Open Access
Add to BibSonomy
Abstract
In general, the functions of most metalenses cannot be adjusted dynamically after being fabricated. Here, we theoretically propose an electrically tunable metalens composed of single-layered and non-structured doped graphene loaded with ribbon-shaped metallic strip arrays with varied widths and gaps. The combination of the different widths and gaps can provide full phase coverage from 0 to 2π, which is necessary for a plane wave to be focused. The metalens exhibits obvious tunability of focal length and focal intensity as we varied the Fermi levels of the doped graphene at 10 THz. The focus is able to be shifted within 90.4 µm (∼3λ), with maximum focusing efficiency up to 61.62%. The tunable metalens can also be expanded to other operation frequencies from mid-infrared to terahertz range by properly designing structural parameters. The metalens consisting of nanostructured metal and non-structured graphene utilizes mature metal nanostructure preparation process and avoids the graphene processing, which consequently facilitates the fabrication and promotes the application.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
At present, optical focusing is mainly realized by the combination of multiple geometric lenses. However, contradiction exists between the miniaturization of lenses and the large physical movement space required by dynamic focusing. In order to solve this problem, alternative solutions are currently being researched internationally. Metasurfaces, composed of arrays of metallic or dielectric units, with unique electromagnetic responses, may provide a feasible solution [1]. Different from conventional lenses, which rely on light propagation along the optical path to change phase, metasurfaces realize the modulation of phase through interaction between electromagnetic waves and free electrons [2–4], providing a new method for lenses designing.
Metalenses have been developed rapidly since the concept of metasurface devices was proposed [5], and been used in many aspects due to their unique characteristics, such as focusing [1,2], eliminating chromatic aberration [4,6], eliminating monochromatic aberration [7], etc. However, the functions of most metalenses cannot be adjusted dynamically after being fabricated. An effective method is to add active or tunable materials to metalens such as transparent conductive oxides [8], ferroelectrics [9], elastic material [10] and two-dimensional materials (for example, graphene and MoS2) [11].
As a typical representative of two-dimensional materials, graphene has received widespread attention from researchers due to its unique electrical and optical properties. Rely on adjustable Fermi level (by gate voltage biasing, chemical doping, or light doping [12–14]) and high carrier mobility, graphene can act as an ideal candidate for plasmon materials with relatively low losses [15,16]. Compared with conventional metals, graphene plasmons have characteristics of long propagation distance, good tunability, and strong energy limitation at lower frequencies [17–20]. In terahertz and far infrared regions, in-band transitions dominate and graphene plasmons are generated. Combining graphene with metals or dielectric, the tunable metasurface can achieve diverse functions, such as optical phase or amplitude modulation [21–25], coded imaging [26], hologram [27], and dynamic focusing [28–35]. However, hybrid metal-graphene metalens for dynamic focusing still face some challenges. Some metalenses with lots of independent graphene strips [28,29] needs a field programmable gate array (FPGA). Other metalenses require nanostructured graphene [30,31] or metal nanostructures with gradually varying orientation [32–35]. The too many truncation edges of nanostructured graphene might lead to some unexpected edge effects and influence the unique properties of graphene. The gradually varying orientation has higher requirements on the micro-nano fabrication equipment and process.
In this paper, we demonstrate a metalens for dynamic focusing based on a hybrid structure of simple metallic strip arrays and non-structured monolayer graphene. The interaction between incident light and the metalens can be adjusted by varying a voltage of the whole piece of graphene. The metalens exhibits obvious characteristics of controlling focal length and focal intensity at 10 THz. When the Fermi level of graphene varies from 0.1 eV to 0.9 eV, the focus accordingly shifts by 90.4 µm (∼3λ) and the maximum focusing efficiency is up to 61.62%.
