Programmable VO2 metasurface for terahertz wave beam steering

•The reversible phase-transition material VO2 is integrated into the metasurface•Programmable VO2 metasurfaces are proposed to achieve THz beam steering•Wide-angle beam scanning from −60° to +60° is realized in the digitalized metasurface Programmable vanadium dioxide (VO2) metasurface is proposed at THz frequencies. The insulating and metallic states of VO2 can be switched via external electrical stimulation, resulting in the dynamical modulation of electromagnetic response. The voltages of different columns of the metasurface can be controlled by the field-programmable gate array, and thus the phase gradients are realized for THz beam steering. In 1-bit coding, we design periodic and nonperiodic 24 × 24 coding sequences, and achieve wide-angle beam scanning with the deflection angles from −60° to +60°. In 2-bit coding, we use two different meta-atoms to design 18 × 18 coding sequences. Compared with 1-bit coding, 2-bit coding has more degree of freedom to control the optical phase, and 3 dB diffraction efficiency is improved by generating a single deflection angle. The proposed programmable metasurfaces provide a promising platform for manipulating electromagnetic wave in 6G wireless communication. Programmable vanadium dioxide (VO2) metasurface is proposed at THz frequencies. The insulating and metallic states of VO2 can be switched via external electrical stimulation, resulting in the dynamical modulation of electromagnetic response. The voltages of different columns of the metasurface can be controlled by the field-programmable gate array, and thus the phase gradients are realized for THz beam steering. In 1-bit coding, we design periodic and nonperiodic 24 × 24 coding sequences, and achieve wide-angle beam scanning with the deflection angles from −60° to +60°. In 2-bit coding, we use two different meta-atoms to design 18 × 18 coding sequences. Compared with 1-bit coding, 2-bit coding has more degree of freedom to control the optical phase, and 3 dB diffraction efficiency is improved by generating a single deflection angle. The proposed programmable metasurfaces provide a promising platform for manipulating electromagnetic wave in 6G wireless communication. Terahertz (THz) wave, which is located between the infrared and microwave bands, has several unique characteristics such as extracting molecular spectral information, signal detection, and material characterization compared with mmWave bands (Ferguson and Zhang, 2002Ferguson B. Zhang X.C. Materials for terahertz science and technology.Nat. Mater. 2002; 1: 26-33https://doi.org/10.1038/nmat708Crossref PubMed Scopus (2712) Google Scholar; Rappaport et al., 2019Rappaport T.S. Xing Y. Kanhere O. Ju S. Madanayake A. Mandal S. Alkhateeb A. Trichopoulos G.C. Wireless communications and applications above 100 GHz: opportunities and challenges for 6G and beyond.IEEE Access. 2019; 7: 78729-78757https://doi.org/10.1109/ACCESS.2019.2921522Crossref Scopus (781) Google Scholar). Up to now, THz technology has already attracted significant attention in security checking, wireless communication, radar monitoring, biomedical applications, and other areas (Nagatsuma et al., 2016Nagatsuma T. Ducournau G. Renaud C.C. Advances in terahertz communications accelerated by photonics.Nat. Photonics. 2016; 10: 371-379https://doi.org/10.1038/nphoton.2016.65Crossref Scopus (996) Google Scholar; Tonouchi, 2007Tonouchi M. Cutting-edge terahertz technology.Nat. Photonics. 2007; 1: 97-105https://doi.org/10.1038/nphoton.2007.3Crossref Scopus (5177) Google Scholar; Heinz et al., 2015Heinz E. May T. Born D. Zieger G. Anders S. Zakosarenko V. Meyer H.G. Schäffel C. Passive 350 GHz video imaging systems for security applications.J. Infrared, Millim. Terahertz Waves. 2015; 36: 879-895https://doi.org/10.1007/s10762-015-0170-8Crossref Scopus (43) Google Scholar; Siegel, 2002Siegel P.H. Terahertz technology.IEEE Trans. Microw. Theory Tech. 2002; 50: 910-928https://doi.org/10.1109/22.989974Crossref Scopus (2798) Google Scholar, Siegel, 2004Siegel P.H. Terahertz technology in biology and medicine.IEEE Trans. Microw. Theory Tech. 2004; 52: 2438-2447https://doi.org/10.1109/TMTT.2004.835916Crossref Scopus (1112) Google Scholar; Zhang et al., 2014Zhang B. Pi Y. Li J. Terahertz imaging radar with inverse aperture synthesis techniques: system structure, signal processing, and experiment results.IEEE Sens. J. 2014; 15: 290-299https://doi.org/10.1109/JSEN.2014.2342495Crossref Scopus (76) Google Scholar; Choi et al., 2011Choi M. Lee S.H. Kim Y. Kang S.B. Shin J. Kwak M.H. Kang K.Y. Lee Y.H. Park N. Min B. A terahertz metamaterial with unnaturally high refractive index.Nature. 