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Abstract
Multifunctional coding metasurfaces (CMs) have attracted extensive attention due to their ability to realize the multifunctional integration in optical devices. However, the researches on multifunctional CM mainly focus on dual functionality in reflected or transmitted space. Here, based on “Fabry-Pérot-like” cavity, we propose a novel multifunctional CM to simultaneously control different polarized light in full-space. It is revealed that the designed CM possesses asymmetric transmission characteristic, which can simultaneously achieve three different functionalities by changing the polarization state and the propagation direction of incident light. As a proof of concept, a single CM is designed to simultaneously realize the functionalities of beam splitting, diffusion scattering for co-polarized reflection and beam focusing for cross-polarized transmission. The simulated results are consistent with the experimental results, which demonstrates the feasibility of the design. This finding provides an effective approach to design multifunctional devices with miniaturization and high integration, which can also be used to achieve desired functionalities in other frequency domains.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Controlling the electromagnetic (EM) properties of light as desired is the foundation and core of modern optical devices and communication systems. As an artificial metamaterials, metasurfaces have attracted significant interest from researchers, owning to their extraordinary performance in manipulating EM waves [1–5]. Many significant applications were realized based on metasurfaces, such as vortex-beam generation [6–8], holographic imaging [9–11], and diffusion scattering [12–16]. Since Cui et al put forth the concept of coding metasurface (CM) which combines metasurfaces with binary codes, metasurfaces have been developing rapidly [18]. On this basis, some digital metasurfaces and programmable metasurfaces were designed which can dynamically control the EM wave with the aid of biased diodes and field-programmable gate array [17–20]. Except for its physical features, CM also possesses the characteristic of information. In order to explore the application of CM in modern information systems, a method for measuring the information of a CM was proposed by using Shannon entropy [21]. In 2017, the concept of coding phase gradient metasurface was proposed by simultaneously controlling the primary pattern and array pattern, which provides a more flexible strategy to manipulate the EM wave [22]. On the other hand, by considering the temporal dimension, the theory of space-time-coding digital metasurface was proposed which broadened the applications of CM significantly [23]. With the rapid development of machine-learning, some intelligent methods to improve the efficiency of designing metasurface using machine-learning are reported in recent years [24–26].
Although many significant achievements have been made, most metasurfaces so far cannot satisfy the demands of modern integration systems because of the simple function. Various multifunctional metasurfaces come into being in this condition. One of the solutions is designing active metasurfaces, which can achieve diversified functionalities in a single device and these functionalities can be adjusted dynamically [18–21,37]. But the design and machining process of active metasurfaces are very complicated which extremely restricts their application. Besides, many passive multifunctional metasurfaces have been demonstrated recently, in which anisotropic metasurfaces [27–32] and helicity dependent metasurfaces [33–36] are the two mainstreams. By changing the polarization and helicity of incident waves, two different functionalities can be achieved in a single device. Meanwhile, frequency dependent metasurfaces [38] and isotropic holographic metasurfaces [39] are proposed to design dual-functional devices. Nevertheless, most of the existing multifunctional metasurfaces are bifunctional metasurfaces. In addition, these multifunctional metasurfaces can only control EM waves in either reflected wavefronts or transmitted wavefronts, and the other space is unmodulated. So, the modulation of EM waves in full-space is still a challenging task in multifunctional CM.
In this paper, we propose a novel multifunctional CM which can simultaneously modulate different polarized EM waves in full-space. The proposed CM subtly combines the anisotropic CM with the “Fabry-Pérot-like” cavity, which can achieve three functionalities by changing the polarization state and propagation direction of incident EM waves. In addition, the multifunctional CM based on “Fabry-Pérot-like” possesses asymmetric transmission characteristic and can be used as a linear polarization converter. As a proof of concept, we design three different patterns in a single CM, including beam splitting and diffusion scattering for co-polarized reflection, beam focusing for cross-polarized transmission, and the schematic diagram is shown in Fig. 1. We experimentally demonstrate that the designed multifunctional CM can achieve three different functionalities. This results indicate that the combination of anisotropic CM and “Fabry-Pérot-like” cavity is an effectively strategy to realize full-space light control for the passive device, which may have profound effect on the development of optical devices.
