Open Access
Add to BibSonomy
Abstract
Coding metamaterials have offered unprecedented degrees of freedom to manipulate electromagnetic waves in time and frequency domains in terms of various coding sequences, however, it is still challenging to realize dynamic coding metamaterials in the terahertz range. Here, we propose VO2-enabled transmission-reflection switchable coding terahertz metamaterials consisting of multilayered gold and VO2 patterns. The insulator-to-metal transition of VO2 leads to switch between the refractive and reflective scattering beams by changing the temperature. The four 2-bit elements are used to construct coding metasurface-based OAM generator with l = 1. Remarkably, the transmission-reflection switching functionality of the coding metasurface can be achieved at different frequencies. In addition, the novel designs in our work can achieve EM waves manipulation and provide a useful method to dynamically switch transmission-reflection response in the THz frequency regime.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Over the past decade, metamaterials with artificially designed subwavelength meta-atoms have attracted tremendous attention due to exotic phenomena and applications such as negative refraction [1], cloaking [2] and perfect absorption [3] and camouflage [4]. Newly reported metasurfaces with transverse phase discontinuities, as two-dimensional metamaterials [5], can realize versatile wavefront and polarization manipulations that are dictated by the generalized Snell’s law. Metasurfaces have been designed to achieve extraordinary applications such as holography [6,7], polarization conversion [8] and orbital angular momentum (OAM) generation [5,9,10]. As one of the most promising candidates, digital and coding metasurfaces and metamaterials have been proposed to powerfully manipulate electromagnetic waves [11,12]. Different from conventional metamaterials, coding metamaterials with well-defined elements can be digitalized and programmed via field-programmable gate array (FPGA) and machine learning [12,13]. For example, 1-bit coding metasurfaces are composed of two elements ‘0’ and ‘1’, corresponding to 0 and π phase responses, respectively. The coding metamaterials with optimized spatial sequences can achieve more freedoms to control electromagnetic waves and bridge physics and information fields [14]. More importantly, well-known theorems of information sciences including convolution operations [15], addition theorem [16] and information entropy [17] have been introduced to coding metasurfaces. Such schemes are beneficial to broaden practical applications and promote their developments including spin-to-orbital angular momentum conversion [18], multifunctional full-space wave control [19,20], spectral imaging [21], independent magnitude, phase and polarization manipulation [22–24], space-time modulation [25–29] to programmable diffractive deep neural network [30].
Recently, coding metasurfaces have also received much attention in the terahertz frequency range due to flexible and tunable wave manipulations [15,21,31–38]. Based on coding elements, various phenomena and applications have been studied, including convolution operations [15], spectral imaging [21], broadband diffusion [31], Bessel-beam generation [32], polarization manipulation [33,34] and anomalous scattering [35]. But diodes and varactors cannot be applied in the terahertz frequency range, it is challenging to develop programmable coding terahertz metamaterials that are comparable to ones in the microwave range [14,30]. With the integration of active materials such as graphene [36–38], GeTe [39] and VO2 [40–42], several attempts have been made to achieve reconfigurable beam shaping of terahertz waves. VO2 experiences its phase transition within picoseconds timescale [43,44]. Since the insulator-to-metal phase transition of the VO2 material can be readily triggered optically, thermally or electrically by external stimuli at around 68 °C [45–49], it is regarded as a promising candidate for designing tunable coding terahertz metamaterials [40–42,50–52]. Individual reflective or transmissive beam shaping and polarization manipulation have been dynamically achieved in coding metamaterials with patterned VO2 films [50–53]. The reflection-transmission switching modulation is promising for tailoring electromagnetic wave propagation direction, independent polarization manipulation and multi-channel information processing, however, in all previous literatures polarization-dependent reflection-transmission switching phenomena have been mainly investigated in the microwave range [19,20,54–57]. To achieve various functionalities, passive metamaterials without tunability need to be redesigned and fabricated, which hampers practical applications as well as functional extension. Transmission and reflection bi-direction terahertz encoding metasurface with silicon microstructures and VO2 layer has been numerically investigated [58], but the fabrication of silicon microstructures requires great efforts. With the increasing demands in integrated and multifunctional devices, tunable reflection-transmission switching phenomena are highly desirable and promising, but still challenging in the terahertz range.