2011; 470: 369-373https://doi.org/10.1038/nature09776Crossref PubMed Scopus (504) Google Scholar; Chan et al., 2007Chan W.L. Deibel J. Mittleman D.M. Imaging with terahertz radiation.Rep. Prog. Phys. 2007; 70: 1325-1379https://doi.org/10.1088/0034-4885/70/8/R02Crossref Scopus (814) Google Scholar; Liu et al., 2007Liu H.B. Zhong H. Karpowicz N. Chen Y. Zhang X.C. Terahertz spectroscopy and imaging for defense and security applications.Proc. IEEE. 2007; 95: 1514-1527https://doi.org/10.1088/0034-4885/70/8/R02Crossref Scopus (806) Google Scholar; Plusquellic et al., 2007Plusquellic D.F. Siegrist K. Heilweil E.J. Esenturk O. Applications of terahertz spectroscopy in biosystems.ChemPhysChem. 2007; 8: 2412-2431https://doi.org/10.1016/j.dit.2013.03.009Crossref PubMed Scopus (217) Google Scholar). With the further expanding applications of THz technology, efficient functional devices and components are highly desirable. However, most of the natural materials cannot strongly respond to THz wave, which hampers the development of THz devices (Withayachumnankul and Abbott, 2009Withayachumnankul W. Abbott D. Metamaterials in the terahertz regime.IEEE Photonics J. 2009; 1: 99-118https://doi.org/10.1109/JPHOT.2009.2026288Crossref Scopus (260) Google Scholar). As a subwavelength structure, the meta-atom can exhibit electrical polarization and magnetic polarization defined by the material and geometry (Meinzer et al., 2014Meinzer N. Barnes W.L. Hooper I.R. Plasmonic meta-atoms and metasurfaces.Nat. Photonics. 2014; 8: 889-898https://doi.org/10.1038/nphoton.2014.247Crossref Scopus (727) Google Scholar). The metasurface can be formed by periodic arrays of meta-atoms, providing an ideal platform for the realization of THz functional devices (Zhang et al., 2008Zhang S. Genov D.A. Wang Y. Liu M. Zhang X. Plasmon-induced transparency in metamaterials.Phys. Rev. Lett. 2008; 101: 047401https://doi.org/10.1103/PhysRevLett.101.047401Crossref PubMed Scopus (2039) Google Scholar, Zhang et al., 2013Zhang X. Tian Z. Yue W. Gu J. Zhang S. Han J. Zhang W. Broadband terahertz wave deflection based on c-shape complex metamaterials with phase discontinuities.Adv. Mater. 2013; 25: 4567-4572https://doi.org/10.1002/adma.201204850Crossref PubMed Scopus (324) Google Scholar; Landy et al., 2008Landy N.I. Sajuyigbe S. Mock J.J. Smith D.R. Padilla W.J. Perfect metamaterial absorber.Phys. Rev. Lett. 2008; 100: 207402https://doi.org/10.1103/PhysRevLett.100.207402Crossref PubMed Scopus (5161) Google Scholar; Ben Mbarek et al., 2019Ben Mbarek S. Tennich A. Choubani F. Analytical modeling of cross metallic metasurfaces absorption for terahertz band.J. Electromagn. Waves Appl. 2019; 33: 1343-1353https://doi.org/10.1080/09205071.2019.1608317Crossref Scopus (3) Google Scholar; Wang et al., 2020Wang L. Lan F. Zhang Y. Liang S. Liu W. Yang Z. Meng L. Shi Z. Yin J. Song T. et al.A fractional phase-coding strategy for terahertz beam patterning on digital metasurfaces.Opt. Express. 2020; 28: 6395-6407https://doi.org/10.1364/OE.385691Crossref PubMed Scopus (9) Google Scholar; Wu et al., 2020Wu J. Shen Z. Ge S. Chen B. Shen Z. Wang T. Zhang C. Hu W. Fan K. Padilla W. et al.Liquid crystal programmable metasurface for terahertz beam steering.Appl. Phys. Lett. 2020; 116: 131104https://doi.org/10.1063/1.5144858Crossref Scopus (93) Google Scholar; Rouhi et al., 2018Rouhi K. Rajabalipanah H. Abdolali A. Real-time and broadband terahertz wave scattering manipulation via polarization-insensitive conformal graphene-based coding metasurfaces.Ann. Phys. 2018; : 1700310https://doi.org/10.1002/andp.201700310Crossref Scopus (60) Google Scholar; Shabanpour et al., 2020Shabanpour J. Beyraghi S. Cheldavi A. Ultrafast reprogrammable multifunctional vanadium-dioxide-assisted metasurface for dynamic THz wavefront engineering.Sci. Rep. 2020; 10: 8950-9014https://doi.org/10.1038/s41598- 020-65533-9Crossref PubMed Google Scholar; Cong and Singh, 2020Cong L. Singh R. Spatiotemporal dielectric metasurfaces for unidirectional propagation and reconfigurable steering of terahertz beams.Adv. Mater. 2020; 32: 2001418https://doi.org/10.1002/adma.202001418Crossref Scopus (39) Google Scholar; Cong et al., 2018Cong L. Srivastava Y.K. Zhang H. Zhang X. Han J. Singh R. All-optical active THz metasurfaces for ultrafast polarization switching and dynamic beam splitting.Light Sci. Appl. 2018; 7: 28https://doi.org/10.1038/s41377-018-0024-yCrossref PubMed Scopus (118) Google Scholar). Nevertheless, the properties of most metasurfaces are restricted by the fixed geometric parameters of meta-atoms. The dynamic functions such as beam scanning, frequency shifting, or amplitude modulation cannot be implemented on the basis of the mentioned metasurfaces. Therefore, hybrid metasurface combined with tunable materials such as graphene (Tamagnone et al., 2018Tamagnone M. Capdevila S. Lombardo A. Wu J. Centeno A. Zurutuza A. Ionescu A.M. Ferrari A.C. Mosig J.R. Graphene reflectarray metasurface for terahertz beam steering and phase modulation.arXiv. 