurfaces with different coding sequences, the corresponding electric field distributions of the reflected terahertz waves are shown in Figs. 4(a)-4(j). In Figs. 4(a) and 4(c) show that four kinds of notched-wheel structures with gradient phase distribution (i.e. a series of the notched-wheel structures are arranged according to the periodic coding sequence “00, 01, 10, 11…”) periodically distributed along x-axis and y-axis direction, respectively. A linearly polarized plane wave is vertical incident onto the designed metasurfaces, then 3D and 2D scattering patterns at the frequency of 1.2THz can be obtained (see Figs. 4(a) and 4(c)). Figures 4(b) and 4(d) show that the backward scattering wave is divided into the direction (θ, φ) = (34.6°, 0°) in the xoz plane or (θ, φ) = (34.6°, 90°) in the yoz plane. The simulated scattering patterns of the 2-bit coding metasurfaces demonstrate the expected manipulation. As an example to demonstrate the capability of such digital metasurface in controlling the reflected terahertz wave, we present the “01” and “11” coding particles with periodic digital sequence of “01, 01, 11, 11…”along x-direction (see in Fig. 4(e)) or y-direction (see in Fig. 4(g)), the reflected terahertz wave energies are split into two symmetrically orientated beams with the angles of θ = ± 34.6° in the xoz plane and in the yoz plane, respectively. The relevant 2D scattering patterns are depicted in Figs. 4(f) and 4(h). The four digital elements (i.e. “00” “01” / “11” “10” coding particles) are periodically distributed in the chessboard and each lattice consists of 3 × 3 one of the equal-sized “00” “01” / “11” “10” digital elements, as shown in Fig. 4(i). The backward reflected terahertz energy will be divided into five main beams and 2D scattering patterns are exhibited in Fig. 4(j). According to these figures, it can be found that the normal reflection of the incoming terahertz wave is sharply suppressed.
Fig. 4 Simulated 3D and 2D scattering patterns of the 2-bit coding metasurfaces with different coding sequences at 1.2THz. (4(a), 4(c)) 3D and (4(b), 4(d)) 2D scattering patterns with the coding sequence “00, 01, 10, 11…”along x- and y-axis direction, respectively. (4(e), 4(g)) 3D- and (4(f), 4(h)) 2D scattering patterns with the coding sequence “01, 01, 11, 11…”along x- and y-axis direction, respectively. 4(i) 3D- and 4(j) 2D- scattering patterns with the coding sequence “00, 01/11, 10…”
2.3 3-bit coding metasurface
In order to make coding metasurface to control the terahertz reflection waves flexibly, we have further designed 3-bit digital metasurfaces with multiple coding sequences. Similarly, 3-bit coding metasurfaces have eight digital elements “000”, “001”, “010”, “011”, “100”, “101”, “110”, and “111”, with the same amplitude and the phases of 0, ± 45°, ± 90°, ± 135°, ± 180°, ± 225°, ± 270°, and ± 315°. When a linearly polarized plane wave is incident onto the designed digital metasurfaces, 3D and 2D scattering patterns of the coding metasurfaces at the frequency of 1.2THz with disparate coding sequence can be obtained, as shown in Figs. 5(a)-5(j). Figures 5(a) and 5(b) or Figs. 5(c) and 5(d) show the simulated 3D and 2D scattering patterns with the periodic digital sequence of “000, 001, 010, 011, 100, 101, 110, 111…” along x-axis or y-axis orientation (i.e. The coding metasurfaces is composed of N × N equal-sized lattices. Each lattice is occupied by one of “000”, “001”, “010”, “011”, “100”, “101”, “110”, and “111” digital elements). One sees that a main lobe clearly appears at xoz plane or yoz plane with the angle of (θ, φ) = (16.5°, 0°) or (θ, φ) = (16.5°, 90°). This mainly produces a 45° constant phase gradient of the coding particles along the x-axis or y-axis direction. As illustrated in Figs. 5(e) and 5(f) or Figs. 5(g) and 5(h), the coding particles have a constant phase gradient of 45°along x- or y-orientation while a phase difference of 180°with a period of two digital elements along the y- or x-orientation. In this case, the scattering patterns will be divided into two symmetrical beams with angles of (θ, φ) = (32.4°, 63.4°), (θ, φ) = (32.4°, −63.4°) or (θ, φ) = (32.4°, −26.6°), (θ, φ) = (32.4°, 153.4°). Likewise, the coding metasurfaces with a period of three basic coding elements along y-orientation and a constant phase gradient of 45° along x-orientation are displayed in Figs. 5(i) and 5(j), which can be used to separate the terahertz incident plane wave into three reflection directions with angles of (θ, φ) = (16.5°, 0°), (θ, φ) = (49.3°, 69.4°), and (θ, φ) = (49.3°, −69.4°), respectively. That is to say, the designed coding metasurfaces can reflect the normal incident terahertz plane wave into arbitrary direction by designing different coding sequences.