In this work, we propose a reflection-transmission reconfigurable coding metasurface with integrated VO2 structures in the terahertz region. The coding metasurface is composed of multilayered gold and VO2 hybrid structures. According to different 2-bit coding sequences, the metasurface can deflect a normal linear polarized wave into a desired direction and enable terahertz vortex generation. The switching effect of the transmission and reflection relies on the phase transition of VO2 triggered by thermal excitation rather than changing the metasurface structure. The proposed coding metamaterial offers dynamically tailored terahertz response and can thermally switch functionalities between reflection and transmission.
2. Design and results
VO2 as a kind of phase transition material can dynamically tailor electromagnetic responses of metamaterials, especially in the terahertz range. The VO2 material experiences an insulator-to-metal phase transition once the temperature exceeds its critical temperature of 68°C. VO2 is in an insulating state when the temperature is below 68°C while it is changed to the metallic state at a temperature beyond 68°C. The permittivity of VO2 can be described by Drude model as follows:
Here, we propose a multilayered coding metamaterial consisting of gold and VO2 hybrid structures. As schematic diagram described in Fig. 1(a), normally incident x-polarized terahertz waves are reflected anomalously by the metamaterial with metallic VO2 films. In Fig. 1(b), the proposed metamaterial allows anomalous refraction of x-polarized terahertz waves along the -z direction when the VO2 films are in the insulating phase. Therefore, the reflection-transmission switching functionality can be achieved by the VO2 phase transition in Fig. 1.
Fig. 1. Conceptual illustration of reflection-transmission reconfigurable terahertz coding metamaterial switched by the insulator-to-metal transition of VO2. (a) Reflection-type coding metasurface with metallic VO2 for incident x-polarized wave. (b) Transmission-type coding metasurface with insulating VO2 for incident x-polarized wave.
The proposed multilayer coding metasurface in this work has five layers consisting of hybrid gold with the conductivity σ = 4.56×107 S/m [45] and VO2 patches as shown in Fig. 2(a). Two adjacent structure layers are separated by a dielectric layer. The metasurface is an array of square lattices, in which both the periods along the x and y directions are P = 100 µm. All dielectric layers have the same thickness of h = 12.7 µm, and its relative dielectric constant and loss tangent are assumed to be ɛ = 2.4 and tanδ = 0.002 [47], respectively. The middle layer is a gold one with a complementary cross-shaped VO2 patch. The dimension of the middle layer is the same as the period in Fig. 2(a) and the geometrical parameters of the cross-shaped VO2 patch are l1 = 15 µm and l2 = 75 µm as displayed in Fig. 2(b). Four identical structured patterns are symmetrically distributed on two sides of the middle layer along the z direction in Fig. 2(a). For each structured pattern with thickness of 0.9 µm in Fig. 2(c), two identical VO2 patches are symmetrically attached to two sides of the gold structure along the x direction. The length and width of each gold structure are defined as l3 and w, respectively. The total length of each hybrid pattern is l4. According to the concept of coding metasurfaces, in order to acquire a 2-bit coding metasurface, it is necessary to elaborately design four coding particles with π/2 difference between two adjacent elements. They are denoted as four binary states 00, 01, 10 and 11, respectively. During the optimization of four coding particles, the width of the gold and the VO2 patch is kept unchanged as w = 62.5 µm while the geometrical parameters l3 and l4 are variable. For achieving the phase requirement, the parameters of l3 and l4 are listed in Table 1. Based on the insulator-to-metal transition of VO2, the proposed coding metasurface can be further classified into two types, in which one is transmissive when VO2 is in the insulating phase and the other is reflective when VO2 is metallic. Actually, the middle layer with complementary gold and VO2 patches is important to switch the reflection and transmission functionalities of the coding metasurface.
Fig. 2. (a) The sketch of the multilayered coding metasurface with square lattices. (b) Structure of the middle layer. (c) Structure of the hybrid gold and VO2 patterns.