2018; (Preprint at)https://doi.org/10.48550/arXiv.1806.02202Crossref Google Scholar; Wu et al., 2018Wu B. Hu Y. Zhao Y.T. Lu W.B. Zhang W. Large angle beam steering THz antenna using active frequency selective surface based on hybrid graphene-gold structure.Opt Express. 2018; 26: 15353-15361https://doi.org/10.1364/OE.26.015353Crossref PubMed Scopus (30) Google Scholar; Cheng et al., 2016Cheng X. Yao Y. Qu S. Wu Y. Yu J. Chen X. Circular beam-reconfigurable antenna base on graphene-metal hybrid.Electron. Lett. 2016; 52: 494-496https://doi.org/10.1049/el.2015.4435Crossref Scopus (26) Google Scholar; Shi et al., 2015Shi S.F. Zeng B. Han H.L. Hong X. Tsai H.Z. Jung H.S. Zettl A. Crommie M.F. Wang F. Optimizing broadband terahertz modulation with hybrid graphene/metasurface structures.Nano Lett. 2015; 15: 372-377https://doi.org/10.1021/nl503670dCrossref PubMed Scopus (96) Google Scholar; Lu et al., 2021Lu Y. Wang C. Zhao S. Wen Y. Magnetically tunable graphene-based terahertz metasurface.Front. Phys. 2021; 8: 661https://doi.org/10.3389/fphy.2020.622839Crossref Scopus (2) Google Scholar; Ghosh and Chaudhuri, 2018Ghosh J. Chaudhuri S.R.B. Design of graphene metasurface to mitigate mutual coupling in monopole antenna at lower THz frequency.ICMAP. 2018; 1–2https://doi.org/10.1109/ICMAP.2018.8354584Crossref Scopus (1) Google Scholar), liquid crystal (Song et al., 2017Song Q.H. Zhu W.M. Wu P.C. Zhang W. Wu Q.Y.S. Teng J.H. Shen Z.X. Chong P.H.J. Liang Q.X. Yang Z.C. et al.Liquid-metal-based metasurface for terahertz absorption material: frequency-agile and wide-angle.Apl. Mater. 2017; 5: 066103https://doi.org/10.1063/1.4985288Crossref Scopus (31) Google Scholar; Meng et al., 2019Meng X. Nekovee M. Wu D. Reconfigurable liquid crystal reflectarray metasurface for THz communications.in: Antennas and Propagation Conference. IET, 2019: 1-6https://doi.org/10.48550/arXiv.1908.02736Google Scholar; Ji et al., 2020Ji Y.Y. Fan F. Zhang X. Cheng J.R. Chang S. Active terahertz anisotropy and dispersion engineering based on dual-frequency liquid crystal and dielectric metasurface.J. Lightwave Technol. 2020; 38: 4030-4036https://doi.org/10.1109/JLT.2020.2985667Crossref Scopus (11) Google Scholar), and phase transition materials (Hashemi et al., 2016Hashemi M.R.M. Yang S.H. Wang T. Sepúlveda N. Jarrahi M. Electronically-controlled beam-steering through vanadium dioxide metasurfaces.Sci. Rep. 2016; 6: 35439-35448https://doi.org/10.1038/srep35439Crossref PubMed Scopus (129) Google Scholar; Li et al., 2020cLi J.S. Li S.H. Yao J.Q. Actively tunable terahertz coding metasurfaces.Opt Commun. 2020; 461: 125186https://doi.org/10.1016/j.optcom.2019.125186Crossref Scopus (4) Google Scholar; Cen et al., 2019Cen G. Deng H. Cheng L. Zhou S. Liao S. Terahertz (THz) metasurface switch by phase change medium.IEEE MTT-S International Wireless Symposium. 2019; : 1-3https://doi.org/10.1109/IEEEIWS.2019.8803956Crossref Google Scholar; Park et al., 2018Park D.J. Shin J.H. Park K.H. Ryu H.C. Electrically controllable THz asymmetric split-loop resonator with an outer square loop based on VO2.Opt Express. 2018; 26: 17397-17406https://doi.org/10.1364/OE.26.017397Crossref PubMed Scopus (33) Google Scholar; Leitis et al., 2020Leitis A. Heßler A. Wahl S. Wuttig M. Taubner T. Tittl A. Altug H. All-dielectric programmable huygens’ metasurfaces.Adv. Funct. Mater. 2020; 30: 1910259https://doi.org/10.1002/adfm.201910259Crossref Scopus (109) Google Scholar; Yin et al., 2017Yin X. Steinle T. Huang L. Taubner T. Wuttig M. Zentgraf T. Giessen H. Beam switching and bifocal zoom lensing using active plasmonic metasurfaces.Light Sci. Appl. 2017; 6: e17016https://doi.org/10.1038/lsa.2017.16Crossref PubMed Scopus (266) Google Scholar; Sreekanth et al., 2019Sreekanth K.V. Ouyang Q. Sreejith S. Zeng S. Lishu W. Ilker E. Dong W. ElKabbash M. Ting Y. Lim C.T. et al.Phase-change material-based low-loss visible-frequency hyperbolic metamaterials for ultrasensitive label-free biosensing.Adv. Opt. Mater. 2019; 7: 1900081https://doi.org/10.1002/adom.201900081Crossref Scopus (57) Google Scholar) is considered as the promising approach to dynamically manipulating the response of THz wave. Among the wide varieties of THz dynamic regulation devices, THz beam steering has drawn more attention in wireless communications. Until now, hybrid metasurfaces have been proposed to realize THz beam steering. For example, R. Singh et al. presented a spatiotemporal metasurface based on silicon to inhibit the backscattering and achieved 34.7° beam deflection for ultrafast beam scanning, which fulfilled the emerging demand for THz communication (Cong and Singh, 2020Cong L. Singh R. Spatiotemporal dielectric metasurfaces for unidirectional propagation and reconfigurable steering of terahertz beams.Adv. Mater. 