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Abstract
Coding metasurfaces have drawn great attention for its digital wave manipulation in deep subwavelength-scale in the last decade, more sophisticated and flexible coding strategies suitable for terahertz wavefront manipulations are becoming more urgently demanded. Due to its rigidity in phase gradient division, both phase gradient metasurfaces and conventional phase coding technique lack the flexibility to expand applications in a large field of view and accurate targeting. This study presents a generalized coding method by precisely reconfiguring the array factor based on the phased array theory and metasurface concept, which can be applied for anomalous scattering and ultrafine radiation patterning. According to our quantitative analysis on the relationship between the deflected angles and the supercell spacing, a fractional coding method for arbitrary phase gradient distribution has been attained by logically discretizing the spacing scale of supercells. By switching on different coding sequences or incident frequencies, a single beam to multiple beam scanning in an expanded angular range with minimal step can be achieved on the fractional phase-coding metasurfaces. As a proof of concept, the 2-bit coding metasurfaces arranged by four fractional coding sequences have been fabricated and measured, demonstrating a consecutive single-beam steering pattern ranging from 22° to 74° in 0.34-0.5 THz. Crosswise verified by the good accordance among numerical prediction, simulation and experiment, the proposed coding strategy paves a path to delicate beam regulation for high-resolution imaging and detection.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Advanced beam steering holds the key to implement imaging and wireless communication in the terahertz range. Due to the lack of efficient dynamic components and regulation strategy, the applicable terahertz scanning system with fast reconfigurability and large field of view is still in its infancy. Metasurfaces, artificially formed by 2-D periodic metallic or dielectric subwavelength structures, have attracted intense attention due to its exotic electromagnetic functionalities, such as polarization manipulation [1–3] and splitting [4,5], holograms [6–9], focusing [10,11], frequency filtering [12,13], beam steering [14–16], and so on. By engineering the subwavelength scaled resonating meta-atoms, metasurfaces enable an effective means to tailor the terahertz wavefront in terms of amplitude, phase, and/or polarization, with wider dynamic range and higher integration level.
Inspired by the seminal work of Yu et al., the Generalized Snell’s Laws were proposed to get more freedom on the designs of devices at THz regions instead of traditional approaches relying on the accumulation of phase delays during wave propagation [17]. Various metasurfaces were investigated for introducing a phase gradient along with the beam path to realize terahertz beam control. Static metasurfaces generate the abrupt phase changes by arranging phase shift units according to phase distributions based on the Generalized Snell’s Laws [18–21]. Other approaches via electrical control, optical control, and frequency control can dynamically reconfigure phase gradients to a certain extent [22,23]. Due to beams can be manipulated by phase gradients and incidence frequencies, Space-time-coding digital metasurfaces are proposed to achieve combined controls [24]. Since 2014, Prof. Cui has put forward the digital metamaterials to bridge between the physical field and the information world, entailing great research enthusiasm worldwide [25–28]. For fast programmable terahertz beam manipulation, digital metasurfaces have been proposed and attracted wide attention. Expectantly, substituted by the binary codes “0” and “1” for its phase responses, the digital metamaterials can exploit limited codes to realize flexible and enormous applications. 1D coding metasurfaces with a one-dimensional phase gradient and 2D coding metasurfaces with two-dimensional phase gradients respectively regulate beams on a spatial plane and whole 3D space [29]. Further, supercells consisting of square arrangements of N × N identical anisotropic cells have been demonstrated to reduce the undesired coupling effect resulting from adjacent units with different structures as the dual-polarization beam control [27]. By engineering anisotropic coding matrixes, the dual-polarization beams can be manipulated as multiple beams, and be real-time reconfigurable by active elements [30]. Above coding metasurfaces can be categorized as the uniform coding strategy because the combination number of in-phase binary codes are consistent, in other words, the spacing of in-phase cells are uniform. However, for deeply digging the potential for multiple functionalities and precise regulations, non-uniform coding strategies have been proposed to break through the boundaries of the conventional wavefront control. Random coding enables each unit cell to radiate along with a random direction to scatter the radiation energy [25]. By performing Fourier operations and the convolution theorem, a synthesized scattered beam along with a predesigned direction has been generated via a non-uniform coding sequence [31,32]. By integrally dividing the coding period, the phase shift states have been prorated distribution to constitute a non-uniform coding period also can improve the continuity of beam steering to a certain extent [33]. Nonetheless, the existed coding methodologies have extended the analog phase gradient period into digital division, a more elaborate digital phase quantification still needs to be studied.
