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Abstract
Graphene-based terahertz (THz) metasurfaces have the advantages of ultra-small thickness, electrical tunability, and fast tuning speed. However, many such structures suffer low efficiency, especially for transmissive devices. Here we propose a hybrid structure for focusing THz waves with tunability and enhanced focusing efficiency, which is composed of a graphene-loaded metallic metasurface sandwiched by two mutually orthogonal gratings. Experimental results show that due to the multi-reflection between the metasurface layer and the grating layer, the focusing efficiency is enhanced by 1.8 times, and the focal length of the metalens is increased by 0.61 mm when the applied gate voltage on the graphene is increased from 0 V to 1.4 V. We hope the proposed structure may open a new avenue for reconfigurable THz metasurfaces with high efficiencies.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) technology has aroused intense research interests in recent years [1]. Because the photon energy of THz waves is much smaller than that of X-rays, and rich spectral information of organic molecules lies in this band, THz has good application prospects in the fields of security checking, material detection, and biomedical sciences [2]. In addition, due to the relatively higher frequency, THz is also promising in next-generation communications [3]. Although rapid developments of THz technology have been obtained, the realization of compact, effective functional devices is highly desired [4]. The rise of metasurface provides a possible solution to this problem.
The metasurface is a two-dimensional artificial structure composed of a metal or dielectric micro-nano optical antenna array that controls the phase, amplitude, and polarization state of a wavefront [5]. The modulation of light waves by conventional optical devices needs an accumulation of optical paths, and thus requires a certain thickness. However, the metasurface introduces an abrupt phase change by engineering the interaction between light and the optical scatterers. Thus, metasurfaces can achieve optical wavefront mutations controllable in two-dimensional planes of micro- or even nano-meter thickness. Besides, the essence of metasurfaces is that the wave modulation is dependent on the geometric parameters of the antennas. Therefore, the light wave can be flexibly controlled by this kind of artificial structure [6]. So far, many metasurface designs for THz modulation have been proposed including abnormal refraction [7], lenses with high beam quality [8,9] or for achromatic focusing [10], and polarization converter [11].
Nevertheless, most of the proposed structures are not tunable, limiting the real application of metasurfaces. In order to realize dynamic control of the wave, active metasurfaces have been proposed based on thermo-tuning using phase-change materials [12,13], mechanical tuning using stretchable materials [14], optical tuning using photoactive silicon [15], and electric tuning using oxide-semiconductors [16] or graphene [17–19]. Among these tuning approaches, the employment of graphene has the advantages of good response to infra-red waves, ultra-small thickness, and fast tuning speed [20–22]. Therefore, people have tried to combine graphene and metallic metasurfaces to achieve active modulation of THz waves [23–25]. In these structures, the conductivity of graphene can be altered by an external gate voltage through changing the graphene chemical potential, and then the interaction between THz waves and the metallic antennas is tuned. However, due to the one-atom thickness of graphene, such graphene-based THz devices usually suffer low efficiency, especially for the transmissive structures [26,27]. Although novel structures were proposed based on graphene damp transition [28], and photonic spin Hall effect [29] to increase the efficiency or phase tuning of the metasurface, these mechanisms have not been applied in active functional devices.
In 2013, Grady et. al. used two perpendicular gratings to enhance the polarization conversion of rectangular metallic antennas [30]. Borrowing this idea, in this manuscript, we propose a tunable THz metalens consisting of C-shaped antennas covered by monolayer graphene and sandwiched by two mutually perpendicular gratings to enhance the focus. By a searching algorithm, a graphene-enable reconfigurable metalens is designed. Experimental results demonstrate that the focal length is changed from 4.44 mm to 5.05 mm when the gate voltage applied on the graphene is increased from 0 V to 1.4 V. Besides, due to the two gratings located before and after the metasurface, respectively, the intensity of the focus is enhanced by 2 times.