2020; 32: 2001418https://doi.org/10.1002/adma.202001418Crossref Scopus (39) Google Scholar). Tamagnone et al. integrated graphene as an active element into metasurface, and the angular steering range reached 25° (Tamagnone et al., 2018Tamagnone M. Capdevila S. Lombardo A. Wu J. Centeno A. Zurutuza A. Ionescu A.M. Ferrari A.C. Mosig J.R. Graphene reflectarray metasurface for terahertz beam steering and phase modulation.arXiv. 2018; (Preprint at)https://doi.org/10.48550/arXiv.1806.02202Crossref Google Scholar). Wu et al. integrated liquid crystal material into the metasurface to achieve coding sequences with a maximum deflection angle of 32° (Wu et al., 2020Wu J. Shen Z. Ge S. Chen B. Shen Z. Wang T. Zhang C. Hu W. Fan K. Padilla W. et al.Liquid crystal programmable metasurface for terahertz beam steering.Appl. Phys. Lett. 2020; 116: 131104https://doi.org/10.1063/1.5144858Crossref Scopus (93) Google Scholar). However, it is difficult to achieve wide-angle scanning for these structures integrated with tunable materials. Wu et al. designed the hybrid coding metasurface to cover 360° beam deflection by utilizing the tunable chemical potential of graphene (Wu et al., 2018Wu B. Hu Y. Zhao Y.T. Lu W.B. Zhang W. Large angle beam steering THz antenna using active frequency selective surface based on hybrid graphene-gold structure.Opt Express. 2018; 26: 15353-15361https://doi.org/10.1364/OE.26.015353Crossref PubMed Scopus (30) Google Scholar). Although the coverage angle is relatively large, it has only six main radiation directions. Therefore, it is still challenging to realize real time controlling the wide deflection angle of THz beam. Programmable metasurfaces have been demonstrated to be suitable for real-time control of electromagnetic wave (Ghorbani et al., 2021Ghorbani F. Beyraghi S. Shabanpour J. Oraizi H. Soleimani H. Soleimani M. Deep neural network-based automatic metasurface design with a wide frequency range.Sci. Rep. 2021; 11: 7102https://doi.org/10.1038/s41598-021-86588-2Crossref PubMed Scopus (14) Google Scholar; Shabanpour et al., 2021aShabanpour J. Beyraghi S. Ghorbani F. Oraizi H. Implementation of conformal digital metasurfaces for THz polarimetric sensing.OSA Continuum. 2021; 4: 1372-1380https://doi.org/10.1364/OSAC.421643Crossref Scopus (8) Google Scholar; Chen et al., 2022Chen B. Wu J. Li W. Zhang C. Fan K. Xue Q. Chi Y. Wen Q. Jin B. Chen J. et al.Programmable terahertz metamaterials with non-volatile memory.Laser Photon. Rev. 2022; 16: 2100472https://doi.org/10.1002/lpor.202100472Crossref Scopus (8) Google Scholar). Vanadium dioxide (VO2) is a reversible phase-transition material triggered by thermal, optical, or electrical excitations, and it has advantages of the fast response and large modulation depth (Huang et al., 2020Huang J. Li J. Yang Y. Li J. Li J. Zhang Y. Yao J. Active controllable dual broadband terahertz absorber based on hybrid metamaterials with vanadium dioxide.Opt Express. 2020; 28: 7018-7027https://doi.org/10.1364/OE.387156Crossref PubMed Scopus (65) Google Scholar). The switch time of the phase transition can reach a scale of some femtoseconds at THz frequency, which can be much shorter than that of liquid crystals (Shabanpour et al., 2021bShabanpour J. Sedaghat M. Nayyeri V. Oraizi H. Ramahi O.M. Real-time multi-functional near-infrared wave manipulation with a 3-bit liquid crystal based coding metasurface.Opt Express. 2021; 29: 14525-14535https://doi.org/10.1364/OE.420972Crossref PubMed Scopus (13) Google Scholar; Bai et al., 2019Bai J. Zhang S. Fan F. Wang S. Sun X. Miao Y. Chang S. Tunable broadband THz absorber using vanadium dioxide metamaterials.Opt Commun. 2019; 452: 292-295https://doi.org/10.1016/j.optcom.2019.07.057Crossref Scopus (38) Google Scholar). Combined with the VO2, metasurface is used to realize the dynamic regulation of THz wave such as frequency shifting and beam steering (Hashemi et al., 2016Hashemi M.R.M. Yang S.H. Wang T. Sepúlveda N. Jarrahi M. Electronically-controlled beam-steering through vanadium dioxide metasurfaces.Sci. Rep. 2016; 6: 35439-35448https://doi.org/10.1038/srep35439Crossref PubMed Scopus (129) Google Scholar; Li et al., 2020bLi J.H. Zhang Y.T. Li J.N. Li J. Li J.T. Zheng C.L. Yang Y. Huang J. Ma Z.Z. Ma C.Q. et al.The Institute of Laser and Opto-electronics, School of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, ChinaKey Laboratory of the Ministry of Education on Optoelectronic Information Technology, Tianjin University, Tianjin 300072, ChinaTerahertz coding metasurface based vanadium dioxide.Acta Phys. Sin. 2020; 69: 228101https://doi.org/10.7498/aps.69.20200891Crossref Scopus (7) Google Scholar). In this paper, we propose programmable VO2 metasurfaces for manipulating terahertz electromagnetic wave. Two different VO2 metasurfaces with 1-bit and 2-bit coding configurations are systematically studied. In 1-bit coding, the meta-atom achieves optical phase difference of π. In 2-bit coding, the two meta-atoms (type-A and type-B) are used to achieve phase difference of π/2. The above meta-atoms are controlled by the field-programmable gate