Within this framework, to address further levels of technical sophistication of the advanced THz super-resolution imaging, a flexible coding strategy with more degree of freedom has been theoretically introduced and experimentally verified by a proof-of-concept reflectarray. Starting with the analysis of beam deflecting by the metasurface reflectarray, we combine the Generalized Snell’s Laws and the phased array theory to illustrate the supercell spacing as a key restructure variable related to the scanning angles. By fractionally dividing the phase gradient distribution, we further propose a logically fractional coding strategy and show that this method can be easily performed by a coding-generation formula. The catalysis of the proposed idea for radiation patterning accuracy has been numerically demonstrated with a series of logically fractional coding sequences. As a demonstration of the proposed method, the measurement on six pieces of 2-bit coding metasurfaces have corroborated the effectiveness of the logically fractional coding strategy by consistent results with the theoretical prediction and full-wave simulation, which indicates that the coding metasurfaces with the novel coding strategy not only improved the flexibility and continuity of the phase-regulated far-field scanning but also laterally extend the frequency-sweeping solution for non-dynamic-component scanning.
2. Method
Traditional coding metasurfaces, based on the generalized Snell’s law, realized beam steering by uniformly engineering the phase gradients distribution at a certain frequency band. To discretize the phase gradient for digital implementation, the unit cells with 0° and 180° phase responses represent the “0” and “1” statuses for the 1-bit phase coding. By reasoning, the phase responses of unit cells with 90° gradient set as the 0°-“00”, 90°-“01”, 180°-“10” and 270°-“11” for the 2-bit phase coding. Obviously, using multi-bit binary coding can provide exponentially increased phase compensation for more accurate beam manipulations.
In what follows, we study the scattering properties of our proposed coding method applied to the reflectarray metasurfaces. Under the normally incident plane wave, the coding metasurfaces deflect beams at different angles (θ, φ) through engineering the coding sequences. According to the radiation pattern theory [25,27,34], we define the normalized form of the metasurface array factor as
For the sake of simplicity, only 1D coding analysis for both phase response and frequency response is discussed below. Referring to the analytical model in Eq. (4), Figs. 1(a) and 1(b) depict 1-bit and 2-bit scattering angle variation with the ratio of in-phase length L to wavelength λ and spacing scale Nx for the main lobe (p=0), first and second-order grating lobes (p=±1, ±2), respectively. Although we set the dx=200 um and f=0.4 THz to relate with the latter design, the universality only lies in the electrical length. Apparently, for the 1D-1bit reflectarray, the dual-beam steering area (where p=0 and p=1, with same reflectance and opposite deflection angles) exists in the blue regions of (-90°, -20°) and (20°, 90°) with L in (0.5λ, 1.5λ) or Nx in (1.875, 5.63). Multi-beam steering with the main lobe and higher-order grating lobes (p=0, ±1, ±2) appears when L is over 1.5λ. For the 1D-2bit reflectarray, attributing to higher phase gradient resolution, the single-beam steering area (where p=0) appears alone in the green region of (20°, 90°) with L in (0.25λ, 0.75λ) or Nx in (0.94, 2.81), which guides to formulate the coding sequences while either the wavelength (or frequency f) of incident wave or the in-phase spacing is fixed.
Fig. 1. The beam scattering analysis on coding metasurfaces. (a) 1-bit coding and (b) 2-bit coding for scattering angle variation (main lobe and grating lobes) with L/λ and Nx. (c) 1-bit coding and (d) 2-bit coding for frequency response of the “supercell reconstructing” scanning for the main lobe.