2. Structure and design method
2.1 Structure
The structure of the tunable terahertz metalens is shown in Fig. 1(a), which consists of three layers separated by two polyimide spacers. The middle layer is composed of a gold C-shaped antenna array, covered by monolayer graphene. The top and bottom layers are composed of two mutually perpendicular gold gratings. The period of the two gratings is Tg=20µm, and the duty cycle is 50%. A linearly polarized THz wave illuminates along the z-direction, and the modulated transmitted wave is observed for the cross-polarization as Ref. [9]. Two electrodes are attached to graphene and one grating separately to apply an external gate voltage Vg to change the graphene chemical potential, and then adjust the wave modulation of the antennas. The unit structure of the gold antenna array is depicted in Fig. 1(b). The width of the antenna is r=10µm. The out radius and the opening angle of the C-shaped antenna are denoted by R and θ, respectively. The orientation of the opening angle is ±45° to the x-axis. The period of the units is TC=120µm. The thicknesses of the grating and antenna layers are all 0.2µm. The thickness of the polyimide spacer is H=60µm, with a relative permittivity of ɛ=3 + 0.15i [30].
Fig. 1. (a) Schematic of the tunable THz metalens. The structure consists of a polyimide substrate with a thickness H=60µm, a C-shaped gold antenna array with different radii and opening angles, a monolayer of graphene, and two layers of gratings perpendicular to each other in both directions with a period T=20µm. The polarization direction of the incident light is in the x-direction, while the output light is observed in the y-direction; (b) The unit structure of the C-shaped antenna, R denotes the outer radius while r denotes the inner radius. θ is the opening angle; (c) The cross section of the metalens, red arrows represent the x-polarized THz waves, and blue arrows represent the y-polarized waves. Because x-polarized waves are reflected by the bottom grating, and only y-polarized waves can transmit the structure, the focus will be enhanced by the multi-modulation on the metasurface plane of the reflected x-polarized waves from the bottom grating.
Figure 1(c) shows the operating mechanism of the metalens. Because the period of the metallic gratings is much smaller than the incident wavelength, only the polarization perpendicular to the slits can pass through the grating, while the cross-polarized wave will be reflected [30]. Therefore, when an incident THz wave is polarized in the x-direction, it can pass the first grating, and interact with the C-shaped antennas. After the antenna array, the cross-polarized (y-polarized) wave ETy, which has been modulated by the antennas, is able to pass the second grating, while the co-polarized wave ETx, which has not been modulated, will be totally reflected by the second grating, and interact with the antennas for the second time. The reflected cross-polarized wave E’Ty with the same modulation as ETy passes the grating, while the unmodulated co-polarized wave E’Tx will be reflected again. Therefore, the finally transmitted THz wave is the superposition of the waves with the same modulations of the multi-reflection in the second spacer, thus the modulation and transmission of the metalens are both enhanced.
In order to study the effect of the gratings on the wave modulation, we calculated the transmitted field with the cross-polarization of a unit cell without and with the gratings, as depicted in Fig. 2(d). The simulations are conducted by the Lumerical FDTD Solutions. Perfect matching layer boundary conditions are implemented on x-, y- and z-directions. The material of C-shaped antenna and gratings is set as a perfect electrical conductor (PEC). The monolayer graphene used in the simulation is modeled as a conductive surface whose complex conductivity σ is defined by the Kubo formula. The outer radius and the opening angle of the C-shaped antenna are set as R=45µm, and θ=10°, respectively. The orientation of the opening angle is −45° to the x-axis, as shown in Fig. 1(b).
Fig. 2. Amplitude and phase modulations on the cross-polarization of the unit cell; (a)–(b) Effects of the gratings on the amplitude and phase modulations for the graphene chemical potential at EF=0.1 eV and EF=0.3 eV, respectively; (c) Transmitted spatial phase profile covering 0 to 2π with the corresponding C-shaped antennas at the frequency of 1 THz. The symmetric axis for the first five antennas (covering 0 to 1 π) is +45π, while for the other five antennas (covering 1 π to 2 π) is −45π. The chemical potential is 0.1 eV; (d) Schematic of the C-shaped antennas without and with the gratings used in the simulations of (a)–(c).
The transmitted intensity and phase spectra of Ey in the wavelength band from 250µm to 350µm, corresponding to the graphene chemical potentials EF=0.1 eV and EF=0.3 eV, are shown in Figs. 2(a) and (b), respectively. It is found in Fig. 2(a) that the intensity of the transmitted cross-polarized wave is almost doubled by the gratings in the whole band for both EF=0.1 eV and EF=0.3 eV, which proves the feasibility of the design. Figure 2(b) shows that the phase of Ey is decreased by the grating, due to the multi-reflection of the wave within the structure. The decreased φ with the chemical potential is also observed in our previous study [27]. It is also worth mentioning that the phase change corresponding to EF increased from 0.1 eV to 0.3 eV, i.e. Δφ=φ0.1eV-φ0.3eV, is also enhanced in the grating structure. For example, in the structure without the gratings, Δφ is 0.45π and 0.12π for λ=250µm and λ=350µm, respectively, while it is increased to 0.6π and 0.22π, respectively, in the structure with the gratings.