Table 1. Structural parameters of 2-bit coding metamaterial
To illustrate the reflection-transmission switching effect of the VO2 pattern, simulations have been completed by use of the commercial software CST Microwave Studio to show electromagnetic responses of the coding particles with different phase states. In the simulations, the periodic boundary conditions are adopted along with the x and y directions and two floquet ports are employed along the z direction. Figure 3 shows the current distributions of the coding element illuminated by x-polarized terahertz wave propagating along the -z direction. It is obvious from Fig. 3(a) that the linear polarized EM waves can pass through the middle layer when the VO2 is in the insulating state, indicating that the coding metasurface is transmission-type. While the incident x-polarized terahertz wave cannot transmit in the coding metasurface with metallic VO2, the coding metasurface is reflective in Fig. 3(b) since the middle layer behaves as a metal plate. The phase and amplitude responses of four transmission-type and reflection-type coding elements are depicted in Fig. 3. The required four coding elements 00, 01, 10 and 11 in the 2-bit coding metasurface can be obtained by changing l3 and l4 as mentioned before. The phase difference between two adjacent transmissive coding elements is nearly 90° around 1.1 THz in Fig. 4(a) and their amplitudes are relatively high over 0.6 at 1.1 THz in Fig. 4(b), in which the metasurface is integrated by insulating VO2. The absorption values of four transmission-type coding elements are about 23%, 34%, 32% and 45%, respectively. The VO2 patterns undergo an insulator-to-metal transition at the temperature above 68 °C, the proposed coding elements are thermally changed to be reflective. The phase difference between two coding elements is π/2 and the whole reflective phase change covers 2π at 1.1 THz in Fig. 4(c). In addition, their amplitudes are ∼ 0.9 in Fig. 4(d). The absorption values of four reflection-type coding elements are about 2%, 12%, 13% and 15%, respectively. Due to the phase transition of VO2, the dynamic reconfiguration between the transmission-type and reflection-type coding metasurfaces can be thermally realized at around 1.1 THz by changing the temperature rather than re-designing a new structure.
Fig. 3. The surface current distributions of the coding elements under x-polarized illumination along -z direction when the VO2 patches are in (a) insulating and (b) metallic states, respectively.
Fig. 4. (a) The phase and (b) amplitude responses of the four 2-bit coding elements when the VO2 patches are in an insulating phase. (c) The phase and (d) amplitude responses of the four 2-bit coding elements when the VO2 films are in a metallic phase. The vertical dashed lines correspond to 1.1 THz.
According to the generalized Snell’s laws, anomalous reflection and transmission phenomena can be achieved by designing metasurfaces with appropriate gradient phase shifts. The deflection angle of the wave can be calculated by the following formula
where λ is the working wavelength and Γ is the period of the coding sequence consisting of the proposed particles. To illustrate the EM waves manipulation, a metasurface is encoded with the predesigned periodic sequence as 00-01-10-11… along the x direction. To decrease the coupling between discrete digital elements, 4×4 identical elements are adopted as a super lattice to construct the coding metasurface. In Fig. 5, the simulated transmissive and reflective far-field scattering beams are plotted at 1.1 THz when the x-polarized beam normally illuminates upon the coding metasurface along the -z direction. Obviously, the incident beam is anomalously refracted and reflected, respectively. The both deflection angles are 19° in good agreement with the result from Eq. (3). Remarkably, the switching effect of refractive and reflective scattering beams can be accomplished by the insulator-to-metal transition of VO2 via changing the temperature.Fig. 5. The transmissive and reflective far-field scattering patterns of the 2-bit coding metasurface under the normal x-polarized incidence along the -z direction when the VO2 films are in (a) insulating phase and (b) metallic phase at 1.1 THz.
The phase and amplitude responses in Fig. 4 indicate that the switching effect of the scattering phenomenon can be achieved at a wide frequency range. For normally incident x-polarized wave along the -z direction, various scattering beams of the coding metasurface at different frequencies are shown in Fig. 6 when the VO2 films are insulating and metallic, respectively. When the VO2 patches are in an insulating phase, the transmissive beams are shown in Figs. 6(a)–6(c) while the reflected scattering patterns of the coding metasurface with metallic VO2 are depicted in Figs. 6(d)–6(e). Since the phase and amplitude responses of the coding elements vary with the frequency, the switching effect from transmissive to reflective far-field scattering patterns in Fig. 6 changes as well. At 0.8 THz, the insulator-to-metal phase transition of VO2 can switch a transmissive deflected beam to a normally reflected beam in Fig. 6(a) and Fig. 6(d). At 0.9 THz, the switching phenomenon in Fig. 6(b) and Fig. 6(e) is the same as the one in Fig. 5. While at 1.28 THz, the double deflected beams are switched from transmissive to reflective ones in Fig. 6(c) and Fig. 6(f). Therefore, the transmission-reflection switching functionality of the coding metasurface can be thermally achieved at different frequencies.