2. Structures and methods
The proposed graphene-based tunable metalens is shown in Fig. 1, which consists of non-structured electrically doped graphene loaded with Au antennas. The single-layered graphene is on a dielectric layer of SiO2 supported by a thick Au film. A bias voltage Vg is imposed between the graphene and the thick Au film to electrically dope and tune the graphene chemical potential. The thickness of Au antennas, SiO2 layer, and Au film are fixed at 0.6 µm, 2.9 µm, and 0.2 µm, respectively. The Au antennas consisting of ribbon-shaped metallic strip arrays with varied widths and gaps are arranged in the x direction with a period of 15 µm. X-direction linearly polarized THz wave is normally incident onto the metalens. The working frequency is set to be 10 THz and the structure can be regarded as an asymmetric Fabry-Perot resonator. Dynamic focus is achieved by adjusting the Fermi level of the whole piece of graphene. All simulations are performed in the FDTD solutions, where the Fermi velocity Vf = c/300, the electron mobility µ under the DC condition is 10000cm2/Vs, the SiO2 layer has a relative permittivity of εr = 5.37 and a loss tangent of tan δ = 0.0903.
Fig. 1. Schematic diagram of the graphene-based tunable metalens. The metalens consists of Au antennas with different width, a single layer of graphene, a dielectric layer of SiO2 and a thick Au film. For the proposed metalens, the thickness of Au antennas, SiO2 layer, and Au film are fixed at 0.6 µm, 2.9 µm, and 0.2 µm, respectively. The incident THz wave is X-direction polarized. Fermi level changes from EF1 to EF2, resulting in a change in focus.
Each unit structure in the metalens acts as a phase shifter to achieve phase modulation. Here, we design two kinds of unit structures as shown in Fig. 2 and Fig. 3. Operating in a reflective manner, these units can change the optical path and increase phase coverage.
Fig. 2. (a) Schematic diagram of unit 1. (b) Main view of unit 1, the width of metal strip (W1) varies from 0 µm to 10 µm, causing a phase delay and the width of unit (W2) is fixed at 15 µm. (c) Phase as a function of width (W1), when the frequency is 10 THz and the Fermi level is 0.5 eV.
Fig. 3. (a) Schematic diagram of unit 2. (b) Main view of unit 2, the width of metal strip (W4) is 10 µm. Some gaps are evenly distributed on the metal strip, introducing new resonance modes. (c), (d) and (e) are the changes of phase with the width of gaps (W3) when the number of gaps is 1, 2 and 3, respectively.
In unit 1 (Fig. 2), the width of metal strip varies from 0 µm to 10 µm causing a varied phase delay. When the frequency is 10 THz and the Fermi level is 0.5 eV, the phase variations versus the width of metal strip is shown in Fig. 2(c), which cannot achieve full coverage from 0 to 2π.
Unit 2 is designed to complement the phase that unit 1 cannot cover as shown in Fig. 3 by evenly adding some gaps into the metal strip with a fixed width of 10 µm to obtain some new resonance modes. Figures 3(c), (d), and (e) are the phase variations versus the width of gaps when the number of gaps is set to be 1, 2, and 3, respectively. In Figs. 3(c) and (d), significant step changes of phase are observed. As the number of gaps increases, the phase curve gradually tends to be smooth. According to the acceptable linearity shown in the phase curve of Fig. 3(e), the number of gaps in unit 2 is finally set to be 3. Thus, the combination of unit 1 and unit 2 achieves full phase coverage of 2π.
In order to achieve tunable functions, the phase delay of each unit must satisfy two conditions. First, different units need to be arranged on the metalens reasonably to realize the basic focusing function. For collimated incident light, the phase distribution φ(x) required to achieve focusing can be expressed as [1–3]:
Where F is the designed focal length, λ is the incident wavelength, x is the distance of the unit to the center of metalens. Second, to achieve dynamic focusing, the phase delay caused by different units on the metalens needs to be different as the Fermi level changes. To better illustrate this point, the phase distributions required for two different focal lengths are shown in Fig. 4(a). Phase distributions p1 and p2 correspond to focal lengths F1 and F2, respectively. Δp is the difference between p1 and p2, changing accordingly with the distance from the center of the metalens. Figure 4(b) shows the dependence of phase on the Fermi level at 10 THz, as the width of metal strip varies from 0 µm to 8 µm. Px is defined as the phase delay of units where the Fermi level is equal to x (EF = x). Further, ΔPx-0.5 eV is calculated by Px-P0.5 eV for describing the phase difference between Px and P0.5 eV as shown in Fig. 4(c). The value of ΔPx-0.5 eV indicates that units with different EF can lead to different phase changes.Fig. 4. (a) Phase distributions of the metalens with a focal length of F1 (p1) and F2 (p2), respectively. The phase difference Δp between p1 and p2 (Δp = p1− p2) along the x-axis is also calculated in red line. (b) When the incident light is 10 THz, phase delay as a function of the width of metal strip as EF varies from 0.1 eV to 0.7 eV. (c) Phase difference ΔPx-0.5 eV as a function of the width of metal strip as EF varies from 0.1 eV to 0.7 eV. ΔPx-0.5 eV represents the difference in phase delay between Px and P0.5eV (ΔPx-0.5 eV = Px-P0.5 eV). The curves from top to bottom correspond to x = 0.1 eV, 0.2 eV, 0.3 eV, 0.4 eV, 0.6 eV and 0.7 eV, respectively.