The above analysis suggests a possible “logically fractional” coding strategy to extend the coverage of the useful angular scope of beam scanning. To corroborate our theory from another point of view, we catalyze a novel substitution for terahertz scanning by combining the fractional coding and frequency sweeping. Accordingly, the frequency response of the “supercell reconstructing” scanning is shown in Figs. 1(c) and 1(d), whereas the theoretical results are limited to main lobes steered by 1D-1bit and 1D-2bit metasurfaces, respectively. The shadow parts indicate the none-scanning zones, owing to imaginary numbers of the complex function. When incident frequency and cell spacing reach the critical points of main-lobe occurrence, the scanning angles of both 1-bit and 2-bit coding metasurfaces vary fast along with frequency sweeping at first, then slow down when the angles fall below 20°, being in good accordance with Figs. 1(a) and 1(b). For 2-bit coding, perceived by the steeper slope than 1-bit coding, the frequency and units spacing threshold of the main lobe achieved ahead of 1-bit coding and the change of beam angles is more sensitive, which suggests a smaller step size for “supercell reconstructing” in 2-bit coding metasurfaces.
Fig. 2(a) demonstrates the angular scope of possible main-lobe scanning in Eq. (4) for the 1D-2bit case (dx=200 µm) as a function of supercell’s spacing scale, from which it suggests that the supercell should be reconstructed logically as small-stepped as possible. Most of the conventional coding metasurfaces physically allocate the in-phase spacing scale Nx into integral numbers, such as 1, 2, 3, …, m (m < M), which are intrinsically confronting the issue of the Blind Zone. For instance, the Blind Zone between Nx=1: 00 01 10 11 and Nx=2: 00 00 01 01 10 10 11 11 indicates a 42° annular scope unavailable for scanning. Correspondingly, the logically fractional coding method by logically discretizing the spacing scale of supercells is proposed to address the issue, which is inherently limited by the fixed physical size of the unit cell. From another perspective of view, it is theoretically possible to achieve any deflection angle by designing enormous amounts of phase gradient combinations whatsoever, inevitably facing the detrimental effect of high precision on small phase-gradient and strong coupling by neighboring variable-sized cells.
Fig. 2. The methodology of logically fractional coding. (a) The angular scope of possible main-lobe scanning for the 1D-2bit case and the Blind Zone between Nx=1 and Nx=2. (b) The general scheme of the logically fractional coding method by exemplifying a 1D-2bit case. (d) To illustrate the numerical coding process.
Fig. 2(b) shows the general scheme of the logically fractional coding method by exemplifying a 1D-2bit case. In step 1, we assume Lx=1.25dx as the supercell logical sidelength, which forms a subarray including all 4 coding states (differentiated by 4 colors). In step 2, the logical coding sequences will be applied to the physical unit cell one by one. In step 3, two coding states in one unit are recoded by choosing the major filling factor as the unit cell’s final state. More specifically, as shown in Fig. 2(c), Code(2) is recoded as “01”, which is derived from the major filling factor of the combination of ‘00’ and ‘01’ (accounting for 25% and 75%, respectively). Worth noting for the half to half situation, Code(3) can be “01” or “10” because of “01” and “10” both accounting for 50%. Similarly, Code(4) is “10” due to that “10” and “11” respectively account for 75% and 25% in the fourth unit. A complete coding circulation ends by the fourth state and the null filling factor simultaneously. For instance, Code(5)=“11” and q(5) = 0, the periodic coding sequence for Nx=1.25 is “00 01 10 10 11”.
Considering the state of the art, it is currently impossible to divide unit-cell spacing into different portions and reconstruct them into a new coding sequence. We define the filling factor $q(i) = i - {N_{x}} \cdot [i/{N_{x}}]$ referred to the proportion of the second coding state in a combined unit henceforth a function to the coding state for the ith unit cell has been derived
Comparatively shown in Fig. 3(a), as Nx=1.2, 1.25, and 1.5, the front-half-choice coding and back-half-choice coding make no difference in radiation pattern, whereas the minor-part-choice obviously off the track in both angle and amplitude. Choosing either front half or back half as the final coding state maintains the desire angles and amplitudes due to the 50% to 50% accountable ratio in phase shift choices. Failed to render the more precise phase compensation, the minor-part-choice coding result in the deviation of the pre-designed angles with amplitudes below 50%.
Fig. 3. The radiation pattern as a function of Nx. (a) Comparison among radiation patterns with the front-half-choice, back-half-choice and minor-part-choice codings. (b) Extendable re-covering in the Blind Zone by thirteen coding sequences in Table 1.
Table 1. Coding sequences.