Fig. 6. The switching effect of the scattering beams in the coding metasurface at different frequencies. The transmissive beams of the coding metasurface with insulating VO2 patches are shown at (a) 0.8 THz, (b) 0.9 THz and (c) 1.28 THz. The reflective beams of the coding metasurface with metallic VO2 patches are shown at (d) 0.8 THz, (e) 0.9 THz and (f) 1.28 THz.
To further exhibit the EM waves manipulation in the coding metamaterial, another periodic coding sequence is designed as 00-01-10-11…along the y direction. Thus, the deflection angles can also be calculated according to Eq. (3) and the value of 19° is kept unchanged. Obviously, different oriented coding sequence leads to the deflection beams along different directions. The scattering patterns are shown as Figs. 7(a) and 7(b). Figure 7(a) indicates the transmitted beam in the coding metasurface with insulating VO2 is deflected along the y direction. The EM waves are anomalously reflected with the same angle along the y direction in Fig. 7(b) when the VO2 patches are metallic. These scattering beams are obtained in the elevation plane, however, the beams at different azimuthal directions are indispensable in many applications. Therefore, to achieve a deflected beam in arbitrary azimuthal directions, the two coding sequences mentioned above are adopted to generate another sequence along the orthogonal directions according to the convolution operations. Thus, the new angles θ and φ can be calculated as
Fig. 7. The switchable scattering beams of the metasurface with different coding sequences. The deflected beams of the coding metasurface with y-oriented coding sequence are presented when the VO2 films are in (a) insulating and (b) metallic states, respectively. The deflected beams of the coding metasurface with orthogonal coding sequences are presented when the VO2 films are in (c) insulating and (d) metallic states.
The aforementioned coding elements can be azimuthally arranged to generate a vortex beam. Hence, the proposed 2-bit elements are employed to generate a vortex beam with propagation phase distribution of eilφ, where l is the topological charge of the OAM mode and φ represents the azimuthal angle around the propagation direction. The front view of the metasurface and the diagram of encoded elements distribution with l = 1 are displayed in Fig. 8(a) and 8(b), respectively. It is obvious that the whole metasurface area can be divided into four regions with π/2 phase interval and the azimuthal phase covers 2π. Figure 8(c) and 8(d) show the phase distributions and far-field patterns of transmissive and reflective OAM generators with mode purity of 73% for the incident x-polarized wave at 1.1 THz, respectively [59]. More importantly, due to the phase transition of VO2 patches, it is available to achieve a dynamic switching between transmissive and reflective vortex beams. Although the experimental work of the proposed coding metamaterial has not been provided here, it can be readily fabricated by lithography and lift off technology [32,60]. Under different external stimuli such as temperature, light or electricity, VO2 can experience its phase transition within picoseconds timescale, please refer to the literatures [43–45]. In practical applications, proper stimuli can be selected, for instance, temperature control was used in Ref. 45. The switching speed of the proposed metadevice is limited by the thermal and input-power parameters at the device level rather than the intrinsic limit of VO2 [53]. It can be believed that intelligent coding metasurfaces with various functional materials offer a significant platform for realizing terahertz sensing, terahertz modulators and wireless communications [30,61,62].
Fig. 8. The switching effect of transmissive and reflective vortex beams with l = 1 in coding metasurface for incident x-polarized wave at 1.1 THz. (a) The front view of the metasurface. (b) The four coding particles distribution. The phase distributions and far-field patterns of the transmissive and reflective coding metasurface with (c) insulting and (d) metallic VO2 patches.