array (FPGA), where all the meta-atoms in a column always have the same state. By adjusting coding sequences, the THz beam can be diffracted to different deflection angles. The results show that 1-bit programmable metasurface can achieve wide beam scanning between −60° and +60°. Since 2-bit programmable metasurface has more degree of freedom on phase control, 3 dB diffracting energy efficiency is improved by generating a single deflection angle. The designed devices show great potential for manipulating electromagnetic wave in THz regime. The schematic of 1-bit programmable VO2 metasurface is shown in Figure 1A , which consists of the meta-atom arrays, dielectric substrate, and reflecting metal film. In this design, low-loss quartz (thickness of 500 μm) is selected to reduce the absorption loss; gold (thickness of 0.2 μm) is implemented as the pattern and substrate. To dynamically control the electromagnetic response of the unit cell, the VO2 patch (thickness of 0.2 μm) is embedded in meta-atoms, as marked with the red region in Figures 1B and 1C. By applying external voltage, it can cause the metal-insulator transition (MIT) of VO2 in the metasurface. Note that the origin of MIT in VO2 remains unclear, it may be caused by joule heat (Kumar et al., 2013Kumar S. Pickett M.D. Strachan J.P. Gibson G. Nishi Y. Williams R.S. Local temperature redistribution and structural transition during joule-heating-driven conductance switching in VO2.Adv. Mater. 2013; 25: 6128-6132https://doi.org/10.1002/adma.201302046Crossref PubMed Scopus (154) Google Scholar; Li et al., 2016Li D. Sharma A.A. Gala D.K. Shukla N. Paik H. Datta S. Schlom D.G. Bain J.A. Skowronski M. Joule heating-induced metal–insulator transition in epitaxial VO2/TiO2 devices.ACS Appl. Mater. Interfaces. 2016; 8: 12908-12914https://doi.org/10.1021/acsami.6b03501Crossref PubMed Scopus (78) Google Scholar) or electric current (Wu et al., 2011Wu B. Zimmers A. Aubin H. Ghosh R. Liu Y. Lopez R. Electric field-driven phase transition in vanadium dioxide.Phys. Rev. B. 2011; 84: 241410https://doi.org/10.1103/PhysRevB.84.241410Crossref Scopus (110) Google Scholar; Shi and Chen, 2019Shi Y. Chen L.Q. Current-driven insulator-to-metal transition in strongly correlated VO2.Phys. Rev. Appl. 2019; 11: 014059https://doi.org/10.1103/PhysRevApplied.11.014059Crossref Scopus (19) Google Scholar). Each column of the structure is independently controlled by the voltage (V1, V2, V3, …) from an FPGA. When one switch is toggled on, FPGA will input the corresponding electrical-voltage coding sequence. Consequently, the voltage distributions on the metasurface can be changed by toggling different triggers, thereby producing the required “0” and “1” states of the meta-atoms and achieving different phase gradient to manipulate THz waves. VO2 has two states, namely, the insulating state and the metallic state. The schematic structure of meta-atom is shown in Figure 1B. The geometric parameters of the meta-atom are as following: a = 320 μm, b = 320 μm, c = 500 μm, d = 240 μm, e = 270 μm, f = 175 μm, g = 120 μm, h = 35 μm, and m = 4 μm. When the VO2 is in the metallic state, the metal arms are connected to form the ring circuit structure. When the VO2 is in insulating state, the ring circuit structure is broken. Therefore, the equivalent circuit is completely different before and after the structural phase change. The electromagnetic response can be controlled through external excitation, and the proposed structure can obtain the phase gradients along the column separately, and then realize the purpose of THz beam steering. As discussed above, the control of the metasurface is realized by exciting the VO2 film. The VO2 conductivity under different temperatures is measured as shown in Figure 2A . When the temperature is below 60°C, the conductivity of VO2 film is <1,000 S/m, which means the insulating state. When the temperature is raised beyond 60°C, VO2 film undergoes a structural phase transition and the conductivity also significantly increases. The film conductivity value is measured of ∼10,000 S/m in metallic state after the end of the phase-transition process. According to the measured conductivity, the Drude model can be used to describe the dielectric properties of VO2 at THz frequency (Li et al., 2020aLi H. Xu W. Cui Q. Wang Y. Yu J. Theoretical design of a reconfigurable broadband integrated metamaterial terahertz device.Opt Express. 2020; 28: 40060-40074https://doi.org/10.1364/OE.414961Crossref PubMed Scopus (29) Google Scholar; Wang et al., 2017Wang S. Kang L. Werner D.H. Hybrid resonators and highly tunable terahertz metamaterials enabled by vanadium dioxide (VO2).Sci. Rep. 2017; 7: 4326https://doi.org/10.1038/s41598-017-04692-8Crossref PubMed Scopus (142) Google Scholar; Liu et al., 2012Liu M. Hwang H.Y. Tao H. Strikwerda A.C. Fan K. Keiser G.R. Sternbach A.J. West K.G. Kittiwatanakul S. Lu J. et al.Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial.Nature. 2012; 487: 345-348https://doi.org/10.1038/nature11231Crossref PubMed Scopus (910) Google Scholar). Therefore, the metasurface uses the great different conductivities between two states of VO2 to realize beam steering. The light diffractions in metasurface follow the generalized Snell’s formula can be written as:sinθr−sinθi=λ02πnidφⅆx(Equation 1) where θr and θi represent the reflection angle and incident angle of THz wave, λ0 is the operating wavelength and ni is refraction index of the medium above the metasurface, and dφ/dx corresponds to the phase gradient endowed by metasurface. Based on the geometric parameters of the metasurface, the formula calculates the deflection direction of the THz beam. Considering the light deflection into air under the normal incident THz wave, the formula can be simplified as:sinθr=λ02πdφⅆx(Equation 2) And the radiation direction of the reflected THz beam can be calculated as:θr=arcsin(λ02πdφⅆx)(Equation 3) The deflection direction of THz beam can be obtained by setting the appropriate phase gradient. In this design, the phase gradient is generated when the metallic and insulating elements have the same reflection amplitude and phase difference of π. The simulations are performed by CST Microwave Studio to effectively investigate the electromagnetic responses of the metasurface. As shown in Figure 2C, the phase difference of meta-atom approaches π under the phase transition of VO2 at 0.218 THz. The same reflection amplitude in Figure 2B ensures the accuracy of generalized Snell’s law used in the beam steering. Note that the reflection amplitude can be increased by using the higher value of conductivity in the metallic state of the VO2 (Shabanpour et al., 2020Shabanpour J. Beyraghi S. Cheldavi A. Ultrafast reprogrammable multifunctional vanadium-dioxide-assisted metasurface for dynamic THz wavefront engineering.Sci. Rep. 2020; 10: 8950-9014https://doi.org/10.1038/s41598- 020-65533-9Crossref PubMed Google Scholar; Li et al., 2020cLi J.S. Li S.H. Yao J.Q. Actively tunable terahertz coding metasurfaces.Opt Commun. 2020; 461: 125186https://doi.org/10.1016/j.optcom.2019.125186Crossref Scopus (4) Google Scholar). We first analyze the change of the field distributions before and after the VO2 phase transition. The designed structure is illuminated by an incident plane wave; meanwhile, the electric field monitor is selected to observe the field distributions. Figures 3A and 3B show the electric field patterns before and after the phase transition of VO2 at 0.218 THz. Before the phase transition, the VO2 patch is in an insulating state and acts as a capacitor, this resonance circuit forms a split-ring resonator. It can be seen in Figure 3 that the free charges accumulate at the patch with a strong electric field intensity. When the VO2 patch is in the metallic state, the metal arms are connected which results in a weaker electric field intensity. The VO2 conductivity of metallic state is lower than that of gold, thus the accumulated charges cannot disappear completely. The electric field vector distributions before and after the phase transition of VO2 are researched, as shown in Figures 3C and 3D. When the VO2 is in the insulating state, the electric field vectors are concentrated on the VO2 patch. When the VO2 is in the metallic state, the electric field vectors are low and the distributions are relatively uniform. Therefore, the change of reflection phase before and after the phase transition of VO2 is resulted from the change of capacitance in the circuit model. Furthermore, to verify the effect of the VO2 patch, the influence of the size and position of the VO2 patch on the reflection amplitude and phase is investigated. Figure 4A and 4B show the changes of the reflection amplitude and phase when the offset position P of VO2 patch varies from 0 μm to 20 μm. It is found that the offset position of VO2 patch has little influence on the reflection amplitude and phase of meta-atom. Since the symmetrical structure is not sensitive to the polarization angle, the offset length is selected as 0 μm. When the width of VO2 patch varies, the results are shown in Figures 4C and 4D. Before the phase transition, the reflection amplitude increases and the phase decreases with the increase of VO2 patch width. When the phase transition is triggered, the variation tendency is opposite. The reason for this phenomenon is that the accumulated charge capacity under the insulating state is different. It can be seen that the volume of VO2 patch has significant effect on the amplitude and phase of reflection. In order to achieve the best performance, the same reflection amplitude in the metallic and insulating states is required. When the optical phase difference is satisfied with π, metasurface can achieve beam deflection by generating optical phase