The far-field pattern and coding sequences in Eqs. (1)–(5) are numerically predicted by the MATLAB code. By gradually fractionalizing the supercell sidelength between Nx=1∼2 according to the trend shown in Fig. 2(a), thirteen coding sequences uniformly cover the Blind Zone, as shown in Fig. 3(b), and more details are listed in Table 1. There are three blocks in Table 1, which classify the increment of Nx as=0.05 between Nx=1∼1.5, as 0.1 between Nx=1.5∼1.8, and as 0.2 between Nx=1.8∼2.2, along with average scanning step of 3.2°, 2.3°, and 3°, correspondently. Hereafter, the metasurface design and cross-validation use the finite-element-based commercial package CST to obtain more accurate full-wave results. In practical designs, due to the mismatch between the ideal length of coding sequences and the size of metasurface array, a trade-off between the precision of beam steering and range of coding sequences needs to be adopted. Compared to an analogous coding scheme [27], the logically fractional coding strategy we proposed is more flexible and adaptable to 2-bit and multi-bit metasurfaces.
3. The 2-bit logically fractional coding metasurfaces
As a proof-of-concept, the schematic diagram of a 1D-2bit coding metasurface is as shown in Fig. 4(a). The planar structure consists of an aluminum stacked-square-loop array as the upper layer, a polyimide spacer with a low dielectric ɛ=3.5 + 0.05i, and a backed aluminum film as the bottom layer, utilizing the Cartesian (x, y, z) and associated spherical (r, θ, φ) coordinate systems for spatial orientation. Figures 4(b) and 4(c) depict the unit-cell geometry and a typical 2-bit coding combination, respectively. More specifically, the 360° phase circulation combined by four consecutive element types “00”-0°, “01”-90°, “10”-180° and “11”-270° are implemented via variable-sized patches for 90° phase difference, labeled by a=10 µm, a=57 µm, a=81 µm, and a=119 µm. The other parameters tagged in Fig. 4(b) are d=200 µm, h=75 µm, w=12.5 µm, and g=12.5 µm, which are fixed while the element types switch. Due to the four-fold symmetry of the unit cell, the proposed metasurface is polarization-independent and without cross-polarization. Optimized by a Floquet-modeled simulation in CST, a 90°±15° phase gradient with an average 95% reflectance keeps in fair linearity in a broad bandwidth ranging from 0.34 to 0.5 THz, as shown in Fig. 4(d).
Fig. 4. The logically fractional 1D-2bit coding metasurfaces. (a) The schematic diagram. (b) The unit-cell geometry. (c) An elementary 2-bit coding cycle. (d) A 90°±15° phase gradient with an average 95% reflectance in a broad bandwidth ranging from 0.34 to 0.5 THz.
To validate the prementioned concept for suitably synthesizing the coding sequences to realize precise single-beam steering, we apply the six pre-engineered 2-bit coding cases in Table 1 to the above one dimensional metasurfaces. By reconstructing the metasurface reflectarray along with x direction by using the 2-bit elementary unit cells, a full-wave simulation model is built in CST. The phototypes of six 2-bit coding metasurface with Nx=1, 1.2, 1.25, 1.5, 2, and 2.2, have been fabricated by a standard photolithography process, using the identical parameters within the simulation, as shown in Fig. 5(a).
Fig. 5. The measurement on six samples with Nx=1, 1.2, 1.25, 1.5, 2, and 2.2. (a) Six pieces of the coding metasurface phototypes and micrographs. (b) The schematic of the scanning measurement platform. (c) On-site picture of the scanning measurement platform.
Figs. 5(b) and 5(c) show the schematic and on-site picture of the scanning measurement platform, respectively. The experiment setup consists of the emitting and receiving modules with conical horns, an off-axis parabolic mirror, a focusing lens, and a rotating platform. Terahertz waves from the emitter shine on the metasurface after being collimated by the off-axis parabolic mirror, and it is collected by the receiver after passing through the focusing lens, ensuring normally incident plane wave is scattered in/from the test samples. For measuring the reflection angle, the incident wave keeps perpendicular to the sample and the receiver on the rotating platform is turned from the angle of 22° to 75° with a 1° increment.