Fig. 1 The schematic of the proposed multifunctional CM. (a) The metasurface can achieve diffusion scattering for co-polarized reflection and beam focusing for cross-polarized transmission. (b) Beam splitting for co-polarized reflection and beam focusing for cross-polarized transmission can be achieved by changing the propagation direction of incident EM wave.
2. Design of the unit cell
The design objective is to modulate EM wave in full-space, and the “Fabry-Pérot-like” cavity provides an excellent reference model. Metasurfaces composed of “Fabry-Pérot-like” cavity can achieve high performance linear polarization conversion and anomalous refraction in transmission mode, which had been proved in 2013 [5]. The schematic of the “Fabry-Pérot-like” cavity is shown in Fig. 2, two orthogonal metal gratings serve as the top and bottom of the unit cell, respectively, and in the middle is an oblique metal structure. The oblique metal structure of the middle layer can be used as a linear polarization conversion structure, and the two orthogonal metal gratings act as metal backboards for cross-polarized waves reflected or transmitted by polarization converted structures. Therefore, the whole structure forms a “Fabry-Pérot-like” cavity and can be acted as linear polarization converter for transmitted wave. When normally incident y-polarized wave propagates along the -z direction, the upper metal grating acts as a metal backboard and y-wave is reflected efficiently. However, for normal incident x-polarized wave along the -z direction, it can pass through the upper metal grating and be converted into y-polarized wave efficiently since the upper metal grating is placed along the y direction. The phase of transmission can be controlled by changing the physical dimension of the oblique metal structure.
It is worth stressing that the conventional transmission-type CM based on “Fabry-Pérot-like” cavity only modulate the transmitted wave-fronts, whereas the reflected wave-fronts have not been exploited. In our design, the unit cell is designed by combining the “Fabry-Pérot-like” cavity with anisotropic unit cell, which can control the transmitted and reflected wave-fronts simultaneously. The transmitted wave-fronts and reflected wave-fronts are manipulated by the “Fabry-Pérot-like” cavity and anisotropic unit cell, respectively. More importantly, the unit cell possesses the characteristics of polarization dependent and asymmetrical transmission. In order to express the EM characteristics of a certain unit cell (m,n) more clearly, four Jones matrixes can be adopted:
where Ri(m,n) and Ti(m,n) represent the Jones matrixes of the unit cell for the reflected and transmitted mode, respectively, and the subscript f and b respectively represent the forward and backward incidence. , and denote the co-polarized reflection coefficients, , and denote the cross-polarized transmission coefficients. From the Jones matrixes above, it is seen that different polarized wave in the full-space can be modulated. Due to the reciprocity and non-magnetic properties, the transmission coefficients and are equal. Therefore, the designed unit cell possesses asymmetric transmission characteristic. In the ideal case, |ryy(m,n)| = |rxx(m,n)| = |tyx(m,n)| = |txy(m,n)| = 1, reflected phase φyy(m,n), φxx(m,n) and transmitted phase φxy(m,n) (or φyx(m,n)) can be engineered independently to implement the desired functionalities.According to the above analysis, a special unit cell is designed. As shown in Fig. 3(a), the unit cell is composed of multilayer structure with the period p = 5 mm, and including two FR4 substrates (εr = 4.3, tan (δ) = 0.025) with the thickness of h1 = 0.1 mm, two polymethacrylimide (PMI) foam substrates (εr = 1.1) with the thickness of h2 = 1.5 mm, two F4B substrates (εr = 2.65, tan (δ) = 0.001) with the thickness of h3 = 1.5 mm and five copper layers with thickness of 0.017 mm. The reason for using PMI foam is that it has little negative effect on transmitted amplitudes of cross-polarized wave. At the top and bottom of the unit cell are two orthogonal “I” shaped anisotropic structures (Figs. 3(b) and 3(d)), and they are parallel to the upper and lower metal gratings, respectively. In the middle of the unit cell is a “split ring” shaped which is canted 45° (Fig. 3(c)).