3. Conclusion
In conclusion, we have proposed a transmission-reflection switchable 2-bit coding metasurface by use of the insulator-to-metal transition of VO2 patches in the terahertz range. The metamaterial is composed of multilayered gold and VO2 patterns. The functionality switching between transmission and reflection is thermally dictated by the complementary gold and VO2 middle layer. The insulator-to-metal transition of VO2 leads to switch between the refractive and reflective scattering beams by changing the temperature. Remarkably, the transmission-reflection switching functionality of the coding metasurface can be achieved at different frequencies. In addition, the four 2-bit elements are used to construct coding metasurface-based OAM generator with l = 1. Due to the phase transition of VO2 patches, it is available to achieve a dynamic switching between transmissive and reflective vortex beams. The novel designs in our work can achieve EM waves manipulation and provide a useful method to dynamically switch transmission-reflection response in the THz frequency regime.
Funding
National Natural Science Foundation of China (62175049); Natural Science Foundation of Heilongjiang Province (ZD2020F002, LH2021A008); 111 Project (B13015); Fundamental Research Funds for the Central Universities (3072021CFT2501).
Acknowledgments
The authors thank numerical calculation supports from the State Key Laboratory of Millimeter Waves of Southeast University.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
References
1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef]
2. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef]
3. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef]
4. F. Y. Dong, S. Xu, W. R. Guo, N. R. Jiang, D. D. Han, X. Y. He, L. Zhang, Z. J. Wang, J. Feng, W. M. Su, and H. B. Sun, “Solar-energy camouflage coating with varying sheet resistance,” Nano Energy 77, 105095 (2020). [CrossRef]
5. N. F. 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]
6. L. L. Huang, X. Z. Chen, H. Mühlenbernd, H. Zhang, S. M. Chen, B. F. Bai, Q. F. Tan, G. F. 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]
7. X. J. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4(1), 2807 (2013). [CrossRef]
8. 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]
9. R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358(6365), 896–901 (2017). [CrossRef]
10. Y. J. Shen, X. J. Wang, Z. W. Xie, C. J. Min, X. Fu, Q. Liu, M. L. Gong, and X. C. Yuan, “Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities,” Light: Sci. Appl. 8(1), 90 (2019). [CrossRef]
11. C. D. Giovampaola and N. Engheta, “Digital metamaterials,” Nat. Mater. 13(12), 1115–1121 (2014). [CrossRef]
12. 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]
13. L. L. Li, H. X. 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]
14. T. J. Cui, L. L. Li, S. Liu, Q. Ma, L. Zhang, X. Wan, W. X. Jiang, and Q. Cheng, “Information metamaterial systems,” iScience 23(8), 101403 (2020). [CrossRef]
15. S. Liu, T. J. Cui, L. Zhang, Q. Xu, Q. Wang, X. Wan, J. Q. Gu, W. X. Tang, M. Q. 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]
16. R. Y. Wu, C. B. Shi, S. Liu, W. Wu, and T. J. Cui, “Addition theorem for digital coding metamaterials,” Adv. Opt. Mater. 6(5), 1701236 (2018). [CrossRef]
17. T. J. Cui, S. Liu, and L. L. Li, “Information entropy of coding metasurface,” Light: Sci. Appl. 5(11), e16172 (2016). [CrossRef]