Figure 2(c) shows 10 C-shaped antennas with various geometric parameters that cover 0–2π phase modulations of Ey, at the frequency of 1THz, when the graphene chemical potential is 0.1 eV. The radius and opening angles of the first five C-shaped antennas are 55, 50, 45, 35, 25µm, and 60°, 70°, 80°, 90°, 100°, respectively. It can be seen that 2π phase modulation can be realized by changing the size, the opening angle and orientation of the C-shaped antennas in both the structures without and with the gratings. However, the transmitted intensity of the grating structure is much higher than that of the structure without the gratings.
2.2 Design principle of the metalens
A planar lens based on metasurfaces is required to provide different phase changes to the beam at different locations, allowing the transmitted light waves to be converged at the designed focus. The phase modulation of a metalens is calculated by [31,32]:
where f is the designed focal length, λ is the wavelength, r is the distance of the unit cell to the center of the metasurface. However, to realize a tunable metalens, Eq. (1) is not sufficient. For each unit cell of the metalens, besides the abrupt phase calculated by Eq. (1), a correspondent abrupt phase change of one designed focal length to another is also required [27]. Take the design of a metalens whose focal length can be tuned from 7 mm to 11 mm when the graphene chemical potential is increased from 0.1 eV to 0.3 eV as an example, the purple and blue curves in Fig. 3(a) are the desired abrupt phase distributions along the x-axis of two designed focal lengths f1=7 mm, and f2=11 mm, respectively. The orange curve indicates the phase difference between the two phase distributions. Therefore, if we want to design a metalens whose focal length is increased from 7 mm to 11 mm, when the graphene chemical potential is changed from 0.1 eV to 0.3 eV, we need to find C-shaped antennas with proper geometric parameters, whose phase distribution fulfill the purple curve under the chemical potential of EF=0.1 eV, while when EF is increased to 0.3 eV, the phase changes of the antennas are different, and fulfill the orange curve. In our design, the unit cells of the metalens is found by adjusting the opening angle and outer diameter of an antenna. We first sweep a large number of parameters of the unit structure with the gratings to obtain sufficient phase and intensity parameters, then filter and analyze the obtained data, and find the structural parameters that meet the design requirements.The simulation results of the sweep are shown in Figs. 3(b)–(f). The frequency of the incident light is 1THz. The outer diameter R is changed from 15µm to 55µm with 300 uniform sampling points. The opening angle θ is changed from 10° to 200° with 300 uniform sampling points. The field intensity dependent on R and θ corresponding to EF=0.1 eV and 0.3 eV is depicted in Figs. 3(b) and (d), respectively. The phase dependent on R and θ corresponding to EF=0.1 eV and 0.3 eV is depicted in Figs. 3(c) and (e), respectively. An additional π phase shift can be obtained by changing the orientation of the opening angle to +45° [9]. The phase change Δφ caused by the graphene chemical potential dependent on R and θ is then calculated and depicted in Fig. 3(f). It can be seen clearly from the above figures that when the outer diameter of the C-shaped antenna becomes larger, the entire structure has a stronger transmission intensity. However, when R is larger than 30µm, Δφ changes slowly, which means the tuning effect of the graphene is not obvious. The fact that Δφ is dependent on the geometry of the antenna is due to the resonant frequency shift of the structure caused by the change of the graphene chemical potential [20,33]. Therefore, comprehensive consideration of the intensity, phase, and phase change is needed in the design.