Fig. 3 Geometrical parameters and the surface current distributions of the multilayer unit cell. (a) The overall structure of the unit cell. (b) The “I” shaped anisotropic structures at the bottom. (c) The middle “split ring” shaped. (d) The “I” shaped anisotropic structures at the top. (e), and (f) The surface currents of the unit cell illuminated by y-polarized and x-polarized wave propagating along -z direction, respectively. (g), and (h) The surface currents of the unit cell illuminated by x-polarized and y-polarized wave propagating along + z direction, respectively.
To verify the design CM, the numerical simulations are carried out by using the commercial software program CST Microwave Studio. In the simulation, the x and y directions are set as the unit cell boundary, and the direction of z is set as open (add space) boundary. When y-polarized wave propagates along -z direction, the upper metal grating can be equivalent to a metal backboard and the incident y-polarized wave is reflected efficiently. The normally incident y-polarized wave can be manipulated by change the length (l1) of the upper “I” shaped. Figure 3(e) show the surface current of the unit cell at 21 GHz illuminated by y-polarized wave propagating along -z direction, and the surface current indicates that the y-polarized wave is completely reflected. When the polarized direction of incident wave changed from y-polarized to x-polarized, the simulated surface current at 16 GHz is shown in Fig. 3(f). The surface current shows that the normally incident x-polarized wave can pass through the middle “Fabry-Pérot-like” cavity and be converted into y-polarized wave without being affected by the upper and lower “I” shaped. On the contrary, when the direction of propagation of incident wave changed from -z to + z, the x-polarized wave is completely reflected (see Fig. 3(g)). However, y-polarized wave can pass through the middle “Fabry-Pérot-like” cavity and be converted into x-polarized wave (see Fig. 3(h)). All the simulated results above indicate that the unit cell has the characteristics of both polarization isolation and asymmetrical transmission. Hence, the designed multilayer unit cell meet our design objective and can be adopted to design the multifunctional CM.
3. Design of the multifunction
Based on the proposed unit cell, a multifunctional CM can be designed which can simultaneously control EM waves with reflected mode and transmitted mode. As a proof of concept, we design three different functionalities. For the reflected mode, the functionalities of diffusion scattering and beam splitting are respectively designed at the top and bottom. For transmitted mode, the CM works as a lens which can focus the beam and has the characteristic of asymmetrical transmission. These functionalities are not unalterable, and they can be designed flexibly based on the requirements in actual application.
Firstly, the reflected mode is analyzed, which is controlled by the upper and lower “I” shaped. When y-polarized wave propagates along -z direction, the reflected phase can be manipulated by the length l1. For 2-bit CM, the length l1 are optimized as 1.4 mm, 3.55 mm, 3.94 mm, and 4.46 mm at 21 GHz, while keep other geometrical parameters unchanged (l2 = 0.5 mm, l3 = 1.5 mm, l4 = 3.94 mm, w1 = 0.1 mm, w2 = 0.2 mm, w3 = 0.3 mm, s = 1.93 mm, r = 2.2 mm). The reflected amplitudes and phases of co-polarized wave (Ryy) are shown in Fig. 4(a). It is found that the reflected amplitudes are more than 90% within 18–26 GHz, and the reflected phase meets the design requirements of 2-bit CM around 21GHz. Meanwhile, the transmitted amplitudes and phases of cross-polarized wave (Tyx) are simulated (see Fig. 4(b)), and the simulated results indicate that they are insensitive to the l1, which further supports the characteristic of polarization isolation. In the design, the CM consists of 48 × 48 unit cells with a size of 240 × 240 mm2. In order to achieve diffusion scattering, the 2-bit random coding pattern is optimized by using fast coding method [12], and the phase distribution is shown in Fig. 5(a). In theory, the radar cross section (RCS) of the metasurface is reduced due to the diffusion scattering. The 3D RCS pattern of the metasurface under incident y-polarized plane wave propagating along -z direction at 21 GHz is shown in Fig. 5(d). The simulated mono-static RCS of the CM is shown in Fig. 5(f) (the red line), and the results indicate that the RCS reduction is more than 10 dB within the frequency band 19–22.7 GHz, compared with a same size metal plate.