18. G. W. Ding, K. Chen, X. Y. Luo, J. M. Zhao, T. Jiang, and Y. J. Feng, “Dual-helicity decoupled coding metasurface for independent spin-to-orbital angular momentum conversion,” Phys. Rev. Appl. 11(4), 044043 (2019). [CrossRef]
19. 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]
20. L. W. Wu, H. F. Ma, R. Y. Wu, Q. Xiao, Y. Gou, M. Wang, Z. X. Wang, L. Bao, H. L. Wang, Y. M. Qing, and T. J. Cui, “Transmission-reflection controls and polarization controls of electromagnetic holograms by a reconfigurable anisotropic digital coding metasurface,” Adv. Opt. Mater. 8(22), 2001065 (2020). [CrossRef]
21. T. F. Wang, B. W. Chen, J. B. Wu, S. X. Yang, Z. Shen, J. C. Cai, W. L. Li, C. H. Zhang, B. B. Jin, J. Chen, and P. H. Wu, “Spectral imaging of flexible terahertz coding metasurface,” Appl. Phys. Lett. 118(8), 081101 (2021). [CrossRef]
22. J. Zhang, H. Zhang, W. X. Yang, K. Chen, X. Z. Wei, Y. J. Feng, R. H. Jin, and W. R. Zhu, “Dynamic scattering steering with graphene-based coding meta-mirror,” Adv. Opt. Mater. 8(19), 2000683 (2020). [CrossRef]
23. J. Shabanpour, M. Sedaghat, V. Nayyeri, H. Oraizi, and O. M. Ramahi, “Real-time multi-functional near-infrared wave manipulation with a 3-bit liquid crystal based coding metasurface,” Opt. Express 29(10), 14525–14535 (2021). [CrossRef]
24. C. Huang, J. M. Liao, C. Ji, J. Q. Peng, L. M. Yuan, and X. G. Luo, “Graphene-integrated reconfigurable metasurface for independent manipulation of reflection magnitude and phase,” Adv. Opt. Mater. 9(7), 2001950 (2021). [CrossRef]
25. 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]
26. S. Taravati and G. V. Eleftheriades, “Microwave space-time-modulated metasurfaces,” ACS Photonics 9(2), 305–318 (2022). [CrossRef]
27. A. M. Shaltout, V. M. Shalaev, and M. L. Brongersma, “Spatiotemporal light control with active metasurfaces,” Science 364(6441), eaat3100 (2019). [CrossRef]
28. M. S. Masyukov and A. N. Grebenchukov, “Temporally modulated metamaterial based on a multilayer graphene structure,” Phys. Rev. B 104(16), 165308 (2021). [CrossRef]
29. S. Taravati and G. V. Eleftheriades, “Pure and linear frequency-conversion temporal metasurface,” Phys. Rev. Appl. 15(6), 064011 (2021). [CrossRef]
30. C. Liu, Q. Ma, Z. J. Luo, Q. R. Hong, Q. Xiao, H. C. Zhang, L. Miao, W. M. Yu, Q. Cheng, L. L. Li, and T. J. Cui, “A programmable diffractive deep neural network based on a digital-coding metasurface array,” Nat. Electron. 5(2), 113–122 (2022). [CrossRef]
31. 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]
32. S. Liu, A. Noor, L. L. Du, L. Zhang, Q. Xu, K. Luan, T. Q. Wang, Z. Tian, W. X. Tang, J. G. Han, W. L. Zhang, X. Y. Zhou, Q. Cheng, and T. J. Cui, “Anomalous refraction and nondiffractive Bessel-beam generation of terahertz waves through transmission-type coding metasurfaces,” ACS Photonics 3(10), 1968–1977 (2016). [CrossRef]
33. C. L. Zheng, J. Li, G. C. Wang, J. T. Li, S. L. Wang, M. Y. Li, H. L. Zhao, Z. Yue, Y. T. Zhang, Y. Zhang, and J. Q. Yao, “All-dielectric chiral coding metasurface based on spin-decoupling in terahertz band,” Nanophotonics 10(4), 1347–1355 (2021). [CrossRef]
34. S. Liu, T. J. Cui, Q. Xu, D. Bao, L. L. Du, X. Wan, W. X. Tang, C. M. Ouyang, X. Y. Zhou, H. Yuan, H. F. Ma, W. X. Jiang, J. G. Han, W. L. Zhang, and Q. Cheng, “Anisotropic coding metamaterials and their powerful manipulation of differently polarized terahertz waves,” Light: Sci. Appl. 5(5), e16076 (2016). [CrossRef]