In order to achieve the focus shift from F1 to F2, the phase difference should increase monotonically with the increase of the distance from the center of the metalens, as shown by the red line in Fig. 4(a). Therefore, the phase difference between different Fermi levels distributed on the metalens need to conform to this trend, which is the key to achieving dynamic focusing. The parameter φd is added into Eq. (1) to affect the distribution of the phase difference, thus Eq. (1) is rewritten as:
Let φd, f, EF, and F be equal to 4.157, 10 THz, 0.5 eV and 200 µm, respectively. In order to obtain the maximum range of focus shift, we use simulations to optimize, and finally set the diameter of the metalens to be 300 µm (D = 300 µm). The metalens we designed includes 20 units, and the phase delay of each unit is calculated by Eq. (2). Detailed parameters and phase delay of 10 units on the right side of the metalens are shown in Fig. 5.
Fig. 5. Detailed parameters and phase delay of 10 units on the right side of the metalens (f = 200 µm, D = 300 µm), when frequency is 10 THz and Fermi level is 0.5 eV. From left to right, the width of metal strips is 7.731 µm, 5.988 µm, 5.022 µm, 4.456 µm, 4.4248 µm, 3.803 µm, 0.18403 µm (the width of gaps), 8.500 µm, 4.506 µm, and 3.882 µm, respectively.
3. Results and discussion
To further explore the mechanism about the resonance of units, electric filed distributions of reflected wave are calculated for two structures in the case of f = 10 THz and W = 8 µm, one is all-metal structure and the other is hybrid metal-graphene structure. Simulation results (in x-z plane) are shown in Figs. 6(a), (b), and (c), where white arrows represent electric filed vector. In the all-metal structure, as shown in Fig. 6(a), stronger localized electric filed emerges at the edges of the metal strip. Plasmon resonance occurs at the interface between the metal strip and the dielectric. In the hybrid metal-graphene structure, as shown in Figs. 6(b) and (c), stronger localized electric filed emerges on both sides of the metal strip. In addition to plasmon resonance generated by the metal strip, electric filed vector also demonstrates a typical dipole resonance generated by graphene. There is an evident difference regarding dipole resonance between EF = 0.5 eV and EF = 1.0 eV, indicating that Fermi level of graphene has a significant effect on the dipole moment.
Fig. 6. (a) The distribution of electric filed in x-z plane for all-metal structure. (b) and (c) are distributions of electric filed in x-z plane for hybrid metal-graphene structure with EF = 0.5 eV and EF = 1.0 eV, respectively. In (a), (b), and (c), the width of metal strip is 8 µm, and white arrows represent electric filed vector. (d) The phase delay under different width of metal strips in the case of hybrid metal-graphene (EF = 0.5 eV) and all-metal structures, respectively.
Moreover, the phase of reflected wave is also calculated for two structures in the case of f = 10 THz and EF = 0.5 eV. Figure 6(a) shows the dependence of phase delay on the width of metal strip for two structures, implying that the range of phase delay of hybrid metal-graphene structure covers much more than all-metal structure.
3.1 Characteristics of controlling focal length
Numerical simulations are performed at 10 THz to verify characteristics of controlling focal length of the metalens. When EF changes, units of the metalens generate different resonance to cause different phase delay and lead to tunable focusing effects as shown in Figs. 7(a)-(e). For example, Fig. 7(c) shows the simulation results at EF = 0.5 eV, where the focal length is 205.5 µm, close to the theoretical value of 200 µm. The small deviation between the design value and the simulation value is mainly attributed to the finite size of the unit cell [29].