gradient. Therefore, the VO2 patch width is selected as 4 μm. The optimized geometric parameters are what we selected in the structural design. In the analysis of Figure 2, the meta-atom has the same reflection amplitude and π phase difference in the insulating and metallic states, which are coded as “0” and “1”. In order to realize the beam steering in far-field scattering pattern, meta-atoms should be symmetrically arranged in a spatial staggered manner to form a metasurface. The elements in the column are controlled by the same voltage. Therefore, the far-field radiation patterns of different encoded 24 × 24 metasurfaces are researched in detail, as shown in Figures 5A–5C. Figure 5A exhibits the reflection angle of all meta-atoms which are encoded as “0”. Because the coding sequence ‘‘0000…” represents the insulating state, no phase gradient is generated between the columns; the metasurface mainly produces a reflected beam around in 0°. Then, the 1-bit coding is encoded with “000111…”, as shown in Figure 5B. At 0.218 THz, two deflected beams are observed on −45°/+45°. Figure 5C gives the 1-bit coding which is encoded with “00001111…” and the two beam directions are −30°/+30° at 0.218 THz. In addition to the target beam deflection, metasurface also generates zero-order diffraction, which can be suppressed by introducing supercell structures (Shabanpour et al., 2020Shabanpour J. Beyraghi S. Cheldavi A. Ultrafast reprogrammable multifunctional vanadium-dioxide-assisted metasurface for dynamic THz wavefront engineering.Sci. Rep. 2020; 10: 8950-9014https://doi.org/10.1038/s41598- 020-65533-9Crossref PubMed Google Scholar). Moreover, the diffraction characteristics of the far field are calculated by the classical Fraunhofer diffraction formula. As shown in Figure 5D, when the elements are completely coded as “0000…”, the reflected beam is focused on 0°. In Figures 5E and 5F, two deflected beams of the coding sequence ‘‘000111…” and ‘‘00001111…” are observed on −44.7°/+44.7° and −31.5°/+31.5°, respectively. The periodic design means that the number of columns is divisible by the number of a single coding period. Since the number of periodic coding sequence is finite, beam scanning requires more coding sequences to improve the accuracy of beam directions. Therefore, the nonperiodic design, i.e. the total columns are not divisible by a single coding period, is proposed to realize the deflection of beams. As shown in Figures 6A–6C), when the metasurface is coded as “000011111…”, “0001111…”, and “00111…”, two deflected beams are observed on −28°/+28°, −35°/+35°, and −60°/+60°, respectively. Note that the nonperiodic coding sequence affects the phase gradient distribution on the metasurface, resulting in asymmetric beams. In Figures 6D–6F, two deflected beams of the above coding sequences are observed on −28.4°/+28.4°, −37.1°/+37.1°, and −58.9°/+58.9° by numerical calculation. The simulations coincide with theoretical results. Table 1 shows the comparisons of the different metasurfaces for THz beam steering. In this work, the 1-bit programmable metasurface can achieve tunable and wide beam scanning between −60° and +60°, which provides a promising platform for beam steering at 6G frequencies.Table 1Comparisons of different metasurfaces for THz beam steeringMaterialTuning methodsPerformanceSilicon (Cong and Singh, 2020Cong L. Singh R. Spatiotemporal dielectric metasurfaces for unidirectional propagation and reconfigurable steering of terahertz beams.Adv. Mater. 2020; 32: 2001418https://doi.org/10.1002/adma.202001418Crossref Scopus (39) Google Scholar)Femtosecond laser pulses34.7° deflection angle Non-tunableGraphene (Tamagnone et al., 2018Tamagnone M. Capdevila S. Lombardo A. Wu J. Centeno A. Zurutuza A. Ionescu A.M. Ferrari A.C. Mosig J.R. Graphene reflectarray metasurface for terahertz beam steering and phase modulation.arXiv. 2018; (Preprint at)https://doi.org/10.48550/arXiv.1806.02202Crossref Google Scholar)Voltage controlled by Arduino25° deflection angle TunableGraphene (Wu et al., 2018Wu B. Hu Y. Zhao Y.T. Lu W.B. Zhang W. Large angle beam steering THz antenna using active frequency selective surface based on hybrid graphene-gold structure.Opt Express. 