Fig. 4 The reflection and transmission amplitudes and phase when changing l1. (a) The reflected amplitudes and phase of co-polarized wave (Ryy). (b) The transmitted amplitudes and phase of cross-polarized wave (Tyx).
Fig. 5 The designed coding patterns and simulated results.(a) The optimized 2-bit random coding pattern for reflected mode under y-polarized wave toward the -z direction. (b) The 1-bit chessboard coding pattern for reflected mode under x-polarized wave toward + z direction. (c) The focused phase distribution for transmitted mode. (d) The 3D RCS pattern of the CM under y-polarized normally incident plane wave propagating along -z direction at 21 GHz. (e), and (g) The 3D RCS and 2D far-field patterns of the CM under x-polarized normally incident plane wave propagating along + z direction at 21 GHz. (f) Monostatic RCS of the metal plate and the CM with random coding and chessboard pattern.
In addition, if the propagation direction of the incident plane wave is changed from –z to + z, the x-polarized wave is reflected and the reflected phase is manipulated by the length l4. In this situation, a 1-bit chessboard coding pattern is designed (as shown in Fig. 5(b)), and the length l4 are optimized as 1.4 mm and 3.55 mm at 21 GHz. The corresponding reflected amplitudes and phases of polarized wave (Rxx) are same as the Ryy in Fig. 4(a). Under the normal incidence of plane waves, the direction (elevation angle θ, azimuth angle φ) of the anomalous reflection waves can be obtained by Eqs. (5) and (6) [27]:
where 𝜆 is the free-space wavelength, Hx and Hy are the lengths of the coding sequence along x direction and y direction respectively, and Dx and Dy are the lengths of one period of the gradient phase along the x direction and y direction respectively. According to Eqs. (5) and (6), the incident x-polarized wave is split into four symmetrical pencil beams (φ = 45°, 135°, 225°, 315°; θ = 42.3°). Since the wave is split into four large angle beams, the RCS of the CM has also be reduced. The simulated 3D and 2D far-field scattering patterns of the metasurface under x-polarized normally incident plane wave propagating along + z direction at 21 GHz are shown in Figs. 5(e) and 5(g) respectively. The results show that the normally incident wave is split into four symmetrical pencil beams, and is in good agreement with theoretical value. The Fig. 5(f) (the blue line) depicts the simulated the RCS of the metasurface, and the RCS reduction of the metasurface is more than 10 dB within the frequency band 20.5–22.3 GHz compared with a same size metal plate.For the transmitted mode of the metasurface, the design goal is to focus the beam, and the coverage range of phase need to reach 360°. The phase of cross-polarized transmission is controlled by the opening width s of the middle “split ring” shaped. As x-polarized wave propagates along -z direction, the function relation between cross-polarization transmission amplitude, phase of the cross-polarized wave (Tyx) and the opening width s at 16GHz are shown Figs. 6(a) and 6(b) respectively. It can be observed that the cross-polarization transmission amplitude is more than 90%, and the phase can span 180° (black line in Fig. 6(b)). The another 180° phase is obtained by turning the split ring 90° around its center (the red line in the Fig. 6(b)). Meanwhile, the inset in Fig. 6(a) depicts the functions of the cross-polarization transmission amplitude and phase with frequency when the opening width s is fixed as 2.5 mm. It is found that the cross-polarization transmission amplitude is more than 90% in a wide frequency band (12-18 GHz). To achieve beam focusing, a hyperbolic phase profile is designed, which can be expressed as:
where k0 is the free-space wave-vector, L denotes the focal length and φ(x,y) denotes the phase at the coordinate (x,y). In the design, 36 different types of the unit cells (one for every 10°) are used to achieve the beam focusing with L = 200 mm at 16 GHz, and the phase distribution is shown in Fig. 5(c). The focal length at other frequencies can be calculated by Eqs. (7). In order to verify the effect of the beam focusing, numerical simulations are carried out for the distributions of electric fields. Under x-polarized wave toward the -z direction, the simulated Ey and |Ey| components of electric fields at 16 GHz in yoz plane are shown in Figs. 6(c) and 6(e) respectively. From the simulated results, it can be clearly see that the incident x-polarized wave can pass through the CMs and be converted into y-polarized wave. Then the converted y-polarized is focused, and the focal length is about 200 mm which is consistent with the theoretical design. Moreover, the designed CM has the asymmetrical transmission characteristic. When the propagation direction of the incident plane wave is changed from -z to + z, the x-polarized is reflected efficiently, while the y-polarized can pass through the CM and be focused. The corresponding Ex and |Ex| components of electric fields in yoz plane are shown in Figs. 6(d) and 6(f) respectively. The efficiency of beam focusing, defined by the ratio of the powers carried by the focal spot and the incident beam [30], almost reaches 71.8% for the simulation at 16 GHz. The simulated results clearly indicate that the incident y-polarized wave is converted into x-polarized wave and is focused.Fig. 6 The transmission amplitude and phase of the cross-polarized wave (Tyx) and the simulated distributions of electric fields at 16GHz. (a) The simulated transmission amplitude of the cross-polarized wave (Tyx). The inset depicts the function of the transmission amplitude with frequency (s = 2.5 mm). (b) The simulated transmission phase of the cross-polarized wave (Tyx). (c), and (e) The simulated Ey and |Ey| components of electric fields in yoz plane under x-polarized wave toward the -z direction. (d), and (f) The simulated Ex and |Ex| components of electric fields in yoz plane under y-polarized wave toward the + z direction.
All the simulated results meet the expectations, which preliminarily proves the feasibility and validity of the designed multifunctional CMs. These functionalities are just designed as an example to demonstrate the proposed design strategy for multifunctional CMs. It needs to be emphasized that in addition to the above functionalities, any different functionalities can be integrated in the CM by designing corresponding coding patterns, such as holograms, orbital angular momentum, which are not go into detail here for brevity.
4. Fabrication and measurement
To further verify the designed multifunctional CMs, one sample was fabricated by printed circuit board (PCB) technology. The components of the fabricated sample are shown in Fig. 7(a). The measurements are carried out in an anechoic chamber, and the entire measurement is divided into two sections: specular reflectivity of the reflected mode and electric field of the transmitted mode. In the measurement of specular reflectivity, a pair of identical horn antennas are used as transmitter and receiver respectively. The two horn antennas are placed closed together, and the distance between the sample and the horn antennas is about 2m. The measured specular reflectivities of the CM with chessboard and random coding patterns are shown in Fig. 7(b). The measured results indicate that the 10 dB specular reflectivity reduction is achieved from 20.5 GHz to 24.5 GHz for the checkerboard coding pattern, and 18.2 GHz to 24.9 GHz for the random coding pattern. The experiment results are in agreement with the simulated results, and a few differences are probably due to machining accuracy. The measured Ey and |Ey| components of electric fields at 16 GHz in yoz plane under x-polarized wave toward the -z direction shown in Figs. 7(c) and 7(e), respectively. The results show that the focal length L is about 210 mm, which is agreement with simulation result (L = 200 mm). Figures 7(d) and 7(f) show the measured Ex and |Ex| components of electric fields at 16 GHz in yoz plane under y-polarized wave toward the + z direction, respectively. It can be seen that the focal length L is about 200 mm. All the experimental results coincide with the simulated results, which verify the accuracy of the design.