Figs. 6(a), 6(b), and 6(c) plot the far-field results at 0.4 THz of numerical calculation, CST simulation, and experimental measurement, respectively. Remarkably, being consistent with theoretical analysis, the 2-bit coding phototypes achieved single-beam scanning through the Blind Zone with angular scope from 28° to 70°. The experimental results are processed to filter the air loss and overflow by using an aluminum plate as a referenced substitution. In the simulation, the simulated reflection angles direct at 25°, 28°, 39°, 48°, 51° and 69° with 83%, 83%, 83%, 71%, 66% and 48% of the normalized reflectance, correspondingly, whose angles error is less than ±1° compared with calculated results. The measured main-lobe beam angles locate at 25°, 28°, 40°, 47°, 51° and 68° with 77%, 78%, 77%, 68%, 62% and 44% of the reflectance, correspondingly. The results reflect the predicted variation of the reflection angle dwindling with the increment of Nx, wherein the beam angle sweeps from 70° to 51° with Nx changes from 1 to 1.2, but only 3° varies by Nx increment from 2 to 2.2. With the deflection angle getting larger, the beam amplitudes of simulation and measurement decrease by effect of the wide beam divergence by neighboring coupling and fringing effect [35], which also are the dominating factor for the reflection loss, but this phenomenon does not occur in the numerical calculation based on the ideal far-field pattern rather than full-wave simulation. Comparing the simulated results and the measured results, the minute deviations of main-lobe angles and normalized reflectance maximize at 1° and 6%, respectively, which are caused by the fabrication errors and the limited stepping accuracy of the rotary platform. Meanwhile, the smoothness of the experimental curves is not as good as the simulations and the numerical calculations because of the stepping difference between 1° and 0.1°, respectively. Besides, the minor sidelobes are missed in the measurement due to its weak energy been covered by the noise. The main lobe beamwidth depends on the dimensions of a reflectarray because the more radiation elements radiate to a direction, the more energy is focused on radiated orientation, which explains that the beamwidth in experiments is wider than the simulations with the larger size of arrays.
Fig. 6. The radiation pattern of six metasurfaces under normal incidence at 0.4 THz. (a) MATLAB calculations, (b) CST simulations, and (c) The experiments.
Figs. 7(i)–7(l) show the normalized angular-frequency results by numerical, simulated, and experimental methods. It’s noteworthy that, varying with frequency in 0.34-0.5 THz, the beam scanning range of the main lobe covers 22°∼74° by the combination of four samples with Nx=1, 1.25, 1.5, and 2, increasing the angular scope by 44.4% than the uniform coding cases. Besides, the scanning peaks shift to smaller angles as frequency increases and/or the supercell spacing. Moreover, the spectral-angular scope narrows down as the supercell spacing grows larger. Noticeably, a sidelobe appears in 0.42-0.5 THz on the case of Nx=2 both in the simulation and measurement, which is caused by the exaggerated deviation of phase shift in 0.42-0.5 THz for long coding sequence with Nx=2. Generally, the cross-validation coincides well with the prediction based on the generalized Snell’s Law, also verified the effectiveness of the proposed coding synthesis.
Fig. 7. The spectral angular characteristics of four metasurfaces (with Nx=1, 1.25, 1.5, Nx=2) from 0.34 THz to 0.5 THz. (a)-(d) Numerical calculations. (e)-(h) The simulations. (i)-(l) The experiments.
4. Conclusion
In this paper, the generalized approach to realize flexible and ultrafine beam control with the logically fractional coding strategy has been presented and cross-verified. To fully cover the Blind Zone and extend the spectral-angular range of beam steering, an analytical model to reconfigure the array factor of the coding metasurfaces has been constructed, entailing with characteristic analysis of the relationship of the anomalous scattering and the sidelengths of supercells. Furthermore, a programmable fractional coding method has been introduced to convert the physical to logical coding sequences on pragmatic metasurfaces, reconfiguring the precise radiation pattern by means of fast numerical prediction and optimization. The measurement results of the 2-bit logically fractional coding samples show a consecutive single-beam steering pattern ranging from 22° to 74° in 0.34-0.5 THz, extending the angular coverage over 44.4% than the uniform coding samples with Nx=1 and Nx=2. The good accordance in the cross-validation has corroborated the effectiveness and generality of our coding theory for ultrafine beam patterning.