Fig. 7. Light intensity distributions of the reflection field in x-z plane for the metalens as EF varies from 0.1 eV to 0.9 eV. The incident frequency is f = 10 THz. (a), (b), (c), (d), and (e), respectively, focal length of 251.5 µm, 236.0 µm, 205.5 µm, 171.0 µm, and 161.5 µm.
Obviously, different focusing spot is observed for different EF. Light intensity distributions of the reflected wave along the z-axis for different EF are shown in Fig. 8(a). The focal length decreases from 251.5 µm to 161.1 µm as EF increases from 0.1 eV to 0.9 eV, namely a focal shift of about 90.4 µm (∼3λ), larger than the previously reported 44 µm in bare graphene metalens [30].
Fig. 8. (a) Light intensity distributions of the reflected wave along the z-axis for different EF. The focal length is decreased from 251.5 µm to 161.1 µm as EF is increased from 0.1 eV to 0.9 eV, and the maximum adjustment range of the focal length is 90.4 µm. (b) Full width at half maximum (FWHM) and focusing efficiency as a function of EF for the metalens. EF is 0.1 eV, 0.3 eV, 0.5 eV, 0.7 eV, and 0.9 eV, the corresponding focusing efficiency is 36.17%, 51.31%, 61.62%, 41.85%, and 27.15%, respectively. The corresponding FWHM is 60.62 µm, 56.42 µm, 53.80 µm, 50.41 µm, and 48.78 µm, respectively.
At the focal plane, focusing efficiency and FWHM of the focal spot for different EF are calculated as shown in Fig. 8(b). The focusing efficiency is obtained by calculating the ratio of the reflected light intensity at the focal spot with a width of three times of the FWHM to the whole incident light intensity [30,31,35]. The maximum value of focusing efficiency is up to 61.62%. The fluctuation ratio of FWHM is 0.2 ((FWHMmax-FWHMmin)/FWHMmax), which indicates that focal spots are similar in size. In the case of EF increasing from 0.1 eV to 0.5 eV, the energy on the focal plane gradually concentrates to the center as shown in Figs. 7(a)-(c), resulting in FWHM monotonically decreasing with EF. In the case of EF increasing from 0.5 eV to 1.0 eV, light spots near both sides of the focus become more and more prominent as shown in Figs. 7(c)-(e), which means that the energy is gradually transferred away from the center of focus to side lobs instead of evenly transferred to the focal plane, causing the FWHM decrease monotonically with EF.
In addition, we explore regular of focal length and focusing efficiency changing with the Fermi level, as shown in Fig. 9. It is obvious that the relationship between focal length and EF is not linear in Fig. 9(a), and the curve of focusing efficiency as a function of EF is not monotonic in Fig. 8(b). As the Fermi level is gradually larger or smaller than 0.5 eV, the change in focal length and the value of focusing efficiency both become smaller. To further explore this phenomenon, we calculated phase delay of 10 units on the right side of the metalens for EF = 0.1 eV, 0.3 eV, 0.5 eV, 0.7 eV and 0.9 eV, respectively, as shown in Figs. 9(b)-(f). In each figure, blue mark represents the phase distribution generated by units in the simulation for a certain EF, and red mark represents the theoretical phase distribution required for corresponding focal length. Obviously, when EF = 0.5 eV, the simulated value of phase distribution is basically consistent with the theoretical value of F = 205.5 µm (Fig. 9(d)). Therefore, the focusing efficiency of the metalens is maximized when EF = 0.5 eV. As EF gradually deviates from 0.5 eV, the deviation of phase distribution between simulation value and theoretical value of corresponding focal length becomes larger, causing a decrease in focusing efficiency.
Fig. 9. (a) Focal length as a function of Fermi levels for incident frequency f = 10.0 THz. Fig (b) to (f) shows phase delay φ of 10 units on the right side of the metalens for EF = 0.1 eV, 0.3 eV, 0.5 eV, 0.7 eV and 0.9 eV, respectively. Among them, red mark is φm (m = 251 µm, 236 µm, 205 µm, 171 µm and 161 µm), which represents the theoretical phase distribution required for focal length F = m. Blue mark is φn (n = 0.1 eV, 0.3 eV, 0.5 eV 0.7 eV and 0.9 eV), which represents the phase distribution generated by units in the simulation for EF = n.