Fig. 5 Simulated 3D- and 2D- scattering patterns of the coding metasurfaces at 1.2THz with disparate coding sequence. (5(a), 5(c)) 3D- and (5(b), 5(d)) 2D- scattering patterns with the sequence of “000, 001, 010, 011, 100, 101, 110, 111…”along x-orientation or y-orientation, respectively; (5(e), 5(g)) 3D- and (5(f), 5(h)) 2D- scattering patterns with the sequence that has a 45° constant gradient along x- or y-direction while with a phase difference of 180° in the y- or x-direction; 5(i) 3D- and 5(j) 2D- scattering patterns of the coding metasurface with a period of three coding elements along y-orientation and has a gradient of 45° along x-orientation.
3. Random coding metasurfaces
Here, a 16 × 16 random coding sequences of coding metasurfaces are generated (see Fig. 6). Figure 7 shows the scattering patterns of random coding metasurface at 0.4THz, 1.0THz, 1.55THz, and 1.8THz with a linearly polarized plane wave illumination onto the random coding metasurfaces. Figures 7(a)-7(d) depict 3D-scattering patterns of random coding metasurfaces at 0.4THz, 1.0THz, 1.55THz, and 1.8THz, respectively. To compare the scattering properties of the designed random coding metasurfaces and the same-sized bare metallic plate quantitatively, 2D-scattering patterns of the random coding metasurfaces on the xoz-plane are simulated at the frequency of our interest, as seen in Figs. 7(e)-7(l). In the Figs. 7(i)-7(l), one sees that the backward scattering peak is evident for the same-sized bare metallic plate. However, the backward scattering is sharply suppressed and there exist numerous side lobes for the random coding metasurfaces at 1.0THz and 1.55THz, as seen in Figs. 7(f)-7(g). According to analysis as above, one sees that the incident terahertz wave energy can be reflected to all directions with various coding sequences. Since the coding metasurfaces reflect terahertz wave to numerous directions and produce diffusion waves, according to the law of energy conservation, it lead to reduce the radar cross section (RCS) obviously.
Fig. 7 3D-scattering patterns of the random coding metasurfaces at (a) 0.4THz, (b)1.0THz, (c) 1.55THz, and (d) 1.8THz. 2D-scattering patterns of the random coding metasurface on the xoz plane at (e) 0.4THz, (f)1.0THz, (g) 1.55THz, and (h) 1.8THz. Scattering patterns of the same sized metallic slab on the xoz-plane at (i) 0.4THz, (j)1.0THz, (k) 1.55THz, and (l) 1.8THz.
Figures 8(a)-8(f) show the simulated results of the coding metasurfaces with the 1-bit coding sequence of “0, 0, 1, 1, 0, 0, 1, 1…”along x-axis direction and random coding sequences under linearly polarized, left-handed and right-handed circularly polarized plane waves incidence at 1.2THz on the xoz plane. As shown in Figs. 8(a)-8(c), when the coding metasurfaces with the 1-bit coding sequence of “00110011…” arranged along x-axis direction are illuminated by linearly polarized, left-handed and right-handed circularly polarized plane waves, all of the incidence polarized plane waves are divided into two symmetrically reflected beams with each direction at the angles of 34.6°. Furthermore, the two mainly reflected beams keep the same deflected degrees. Similarly, the coding metasurfaces with random coding sequences will reflect the linearly polarized, left-handed and right-handed circularly polarized plane waves into numerous directions, as shown in Figs. 8(d)-8(f). Thus the designed coding metasurfaces are polarized insensitive. Moreover, the backward scattering is greatly suppressed with approximately −20dB reduction along the surface normal, which leads to a large RCS reduction.
Fig. 8 Simulated results of the coding metasurfaces with the 1-bit coding sequence of “0, 0, 1, 1, 0, 0, 1, 1…”under linearly polarized (a), left-handed (b)and right-handed (c) circularly polarized plane waves incidence at 1.2THz on the xoz-plane. Simulated results of the coding metasurfaces with random coding sequence under linearly polarized (d), left-handed (e) and right-handed (f) circularly polarized plane waves incidence at 1.2THz on the xoz-plane.
4. Conclusion
To sum up, we have presented 1-bit, 2-bit, and 3-bit polarization insensitive coding metasurfaces for dynamical manipulation of the scattering patterns. The metasurfaces are composed of top layer notched-wheel metallic patterns and bottom layer metallic ground plate separated by a polyimide film. The coding metasurfaces are demonstrated to flexibly control the terahertz waves with exceedingly RCS reduction. Additionally, the polarization insensitivity of the coding metasurfaces are confirmed by using linearly polarized, left-handed and right-handed circularly polarized plane wave illumination the coding metasurfaces. The presented functional device has great application potential in terahertz wave communication and imaging systems.
Funding
National Natural Science Foundation of China (Grant No. 61379024), National Quality Infrastructure Program of China (2016YFF0200306).
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