One of the most salient contributions of this work is presenting a scheme for coding metasurfaces to arbitrarily control anomalous beam deflection in a large field of view and toward accurate targeting. This work has addressed the shortcomings of the traditional coding method, which limited the freedom of radiation patterning due to the lack of phase gradient continuity. It’s noteworthy that this method can also be applied to 2D and multi-bit metasurfaces and extended to microwave and optical frequency. For the 2D coding metasurfaces, our preliminary theoretical analysis shows that coding with Nx and Ny along with x and y directions using the same approach enables continuous beam control in 3D space (in terms of pitch angle θ and azimuth angle φ). Further studies will concentrate on electrically controlled programmable metasurfaces combined with the novel coding strategy and extend to 2D-multibit metasurfaces for beam steering in 3D space to implement computational imaging and wireless communication in the terahertz range. To specifically modify and optimize the proposed coding scheme, it can be applied in multifarious wavefront regulations, such as beam steering, polarization splitting, holograms, focusing, RCS reduction and so on.
Funding
National Natural Science Foundation of China (11775046, 61871419); China Postdoctoral Science Foundation (2017M623000); Department of Science and Technology of Sichuan Province (THZSC201701); Fundamental Research Funds for the Central Universities (2672018ZYGX2018J039); National Basic Research Program of China (973 Program) (2017YFE0130000).
Disclosures
The authors declare no conflicts of interest.
References
1. N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013). [CrossRef]
2. Y. Zhao, X. Cao, J. Gao, X. Liu, and S. Li, “Jigsaw puzzle metasurface for multiple functions: polarization conversion, anomalous reflection and diffusion,” Opt. Express 24(10), 11208–11217 (2016). [CrossRef]
3. X. Gao, W. Yang, W. Cao, M. Chen, Y. Jiang, X. Yu, and H. Li, “Bandwidth broadening of a graphene-based circular polarization converter by phase compensation,” Opt. Express 25(20), 23945–23954 (2017). [CrossRef]
4. T. Niu, W. Withayachumnankul, A. Upadhyay, P. Gutruf, D. Abbott, M. Bhaskaran, S. Sriram, and C. Fumeaux, “Terahertz reflectarray as a polarizing beam splitter,” Opt. Express 22(13), 16148–16160 (2014). [CrossRef]
5. H. Zeng, Y. Zhang, F. Lan, S. Liang, L. Wang, T. Song, T. Zhang, Z. Shi, Z. Yang, X. Kang, X. Zhang, P. Mazumder, and D. M. Mittleman, “Terahertz Dual-Polarization Beam Splitter Via an Anisotropic Matrix Metasurface,” IEEE Trans. Terahertz Sci. Technol. 9(5), 491–497 (2019). [CrossRef]
6. J. Lin, P. Genevet, M. A. Kats, N. Antoniou, and F. Capasso, “Nanostructured holograms for broadband manipulation of vector beams,” Nano Lett. 13(9), 4269–4274 (2013). [CrossRef]
7. X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4(1), 2807 (2013). [CrossRef]
8. L. Li, T. Jun Cui, W. Ji, S. Liu, J. Ding, X. Wan, Y. Bo Li, M. Jiang, C. W. Qiu, and S. Zhang, “Electromagnetic reprogrammable coding-metasurface holograms,” Nat. Commun. 8(1), 197 (2017). [CrossRef]
9. S. C. Malek, H. S. Ee, and R. Agarwal, “Strain Multiplexed Metasurface Holograms on a Stretchable Substrate,” Nano Lett. 17(6), 3641–3645 (2017). [CrossRef]
10. H. Liu, M. Q. Mehmood, K. Huang, L. Ke, H. Ye, P. Genevet, M. Zhang, A. Danner, S. P. Yeo, C. W. Qiu, and J. Teng, “Twisted focusing of optical vortices with broadband flat spiral zone plates,” Adv. Opt. Mater. 2(12), 1193–1198 (2014). [CrossRef]
11. S. Wang, P. C. Wu, V. C. Su, Y. C. Lai, C. Hung Chu, J. W. Chen, S. H. Lu, J. Chen, B. Xu, C. H. Kuan, T. Li, S. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187 (2017). [CrossRef]