3.2 Characteristics of controlling focal intensity
Figures 10(a)-(c) show the simulation results as EF varies from 0.8 eV to 1.0 eV at 10 THz, where focal spots near 161 µm provide the possibility of intensity modulation with fixed focal length. To figure out the reason behind the fixed focal length, we calculate the relationship between phase delay and Fermi level. Figure 11(a) shows the phase difference between Px (x = 0.8 eV, 0.9 eV, and 1.0 eV) and P0.5 eV changes with the width of metal strip. It can be observed that the values of ΔP0.8 eV-0.5 eV, ΔP0.9 eV-0.5 eV, and ΔP1.0 eV-0.5 eV are highly closed, which indicates that the phase delay caused by units of the metalens does not change much as the Fermi level varies from 0.8 eV to 1.0 eV. Furthermore, the intensity of the reflected wave decreasing at the focal plane (z = 161 µm) as EF varies from 0.8 eV to 1.0 eV, as shown in Fig. 11(b), indicates the effect of intensity modulation.
Fig. 10. Light intensity distributions of the reflection field in x-z plane for the metalens as EF varies from 0.8 eV to 1.0 eV. The incident frequency is f = 10 THz. (a), (b), and (c), respectively, the focal length of 162.5 µm, 161.1 µm, and 160.0 µm.
Fig. 11. (a) Phase difference between Px (x = 0.8 eV, 0.9 eV and 1.0 eV) and P0.5 eV as a function of the width of metal strip (ΔPx-0.5 eV = Px-P0.5 eV). (b) Light intensity distribution of the reflected wave along the z-axis for different EF. Reflected lights converge around 161 µm for EF = 0.8 eV, 0.9 eV, and 1.0 eV.
At the focal plane (z = 161 µm), the FWMH and focusing efficiency of the focal spot for different EF (0.8 eV, 0.9 eV, and 1.0 eV) are calculated as shown in Fig. 12(a). Focusing efficiency decreases as EF increases. The maximum and minimum values are 33.15% (0.8 eV) and 20.71% (1.0 eV), respectively. The fluctuation ratio of FWHM is 0.07128 ((FWHMmax-FWHMmin)/FWHMmax), indicating that the size of the focus remains basically the same. To illustrate the energy change in the focal plane more clearly, light intensity distributions of the reflected wave along the focal line for different EF (0.8 eV, 0.9 eV, and 1.0 eV) are calculated as shown in Fig. 12(b). When EF varies from 0.8 eV to 1.0 eV, the energy is gradually transferred from the center to both sides of focus, and two secondary energy peaks are formed.
Fig. 12. (a) Full width at half maximum (FWHM) and focusing efficiency as a function of EF for the metalens. EF is 0.8 eV, 0.9 eV, and 1.0 eV, the corresponding focusing efficiency is 33.15%, 27.15%, and 20.71%, respectively. The corresponding FWHM is 49.1 µm, 48.78 µm, and 45.60 µm, respectively. (b) Light intensity distribution of the reflected wave along the focal plane for EF equal to 0.8 eV, 0.9 eV, and 1.0 eV.
3.3 Characteristics of dispersion
Numerical simulations of this metalens are performed at 9.5 THz and 10.5 THz, and results are shown in Figs. 13(a)-(f). When incident frequency f = 9.5 THz, the focal length decreases from 220.0 µm to 154.0 µm as EF increases from 0.3 eV to 0.7 eV. When incident frequency f = 10.5 THz, the focal length decreases from 247.7 µm to 188.0 µm as EF increases from 0.3 eV to 0.7 eV. These results show that the metalens can achieve dynamic focusing at different frequencies around the designed working frequency f = 10 THz.
Fig. 13. Light intensity distributions of the reflection field in x-z plane for the metalens as EF varies from 0.3 eV to 0.7 eV. The incident light of (a), (b), and (c) is 9.5 THz, and the focal length is 220.1 µm, 176.9 µm, and 154.0 µm, respectively. The incident light of (d), (e), and (f) is 10.5 THz, and the focal length is 247.7 µm, 233.3 µm, and 188.0 µm, respectively.