In our previous works [26,27], the antennas were decided manually, and the intensity was not considered. Here we use an algorithm to find the geometric parameters automatically, in which the phase, the phase change, and the intensity are taken into account. There are two main principles of the searching algorithm: 1. Minimize the difference between the required phase (φ1req)/phase change (Δφreq) and the obtained simulated phase (φ1sim)/phase change (Δφsim) in the data sets of Figs. 3(b)–(f). 2. Maximize the transmitted amplitude of the cross-polarized wave. According to the three data sets of Figs. 3(b), (c) and (f), we use the Matlab software to design a screening program to select the structural parameters. The flow chart is shown in Fig. 4(a). Some key parameters are determined first for the loop process. The entire lens is composed of M×N (M = N=29) unit cells. The number of the swept C-shaped antennas in Figs. 3(b), (c) and (f) is P×Q (P = Q=300, 300 R values, and 300 θ values). Because φ and Δφ in Fig. 3(a) are relative phase and phase change, we need to choose a structure in the data sets as the origin point, which has the zero phase and phase change. Therefore, the P×Q swept structures in the data sets are selected as the origin point alternatively, and the one based on which the designed metalens has the strongest transmitted intensity is the chosen origin structure. When the structure (p, q) is selected as the origin point (p,q∈[1,300]), the relative phase and phase change are denoted by φ1sim=φ1-φ1(p,q), Δφsim=Δφ-Δφ(p,q), respectively. Therefore, for the (m-th, n-th) unit-cell (m,n∈[1,29]), the difference between the required phase and the simulated phase, as well as the difference between the required phase change and the simulated phase change are denoted by Dφ1(m, n)=φ1req(m, n)- φ1sim and DΔφ(m, n)= Δφreq(m, n)- Δφsim, respectively. Then six deviation tolerances (error margins) for Dφ1 and DΔφ are defined as B1=0.0001π, B2=0.01π, B3=0.05π, B4=0.1π, B5=0.2π, B6=π. By traversing the matrices of Dφ1(m, n) and DΔφ(m, n), all the structures fulfill Dφ1(m, n)<Bi and DΔφ(m, n)<Bi are found, which are marked as [k, l]. Then the structure with the highest transmitted intensity |Ey1| is selected. By a bi-circulation searching procedure of m, n∈[1,29], all the M×N unit cells are decided with the highest transmitted intensities. However, the unit cells are only decided based on the structure (p, q) selected as the origin point. Therefore, another bi-circulation searching procedure based on p, q∈1,300] is then conducted. In the end, by comparing the total transmission T(p, q) defined as sum(sum(t(m, n))), the structure [p0, q0] is selected as the origin point, and the geometric parameters of the whole metalens are decided.
Fig. 3. (a) Phase distribution of the metalens corresponding to the focal length is f=7 mm and f=11 mm, respectively. The orange curve indicates the required phase variation Δφ=φ1-φ2, brought by the change of graphene chemical potential. (b)–(e) Sweep simulation results on amplitude and phase modulation of the unit-cell with various radii and opening angles, when the chemical potential is 0.1 eV and 0.3 eV, respectively. (f) Phase variation dependent on R and θ, when EF is increased from 0.1 eV to 0.3 eV.
Fig. 4. Design method of the metasurface. (a) Flow chart of the design algorithm; (b) Error margin of the selected 29×29 c-shaped antennas by the algorithm; (c)–(d) R and θ distributions of the selected C-shaped antennas on the metasurface, respectively.
The final result of the searching algorithm is a set of approximate solutions, as shown in Fig. 4(b). It can be considered that the results are excellent when the error margin is less than 0.1π, good when the error margin is between 0.1π and 0.2π, and failed when the error margin is 0.2π and 1π. It is found that 80% of the unit cells obtained by the algorithm are acceptable, and nearly 20% are unable to be found in the entire database. So we make further efforts to change the value of the deviation tolerance, add more judgment between 0.2π and 1π, reduce the deviation value as much as possible, and finally get the full structure parameters of the optimized tunable terahertz metalens.
The specific parameters of the metal C-shaped antenna in the structure are shown in Figs. 4(c) and (d). X, Y represent the number of metal C-shaped antennas in the x and y directions. The left image shows the outer diameters of the antennas, and the right image shows the opening angles of the antennas.
3. Simulation results and discussion
In order to analyze the functionality of the metalens intuitively, we use the far-field analysis script function in FDTD Solutions, and the normalized field intensity distributions in the x-z plane are shown in Figs. 5(a)–(b). A focus is clearly observed, and when the graphene chemical potential varies from 0.1 eV to 0.3 eV, the focal length is changed from 3.98 mm to 5.81 mm, respectively. However, due to the enhanced ohmic loss, when the chemical potential of graphene is increased, the focusing intensity is decreased for EF=0.3 eV.
Fig. 5. Simulation results of the metalens. (a)–(b) Intensity distributions corresponding to the graphene chemical potential is 0.1ev and 0.3 eV, respectively. The intensity is normalized by the maximum intensity at EF=0.1 eV. The focal lengths are 3.98 mm and 5.81 mm, respectively; (c) FWHM of the focus; (d) Focal length under different chemical potentials.