Fig. 7 The fabricated sample and measured results. (a)The photograph of the sample. (b) Measured specular reflectivities of the CM with chessboard and random coding patterns. (c), and (e) Measured Ey and |Ey| components of electric fields at 16 GHz in yoz plane under x-polarized wave toward the -z direction. (d), and (f) Measured Ex and |Ex| components of electric fields at 16 GHz in yoz plane under y-polarized wave toward the + z direction.
5. Conclusions
To sum up, a general strategy for designing multifunctional metadevices which can modulate different polarized EM wave in full-space has been proposed. With the characteristics of asymmetric transmission and polarization isolation, the proposed strategy can achieve three different functionalities simultaneously. As a demonstration, three different coding patterns are designed and integrated in a single CM. All the simulated results accord with experiment results, which indicates the versatility of the design. The designed CM has potential applications in common-caliber antennas and radomes. Moreover, the work frequency of the CM can be extended to optical, terahertz and other frequency regimes, and the functionalities can be designed to satisfy the needs of different situations. Our strategy simplifies the design of multifunctional metadevice and facilitates the development of photonic integration and device miniaturization.
Funding
National Natural Science Foundation of China (61331005); Youth Talent Lifting Project of the China Association for Science and Technology (17-JCJQ-QT-001).
References
1. 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]
2. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science 335(6067), 427 (2012). [CrossRef] [PubMed]
3. C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O’Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012). [CrossRef]
4. F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Applied optics. Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015). [CrossRef] [PubMed]
5. N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013). [CrossRef] [PubMed]
6. P. Genevet, N. F. Yu, F. Aieta, J. Lin, M. A. Kats, R. Blanchard, M. O. Scully, Z. Gaburro, and F. Capasso, “Ultra-thin plasmonic optical vortex plate based on phase discontinuities,” Appl. Phys. Lett. 100(1), 013101 (2012). [CrossRef]
7. J. T. Heiden, F. Ding, J. Linnet, Y. Yang, J. Beermann, and S. I. Bozhevolnyi, “Gap‐Surface Plasmon Metasurfaces for Broadband Circular‐to‐Linear Polarization Conversion and Vector Vortex Beam Generation,” Adv. Opt. Mater. 7(9), 1801414 (2019). [CrossRef]
8. M. Q. Mehmood, S. Mei, S. Hussain, K. Huang, S. Y. Siew, L. Zhang, T. Zhang, X. Ling, H. Liu, J. Teng, A. Danner, S. Zhang, and C.-W. Qiu, “Visible‐frequency metasurface for structuring and spatially multiplexing optical vortices,” Adv. Mater. 28(13), 2533–2539 (2016). [CrossRef] [PubMed]
9. L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K. W. Cheah, C. W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4(1), 2808 (2013). [CrossRef]
10. W. T. Chen, K. Y. Yang, C. M. Wang, Y. W. Huang, G. Sun, I. D. Chiang, C. Y. Liao, W. L. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, and D. P. Tsai, “High-efficiency broadband meta-hologram with polarization-controlled dual images,” Nano Lett. 14(1), 225–230 (2014). [CrossRef] [PubMed]