4. Conclusion
In conclusion, we propose a metalens based on simple metallic arrays and non-structured monolayer graphene for dynamic focusing in THz band. Due to the tunable feature of graphene layer, the metalens is able to be tuned electrically using an applied gate voltage. Our simulation results demonstrate that the graphene-based metalens can achieve the functions of controlling focal length and focal intensity. The focus is able to be shifted by 90.4 µm (∼3λ) and the maxim focusing efficiency is up to 61.62%, indicating great application potential in terahertz band.
Funding
National Natural Science Foundation of China (11674396).
Disclosures
The authors declare no conflicts of interest.
References
1. M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15(8), 5358–5362 (2015). [CrossRef]
2. K. Mohammadreza, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016). [CrossRef]
3. S. M. Wang, P. C. Wu, V. C. Su, Y. C. Lai, C. H. Chu, J. W. Chen, S. H. Lu, J. Chen, B. B. Xu, C. H. Kuan, T. Li, S. N. Zhu, and D. P. Tsai, “Broadband achromatic optical metasurface devices,” Nat. Commun. 8(1), 187–195 (2017). [CrossRef]
4. W. T. Chen, A. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13(3), 220–226 (2018). [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. S. Wang, P. C. Wu, V. C. Su, Y. C. Lai, M. K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T. H. Huang, J. H. Wang, R. M. Lin, C. H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018). [CrossRef]
7. A. Arbabi, E. Arbabi, S. M. Kamail, Y. Horie, S. Han, and A. Faran, “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations,” Nat. Commun. 7(1), 13682 (2016). [CrossRef]
8. Y. W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16(9), 5319–5325 (2016). [CrossRef]
9. L. Wu, T. Du, N. N. Xu, C. F. Ding, H. Li, Q. Sheng, M. Liu, J. Q. Yao, Z. Y. Wang, X. J. Lou, and W. L. Zhang, “A new Ba0.6Sr0.4TiO3-Silicon hybrid metamaterial device in terahertz regime,” Small 12(19), 2610–2615 (2016). [CrossRef]
10. S. M. Kamali, E. Arbabi, A. Arbabi, Y. Horie, and A. Faraon, “Highly tunable elastic dielectric metasurface lenses,” Laser Photonics Rev. 10(6), 1002–1008 (2016). [CrossRef]
11. X. H. Li, J. M. Zhu, and B. Q. Wei, “Hybrid nanostructures of metal/two-dimensional nanomaterials for plasmon-enhanced applications,” Chem. Soc. Rev. 45(11), 3145–3187 (2016). [CrossRef]
12. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009). [CrossRef]
13. L. Ju, J. Velasco, E. Huang, S. Kahn, C. Nosiglia, H. Z. Tsai, W. Yang, T. Taniguchi, K. Watanabe, and Y. Zhang, “Photoinduced doping in heterostructures of graphene and boron nitrde,” Nat. Nanotechnol. 9(5), 348–352 (2014). [CrossRef]
14. J. Gorecki, V. Apostolopoulos, J. Y. Ou, S. Mailis, and N. Papasimakis, “Optical gating of graphene on photoconductive Fe:LiNbO3,” ACS Nano 12(6), 5940–5945 (2018). [CrossRef]
15. S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012). [CrossRef]
16. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011). [CrossRef]
17. F. J. Garcia and De Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photonics 1(3), 135–152 (2014). [CrossRef]
18. S. S. Xiao, X. L. Zhu, B. H. Li, and N. A. Mortensen, “Graphene-plasmon polaritons: from fundamental properties to potential applications,” Front. Phys. 11(2), 117801 (2016). [CrossRef]
19. P. Tassin, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics 6(4), 259–264 (2012). [CrossRef]
20. P. Ding, Y. Li, M. Li, L. Shao, J. Wang, C. Fan, and F. Zeng, “Tunable dualband light trapping and localization in coupled graphene grating-sheet system at mid-infrared wavelengths,” Opt. Commun. 407, 410–416 (2018). [CrossRef]