35. L. Y. Wang, F. Lan, Y. X. Zhang, S. X. Liang, W. X. Liu, Z. Q. Yang, L. Meng, Z. J. Shi, J. Yin, T. T. Song, H. X. Zeng, and P. Mazumder, “A fractional phase-coding strategy for terahertz beam patterning on digital metasurfaces,” Opt. Express 28(5), 6395–6407 (2020). [CrossRef]
36. S. E. Hosseininejad, K. Rouhi, M. Neshat, A. Cabellos-Aparicio, S. Abadal, and E. Alarcón, “Digital metasurface based on graphene: An application to beam steering in terahertz plasmonic antennas,” IEEE Trans. Nanotechnol. 18, 734–746 (2019). [CrossRef]
37. B. G. Xiao, Y. Zhang, S. J. Tong, J. B. Yu, and L. H. Xiao, “Novel tunable graphene-encoded metasurfaces on an uneven substrate for beam-steering in far-field at the terahertz frequencies,” Opt. Express 28(5), 7125–7138 (2020). [CrossRef]
38. K. Rouhi, S. E. Hosseininejad, S. Abadal, M. Khalily, and R. Tafazolli, “Multi-channel near-field terahertz communications using reprogrammable graphene-based digital metasurface,” J. Lightwave Technol. 39(21), 6893–6907 (2021). [CrossRef]
39. Q. W. Lin, H. Wong, L. Huitema, and A. Crunteanu, “Coding metasurfaces with reconfiguration capabilities based on optical activation of phase-change materials for terahertz beam manipulations,” Adv. Opt. Mater. 10(1), 2101699 (2022). [CrossRef]
40. J. Li, Y. Yang, J. N. Li, Y. T. Zhang, Z. Zhang, H. L. Zhao, F. Y. Li, T. T. Tang, H. T. Dai, and J. Q. Yao, “All-optical switchable vanadium dioxide integrated coding metasurfaces for wavefront and polarization manipulation of terahertz beams,” Adv. Theory Simul. 3(1), 1900183 (2020). [CrossRef]
41. J. H. Li, Y. T. Zhang, N. Ji, J. Li, Y. Yang, J. Huang, C. Q. Ma, Z. Z. Ma, Z. Zhang, L. J. Liang, and J. Q. Yao, “Frequency-switchable VO2-based coding metasurfaces at the terahertz band,” Opt. Commun. 458, 124744 (2020). [CrossRef]
42. Z. L. Li, W. Wang, S. X. Deng, J. Qu, Y. X. Li, B. Lv, W. J. Li, X. Gao, Z. Zhu, C. Y. Guan, and J. H. Shi, “Active beam manipulation and convolution operation in VO2-integrated coding terahertz metasurfaces,” Opt. Lett. 47(2), 441–444 (2022). [CrossRef]
43. T. L. Cocker, L. V. Titova, S. Fourmaux, G. Holloway, H. C. Bandulet, D. Brassard, J. C. Kieffer, M. A. E. Khakani, and F. A. Hegmann, “Phase diagram of the ultrafast photoinduced insulator-metal transition in vanadium dioxide,” Phys. Rev. B 85(15), 155120 (2012). [CrossRef]
44. H. W. Liu, J. P. Lu, and X. R. S. Wang, “Metamaterials based on the phase transition of VO2,” Nanotechnology 29(2), 024002 (2018). [CrossRef]
45. M. K. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keisier, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. W. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487(7407), 345–348 (2012). [CrossRef]
46. T. T. Lv, Y. X. Li, H. F. Ma, Z. Zhu, Z. P. Li, C. Y. Guan, J. H. Shi, H. Zhang, and T. J. Cui, “Hybrid metamaterial switching for manipulating chirality based on VO2 phase transition,” Sci. Rep. 6(1), 23186 (2016). [CrossRef]
47. S. X. Wang, L. Kang, and D. H. Werner, “Active terahertz chiral metamaterials based on phase transition of vanadium dioxide (VO2),” Sci. Rep. 8(1), 189 (2018). [CrossRef]
48. F. Ding, S. M. Zhong, and S. I. Bozhevolnyi, “Vanadium dioxide integrated metasurfaces with switchable functionalities at terahertz frequencies,” Adv. Opt. Mater. 6(9), 1701204 (2018). [CrossRef]