11. X. Li, L. Chen, Y. Li, X. Zhang, M. Pu, Z. Zhao, X. Ma, Y. Wang, M. Hong, and X. Luo, “Multicolor 3D meta-holography by broadband plasmonic modulation,” Sci. Adv. 2(11), e1601102 (2016). [CrossRef] [PubMed]
12. Y. Jing, Y. F. Li, J. Q. Zhang, J. F. Wang, M. C. Feng, S. Sui, T. S. Qiu, H. Ma, and S. B. Qu, “Fast coding method of metasurfaces based on 1D coding in orthogonal directions,” J. Phys. D Appl. Phys. 51(47), 475103 (2018). [CrossRef]
13. X. M. Fu, J. F. Wang, Y. Fan, J. Yang, Y. X. Jia, Y. F. Li, M. B. Yan, J. Q. Zhang, and S. B. Qu, “Lightweight Ultra-Wideband RCS Reduction Structure using Double-Layer Metasurfaces,” J. Phys. D Appl. Phys. 52(11), 115103 (2019). [CrossRef]
14. K. Chen, L. Cui, Y. Feng, J. Zhao, T. Jiang, and B. Zhu, “Coding metasurface for broadband microwave scattering reduction with optical transparency,” Opt. Express 25(5), 5571–5579 (2017). [CrossRef] [PubMed]
15. M. Moccia, S. Liu, R. Y. Wu, G. Castaldi, A. Andreone, T. J. Cui, and V. Galdi, “Coding metasurfaces for diffuse scattering: scaling laws, bounds, and suboptimal design,” Adv. Opt. Mater. 5(19), 1700455 (2017). [CrossRef]
16. 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]
17. T. J. Cui, M. Q. Qi, X. Wan, J. Zhao, and Q. Cheng, “Coding metamaterials, digital metamaterials and programmable metamaterials,” Light Sci. Appl. 3(10), e218 (2014). [CrossRef]
18. X. Wan, M. Q. Qi, T. Y. Chen, and T. J. Cui, “Field-programmable beam reconfiguring based on digitally-controlled coding metasurface,” Sci. Rep. 6(1), 20663 (2016). [CrossRef] [PubMed]
19. Y. B. Li, L. L. Li, B. B. Xu, W. Wu, R. Y. Wu, X. Wan, Q. Cheng, and T. J. Cui, “Transmission-type 2-bit programmable metasurface for single-sensor and single-frequency microwave imaging,” Sci. Rep. 6(1), 23731 (2016). [CrossRef] [PubMed]
20. H. X. Xu, S. Tang, S. Ma, W. Luo, T. Cai, S. Sun, Q. He, and L. Zhou, “Tunable microwave metasurfaces for high-performance operations: dispersion compensation and dynamical switch,” Sci. Rep. 6(1), 38255 (2016). [CrossRef] [PubMed]
21. T. J. Cui, S. Liu, and L. L. Li, “Information entropy of coding metasurface,” Light Sci. Appl. 5(11), e16172 (2016). [CrossRef] [PubMed]
22. Q. Q. Zheng, Y. F. Li, J. Q. Zhang, H. Ma, J. F. Wang, Y. Q. Pang, Y. J. Han, S. Sui, Y. Shen, H. Y. Chen, and S. B. Qu, “Wideband, wide-angle coding phase gradient metasurfaces based on Pancharatnam-Berry phase,” Sci. Rep. 7(1), 43543 (2017). [CrossRef]
23. L. Zhang, X. Q. Chen, S. Liu, Q. Zhang, J. Zhao, J. Y. Dai, G. D. Bai, X. Wan, Q. Cheng, G. Castaldi, V. Galdi, and T. J. Cui, “Space-time-coding digital metasurfaces,” Nat. Commun. 9(1), 4334 (2018). [CrossRef] [PubMed]
24. L. Li, H. Ruan, C. Liu, Y. Li, Y. Shuang, A. Alù, C. W. Qiu, and T. J. Cui, “Machine-learning reprogrammable metasurface imager,” Nat. Commun. 10(1), 1082 (2019). [CrossRef] [PubMed]
25. X. Lin, Y. Rivenson, N. T. Yardimci, M. Veli, Y. Luo, M. Jarrahi, and A. Ozcan, “All-optical machine learning using diffractive deep neural networks,” Science 361(6406), 1004–1008 (2018). [CrossRef] [PubMed]