12. A. M. Melo, M. A. Kornberg, P. Kaufmann, M. H. Piazzetta, E. C. Bortolucci, M. B. Zakia, O. H. Bauer, A. Poglitsch, and A. M. P. A. Da Silva, “Metal mesh resonant filters for terahertz frequencies,” Appl. Opt. 47(32), 6064–6069 (2008). [CrossRef]
13. C. Debus and P. H. Bolivar, “Frequency selective surfaces for high sensitivity terahertz sensing,” Appl. Phys. Lett. 91(18), 1–2 (2007). [CrossRef]
14. J. J. Lynch, F. Herrault, K. Kona, G. Virbila, C. McGuire, M. Wetzel, H. Fung, and E. Prophet, “Coded aperture subreflector array for high resolution radar imaging,” Proc. SPIE 10994, 1099405 (2019). [CrossRef]
15. S. V. Hum and J. Perruisseau-Carrier, “Reconfigurable reflectarrays and array lenses for dynamic antenna beam control: A review,” IEEE Trans. Antennas Propag. 62(1), 183–198 (2014). [CrossRef]
16. H. Zeng, F. Lan, Y. Zhang, S. Liang, L. Wang, J. Yin, T. Song, L. Wang, T. Zhang, Z. Shi, Z. Yang, and P. Mazumder, “Broadband terahertz reconfigurable metasurface based on 1-bit asymmetric coding metamaterial,” Opt. Commun. 458, 124770 (2020). [CrossRef]
17. 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]
18. 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]
19. L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014). [CrossRef]
20. M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U. S. A. 109(31), 12364–12368 (2012). [CrossRef]
21. X. Jing, C. Chu, C. Li, H. Gan, Y. He, X. Gui, and Z. Hong, “Enhancement of bandwidth and angle response of metasurface cloaking through adding antireflective moth-eye-like microstructure,” Opt. Express 27(15), 21766–21777 (2019). [CrossRef]
22. M. R. Hashemi, S. Cakmakyapan, and M. Jarrahi, “Reconfigurable metamaterials for terahertz wave manipulation,” Rep. Prog. Phys. 80(9), 094501 (2017). [CrossRef]
23. H. Zeng, F. Lan, Y. Zhang, T. Song, S. Liang, L. Wang, T. Zhang, L. Wang, Z. Shi, X. Zhang, P. Mazumder, and Z. Yang, “Maximizing beam-scanning angle in an expected bandwidth based on terahertz metasurface with dual-mode resonance,” Appl. Phys. Express 12(9), 095501 (2019). [CrossRef]
24. 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]
25. 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]
26. S. Liu and T. J. Cui, “Flexible Controls of Terahertz Waves Using Coding and Programmable Metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 23(4), 1–12 (2017). [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]
28. 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]
29. B. Fang, X. Bie, Z. Yan, H. Gan, C. Li, Z. Hong, and X. Jing, “Manipulation of main lobe number and azimuth angle of terahertz-transmitted beams by matrix-form-coding metasurface,” Appl. Phys. A: Mater. Sci. Process. 125(9), 651 (2019). [CrossRef]
30. K. Chen, N. Zhang, G. Ding, J. Zhao, T. Jiang, and Y. Feng, “Active Anisotropic Coding Metasurface with Independent Real-Time Reconfigurability for Dual Polarized Waves,” Adv. Mater. Technol. 5(2), 1900930 (2020). [CrossRef]
31. S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Qing Qi, J. G. Han, W. L. Zhang, X. Y. Zhou, and Q. Cheng, “Convolution Operations on Coding Metasurface to Reach Flexible and Continuous Controls of Terahertz Beams,” Adv. Sci. 3(10), 1600156 (2016). [CrossRef]
32. X. Bie, X. Jing, Z. Hong, and C. Li, “Flexible control of transmitting terahertz beams based on multilayer encoding metasurfaces,” Appl. Opt. 57(30), 9070–9077 (2018). [CrossRef]
33. M. Tamagnone, S. Capdevila, A. Lombardo, J. Wu, A. Centeno, A. Zurutuza, A. M. Ionescu, A. C. Ferrari, and J. R. Mosig, “Graphene Reflectarray Metasurface for Terahertz Beam Steering and Phase Modulation,” 1–16 (2018).
34. 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]
35. P. Nayeri, F. Yang, and A. Z. Elsherbeni, “Bifocal design and aperture phase optimizations of reflectarray antennas for wide-angle beam scanning performance,” IEEE Trans. Antennas Propag. 61(9), 4588–4597 (2013). [CrossRef]