2018; 26: 15353-15361https://doi.org/10.1364/OE.26.015353Crossref PubMed Scopus (30) Google Scholar)Changing the graphene chemical potential6 fixed directions cover 360° Tunable but DiscontinuousLiquid crystal (Wu et al., 2020Wu J. Shen Z. Ge S. Chen B. Shen Z. Wang T. Zhang C. Hu W. Fan K. Padilla W. et al.Liquid crystal programmable metasurface for terahertz beam steering.Appl. Phys. Lett. 2020; 116: 131104https://doi.org/10.1063/1.5144858Crossref Scopus (93) Google Scholar)Voltage controlled by FPGA32° deflection angle Tunable and DigitalVanadium dioxide (This work)Voltage controlled by FPGA± 60° deflection angle Tunable and Digital Open table in a new tab The concept of the programmable metasurface can be extended from 1-bit to 2-bit or higher coding (Cui et al., 2014Cui T.J. Qi M.Q. Wan X. Zhao J. Cheng Q. Coding metamaterials, digital metamaterials and programmable metamaterials.Light Sci. Appl. 2014; 3: e218https://doi.org/10.48550/10.1038/lsa.2014.99Crossref Google Scholar). In 2-bit coding, four states with different electromagnetic responses are required to mimic the “00”, “01”, “10”, and “11” coding. The two states of 1-bit programmable metasurface need to achieve π phase difference, then the four states of 2-bit programmable metasurface are required to achieve π/2 phase difference, such as 0, π/2, π, and 3π/2. Therefore, 2-bit coding has more degree of freedom to manipulate electromagnetic waves compared with 1-bit coding. To realize 2-bit coding, we design two meta-atoms labeled type-A and type-B with different geometries, as shown in Figure 7A . It shows that the 2-bit programmable VO2 metasurface is controlled by FPGA, in which type-A and type-B are in a staggered arrangement. The 2-bit programmable metasurface also consists of the meta-atom arrays, the dielectric substrate, and back metal film. The geometric parameters of type-A (type-B) are listed: a = 300 μm, b = 300 μm, c = 500 μm, d = 240 (150) μm, e = 270 (170) μm, f = 175 (110) μm, g = 115 (90) μm, h = 35 (15) μm, and m = 4 (3) μm. Each meta-atom (A or B) can be electrically tuned between insulting and metallic states. The deflection function of the THz beam can be achieved when the condition of phase gradient is satisfied. The 2-bit coding can improve the accuracy of beam directions. As shown in Figure 7B, the amplitudes of the two types before and after phase transition are 0.5. In Figure 7C, the optical phase of type-A has 5π/6 and 11π/6, and the phase of type-B has 4π/3 and π/3. Therefore, both of meta-atoms can satisfy the π/2 phase difference. We use “00” (“01”) for the insulating (metallic) state of type-A and “10” (“11”) for the insulating (metallic) state of type-B. Similar to the 1-bit programmable metasurface, each column has the same element type in the 2-bit programmable metasurface. By controlling each column with FPGA, the conductivity of each column VO2 can be changed, thus realizing the manipulation of the deflection angle. Based on type-A and type-B, the 18 × 18 metasurface with different 2-bit coding sequences has been designed. We remark that “0”, “1”, “2”, and “3” as the “00”, “01”, “10”, and “’11”. It can be seen that the metasurface with coding sequences in Figures 8A–8D has main beam directions of +20°, +30°, +40°, and +50° at 0.22 THz. Correspondingly, the numerical results also show that the beam deflections of +20.1°, +31.5°, +41.8°, and +50.0° are generated in Figures 8E–8H. The 2-bit coding can achieve a single deflection angle. Thus, 3 dB diffraction energy efficiency is improved. When the above coding sequences in Figure 8 are inverted, such as “0123” to “3210”, it can achieve a symmetrical beam deflection between −20° and −50°. To prove the flexibility of 2-bit encoding, we design other coding sequences in Figure 9. It can be seen that the metasurface with 2-bit coding sequences in Figures 9A–9D achieves main beam directions of −20°, −30°, −40°, and −50° at 0.22 THz. The calculated results show that the beam deflections of −22.1°, −31.7°, −42.1°, and −53.1° are generated in Figures 9E–9H. Therefore, the simulations coincide with theoretical results, and the same beam deflection can be achieved with different coding sequences. 2-bit programmable metasurface has higher freedom on phase and more flexible coding sequences.Figure 9Simulated and calculated far-field patterns of the designed 18 × 18 metasurface with different 2-bit coding sequences of “020303031212020303”Show full caption(A–H) (A and E), “031212030303120203” (B and F), “120303120203021203” (C and G), and “031203031203031203” (D and H), respectively at 0.22 THz.View Large Image Figure ViewerDownload Hi-res image Download (PPT) (A–H) (A and E), “031212030303120203” (B and F), “120303120203021203” (C and G), and “031203031203031203” (D and H), respectively at 0.22 THz. In summary, we report 1-bit and 2-bit programmable VO2 metasurfaces which realize phase difference of π and π/2, respectively. Combining with the FPGA, metasurface can be applied to change the direction of beam deflection by dynamically configuring the coding sequences in real-time. The 1-bit coding can achieve wide deflection angles between −60° and +60° by generating two symmetrical deflection angles. The 2-bit programmable metasurface has higher freedom of control on phase and achieves a single deflection angle with 3 dB diffraction efficiency improvement compared with 1-bit programmable metasurface. The simulation results coincide with theoretical results. This work offers a promising method of dynamic beam deflection at 6G frequencies and enables the broad adoption of wireless communication.