26. T. S. Qiu, X. Shi, J. F. Wang, Y. F. Li, S. B. Qu, Q. Cheng, T. J. Cui, and S. Sui, “Deep Learning: A Rapid and Efficient Route to Automatic Metasurface Design,” Adv. Sci. 6(12), 1900128 (2019). [CrossRef]
27. S. Liu, T. J. Cui, Q. Xu, D. Bao, L. Du, X. Wan, W. X. Tang, C. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. Han, W. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light Sci. Appl. 5(5), e16076 (2016). [CrossRef] [PubMed]
28. L. Zhang, R. Y. Wu, G. D. Bai, H. T. Wu, Q. Ma, X. Q. Chen, and T. J. Cui, “Transmission‐reflection‐integrated multifunctional coding metasurface for full‐space controls of electromagnetic waves,” Adv. Funct. Mater. 28(33), 1802205 (2018). [CrossRef]
29. H. F. Ma, G. Z. Wang, G. S. Kong, and T. J. Cui, “Independent controls of differently-polarized reflected waves by anisotropic metasurfaces,” Sci. Rep. 5(1), 9605 (2015). [CrossRef] [PubMed]
30. T. Cai, S. Tang, G. Wang, H. Xu, S. Sun, Q. He, and L. Zhou, “High‐performance bifunctional metasurfaces in transmission and reflection geometries,” Adv. Opt. Mater. 5(2), 1600506 (2017). [CrossRef]
31. H. X. Xu, S. Tang, X. Ling, W. Luo, and L. Zhou, “Flexible control of highly‐directive emissions based on bifunctional metasurfaces with low polarization cross‐talking,” Ann. Phys. 529(5), 1700045 (2017). [CrossRef]
32. F. Aieta, P. Genevet, N. Yu, M. A. Kats, Z. Gaburro, and F. Capasso, “Out-of-plane reflection and refraction of light by anisotropic optical antenna metasurfaces with phase discontinuities,” Nano Lett. 12(3), 1702–1706 (2012). [CrossRef] [PubMed]
33. H. X. Xu, S. Sun, S. Tang, S. Ma, Q. He, G. M. Wang, T. Cai, H. P. Li, and L. Zhou, “Dynamical control on helicity of electromagnetic waves by tunable metasurfaces,” Sci. Rep. 6(1), 27503 (2016). [CrossRef] [PubMed]
34. L. L. Huang, X. Z. Chen, B. F. Bai, Q. F. Tan, G. F. Jin, T. Zentgraf, and S. Zhang, “Helicity dependent directional surface plasmon polariton excitation using a metasurface with interfacial phase discontinuity,” Light Sci. Appl. 2(3), e70 (2013). [CrossRef]
35. D. D. Wen, S. M. Chen, F. Y. Yue, K. L. Chan, M. Chen, M. Ardron, K. F. Li, P. W. H. Wong, K. W. Cheah, E. Y. B. Pun, G. X. Li, S. Zhang, and X. Z. Chen, “Metasurface device with helicity-dependent functionality,” Adv. Opt. Mater. 4(2), 321–327 (2016). [CrossRef]
36. L. Zhang, S. Liu, L. Li, and T. J. Cui, “Spin-Controlled Multiple Pencil Beams and Vortex Beams with Different Polarizations Generated by Pancharatnam-Berry Coding Metasurfaces,” ACS Appl. Mater. Interfaces 9(41), 36447–36455 (2017). [CrossRef] [PubMed]
37. R. Y. Wu, L. Zhang, L. Bao, L. Wu, Q. Ma, G. Bai, H. Wu, and T. Cui, “Digital metasurface with phase code and reflection–transmission amplitude code for flexible full space electromagnetic manipulations,” Adv. Opt. Mater. 7(8), 1801429 (2019). [CrossRef]
38. S. Liu, L. Zhang, Q. L. Yang, Q. Xu, Y. Yang, A. Noor, Q. Zhang, S. Iqbal, X. Wan, Z. Tian, W. X. Tang, Q. Cheng, J. G. Han, W. L. Zhang, and T. J. Cui, “Frequency-dependent dual-functional coding metasurfaces at terahertz frequencies,” Adv. Opt. Mater. 4(12), 1965–1973 (2016). [CrossRef]
39. Y. B. Li, B. G. Cai, Q. Cheng, and T. J. Cui, “Isotropic Holographic Metasurfaces for Dual-Functional Radiations without Mutual Interferences,” Adv. Funct. Mater. 26(1), 29–35 (2016). [CrossRef]