21. A. M. Shaltout, V. M. Shalaev, and M. L. Brongersma, “Spatiotemporal light control with active metasurfaces,” Science 364(6441), eaat3100 (2019). [CrossRef]
22. N. Dabidian, I. Kholmanov, A. B. Khanikaev, K. Tatar, S. Trendafilov, S. H. Mousavi, C. Magnuson, R. S. Ruoff, and G. Shvets, “Electrical switching of infrared light using graphene integration with plasmonic fano resonant metasurfaces,” ACS Photonics 2(2), 216–227 (2015). [CrossRef]
23. N. Dabidian, S. Dutta-Gupta, I. Kholmanov, K. F. Lai, F. Lu, J. Lee, M. Z. Jin, S. Trendafilov, A. Khanikaev, B. Fallahazad, E. Tutuc, M. A. Belkin, and G. Shvets, “Experimental demonstration of phase modulation and motion sensing using graphene-integrated metasurfaces,” Nano Lett. 16(6), 3607–3615 (2016). [CrossRef]
24. X. Y. He, Z. Y. Zhao, and W. Z. Shi, “Graphene-supported tunable near-IR metamaterials,” Opt. Lett. 40(2), 178–181 (2015). [CrossRef]
25. M. C. Sherrott, P. W. C. Hon, K. T. Fountaine, J. C. Garcia, S. M. Ponti, V. W. Brar, L. A. Sweatlock, and H. A. Atwater, “Experimental demonstration of & 230 degrees phase modulation in gate-tunable graphene-gold reconfigurable mid-infrared metasurfaces,” Nano Lett. 17(5), 3027–3034 (2017). [CrossRef]
26. Y. Zhao, L. Wang, Y. Zhang, S. Qiao, S. Liang, T. Zhou, X. Zhang, X. Guo, Z. Feng, F. Lan, Z. Che, X. Yang, and Z. Yang, “High-speed efficient terahertz modulation based on tunable collective-individual state conversion within an active 3 nm two-dimensional electron gas metasurface,” Nano Lett. 19(11), 7588–7597 (2019). [CrossRef]
27. J. Guo, T. Wang, H. Zhao, X. Wang, S. Feng, P. Han, W. Sun, J. Ye, G. Situ, H. T. Chen, and Y. Zhang, “Reconfigurable terahertz metasurface pure phase holograms,” Adv. Opt. Mater. 7(10), 1801696 (2019). [CrossRef]
28. W. Yao, L. Tang, J. Wang, C. Ji, X. Wei, and Y. Jiang, “Spectrally and spatially tunable terahertz metasurface lens based on graphene surface plasmons,” IEEE Photonics J. 10(4), 4800909 (2018). [CrossRef]
29. Z. Zhang, X. Yan, L. Liang, D. Wei, M. Wang, Y. Wang, and J. Yao, “The novel hybrid metal-graphene metasurfaces for broadband focusing and beam-steering in farfield at the terahertz frequencies,” Carbon 132, 529–538 (2018). [CrossRef]
30. P. Ding, Y. Li, L. Shao, X. Tian, J. Wang, and C. Fan, “Graphene aperture-based metalens for dynamic focusing of terahertz waves,” Opt. Express 26(21), 28038–28050 (2018). [CrossRef]
31. H. Zhou, J. Cheng, F. Fan, X. Wang, and S. Chang, “Graphene-based transmissive terahertz metalens with dynamic and fixed focusing,” J. Phys. D: Appl. Phys. 53(2), 025105 (2020). [CrossRef]
32. T. T. Kim, H. Kim, M. Kenney, H. S. Park, H. D. Kim, B. Min, and S. Zhang, “Amplitude modulation of anomalously refracted terahertz waves with gated-graphene metasurfaces,” Adv. Opt. Mater. 6(1), 1700507 (2018). [CrossRef]
33. W. Liu, B. Hu, Z. Huang, H. Guan, H. Li, X. Wang, Y. Zhang, H. Yin, X. Xiong, J. Liu, and Y. Wang, “Graphene-enabled electrically controlled terahertz meta-len,” Photonics Res. 6(7), 703–708 (2018). [CrossRef]
34. N. Ullah, W. Liu, G. Wang, Z. Wang, A. U. R. Khalid, B. Hu, J. Liu, and Y. Zhang, “Gate-controlled terahertz focusing based on graphene-loaded metasurface,” Opt. Express 28(3), 2789–2798 (2020). [CrossRef]
35. N. Ullah, B. Hu, A. U. R. Khalid, H. Guan, M. I. Khan, and J. Liu, “Efficient tuning of linearly polarized terahertz focus by graphene-integrated metasurface,” J. Phys. D: Appl. Phys. 53(20), 205103 (2020). [CrossRef]