49. X. B. Liu, Q. Wang, X. Q. Zhang, H. Li, Q. Xu, Y. H. Xu, X. Y. Chen, S. X. Li, M. Liu, Z. Tian, C. H. Zhang, C. W. Zou, J. G. Han, and W. L. Zhang, “Thermally dependent dynamic meta-holography using a vanadium dioxide integrated metasurface,” Adv. Opt. Mater. 7(12), 1900175 (2019). [CrossRef]
50. J. Shabanpour, “Programmable anisotropic digital metasurface for independent manipulation of dual-polarized THz waves based on a voltage-controlled phase transition of VO2 microwires,” J. Mater. Chem. C 8(21), 7189–7199 (2020). [CrossRef]
51. B. Ren, Y. X. Feng, S. Tang, L. Wang, H. Jiang, and Y. Y. Jiang, “Dynamic control of THz polarization modulation and multi-channel beam generation using a programmable metasurface,” Opt. Express 29(11), 17258–17268 (2021). [CrossRef]
52. W. M. Pan, J. S. Li, and C. Zhou, “Switchable digital metasurface based on phase change material in the terahertz region,” Opt. Mater. Express 11(4), 1070–1079 (2021). [CrossRef]
53. L. Liu, L. Kang, T. S. Mayer, and D. H. Werner, “Hybrid metamaterials for electrically triggered multifunctional control,” Nat. Commun. 7(1), 13236 (2016). [CrossRef]
54. Y. Jing, Y. F. Li, J. Q. Zhang, J. F. Wang, M. C. Feng, H. Ma, and S. B. Qu, “Full-space-manipulated multifunctional coding metasurface based on “Fabry-Pérot-like” cavity,” Opt. Express 27(15), 21520–21531 (2019). [CrossRef]
55. C. Zhang, G. M. Wang, H. X. Xu, X. Zhang, and H. P. Li, “Helicity-dependent multifunctional metasurfaces for full-space wave control,” Adv. Opt. Mater. 8(8), 1901719 (2020). [CrossRef]
56. L. W. Wu, Q. Xiao, Y. Gou, R. Y. Wu, P. Xu, Y. M. Qing, Z. X. Wang, L. Bao, H. F. Ma, and T. J. Cui, “Electromagnetic diffusion and encryption holography integration based on reflection-transmission reconfigurable digital coding metasurface,” Adv. Opt. Mater. 10, 2102657 (2022). [CrossRef]
57. Z. T. Zhang, J. F. Wang, R. C. Zhu, Y. X. Jia, T. H. Liu, M. B. Yan, J. M. Jiang, Y. F. Li, Y. Y. Meng, and S. B. Qu, “Multifunctional full-space metasurface controlled by frequency, polarization and incidence angle,” Opt. Express 29(5), 7544–7557 (2021). [CrossRef]
58. J. S. Li and L. J. Yang, “Transmission and reflection bi-direction terahertz encoding metasurface with a single structure,” Opt. Express 29(21), 33760–33770 (2021). [CrossRef]
59. Q. L. Yang, Y. Wang, L. J. Liang, and M. S. Yang, “Broadband transparent terahertz vortex beam generator based on thermally tunable geometric metasurface,” Opt. Mater. 121, 111574 (2021). [CrossRef]
60. M. Liu, Q. Xu, X. Y. Chen, E. Plum, H. Li, X. Q. Zhang, C. H. Zhang, C. W. Zou, J. G. Han, and W. L. Zhang, “Temperature-controlled asymmetric transmission of electromagnetic waves,” Sci. Rep. 9(1), 4097 (2019). [CrossRef]
61. L. L. Li, H. T. Zhao, C. Liu, L. Li, and T. J. Cui, “Intelligent metasurfaces: control, communication and computing,” eLight 2(1), 1–24 (2022). [CrossRef]
62. O. Tsilipakos, A. C. Tasolamprou, A. Pitilakis, F. Liu, X. C. Wang, M. S. Mirmoosa, D. C. Tzarouchis, S. Abadal, H. Taghvaee, C. Liaskos, A. Tsioliaridou, J. Georgiou, A. C. Aparicio, E. Alarcón, S. Ioannidis, A. Pitsillides, I. F. Akyildiz, N. V. Kantartzis, E. N. Economou, C. M. Soukoulis, M. Kafesaki, and S. Tretyakov, “Toward intelligent metasurfaces: the progress from globally tunable metasurfaces to software-defined metasurfaces with an embedded network of controllers,” Adv. Opt. Mater. 8(17), 2000783 (2020). [CrossRef]