The normalized field intensity distributions along the x-axis on the focal plane are depicted in Fig. 5(c). It is found that the full width at half maximum (FWHM) is 1.6λ and 2.3λ, respectively, corresponding to EF=0.1 eV and EF=0.3 eV. We can calculate the ideal diffraction limit of the design lens by the formula [34]:
where λ is the design wavelength, f is the simulated focal length, D=3.6 mm is the diameter of the metalens. Since f1=3.98mm and f2=5.81mm, the corresponding values are calculated as d1=1.1λ and d2 = 1.61λ, which shows the focal spots are larger than their corresponding ideal diffraction limits. Figure 5(d) illustrates the relationship between the focal length and the chemical potential. The red points are simulation results, and the blue line is the fitted straight. From Fig. 5(d), (a) linear tuning effect of the entire reconfigurable THz metalens is found.In order to visualize the effect of gratings on the metalens, we remove the gratings structure and repeat the entire design process. The transmitted field distributions of simulation results without the gratings are shown in Figs. 6(a)–(b). The intensity is normalized to the highest intensity in Fig. 5(a). It is found that the shift of the focus is 0.6 mm (from 3.92 mm to 4.52 mm) when EF is increased from 0.1 eV to 0.3 eV, which is smaller than the structure with the gratings. In addition, the maximum intensity of the focus is only 0.15 of that in Fig. 5(a). Thus, the focus is dramatically enhanced by the gratings. This effect can also be observed in Fig. 6(c), which depicts the comparison of the intensity distributions along the x-axis on the focal plane, for the metasurfaces with and without the gratings when EF=0.1 eV. We also calculated the focusing efficiency, defined as the ratio of the energy in an area with a radius 3 times of the FWHM to the energy of the incident light [35,36]. When the chemical potential of graphene is 0.1 eV, the focusing efficiency is enhanced 5.6 times by the two orthogonal gratings. For EF=0.3 eV, the focusing efficiency is enhanced 2.2 times.
Fig. 6. (a)–(b) Field distributions of the metalens without the gratings when the graphene chemical potential is 0.1ev and 0.3ev, respectively; (c) Normalized intensity on the focal plane with and without the gratings; (d) Relative focal efficiency of the metalens with and without the gratings at different chemical potentials. All the results are normalized by the focus intensity corresponding to the structure with the gratings at EF=0.1 eV.
In order to fully understand the effect of gratings on metalens under different chemical potentials, we add three chemical potential points, and calculate the corresponding relative efficiencies, which are shown in Fig. 6(d). It can be seen that the focusing efficiency for the structures with the gratings is generally higher than that without the gratings. In addition, with the increase of the chemical potential, the efficiency is decreased.
4. Experiment
4.1 Device fabrication and detection
The fabrication process of the samples is illustrated in Fig. 7(a). First, a high-resistance silicon substrate with a thickness of 500µm is prepared. Then photoresist S1813 is spin-coated on the substrate at a speed of 2000 r/min. Second, a UV lithography system is used to generate a photoresist metasurface pattern under a Cr plated quartz mask. Third, an electron beam evaporation coating technology is performed to add a 10nm-thick Cr layer and a 90nm-thick gold layer onto the sample. The deposition rate is 0.5Ǻ/s, and the vacuum pressure is 4.4×10−6 Torr. In the fourth step, the excess gold layer is stripped to obtain the designed gold metasurface structure. Finally, the monolayer graphene grown by the chemical vapor deposition (CVD) technology is transferred onto the surface of the metasurface structure. For the fabrication of the grating layers, two silicon substrates are used, and the above steps are repeated. Copper tapes are used as adhesive and electrodes to fix and apply gate voltage on the graphene layer. The fabricated samples are shown in Fig. 7(b). The area of the C-shaped antennas is 3.6mm×3.6mm. The area of each grating is 20mm×20mm, which is larger than that of the metasurface in order to be more easily aligned in the experiment. The red rectangle on the left indicates the profile of graphene, and the other two structures on the right are the top and bottom gratings of the metalens. Scanning electron microscopy (SEM) images of the samples are also shown by the insets.
Fig. 7. (a) Fabrication process of the tunable THz metalens; (b) The fabricated gratings and metasurface. Pictures on the left and right are the SEM images of the fabricated structure; (c) Photograph of the THz imaging of the metalens by a THz focal plane imaging system. The red arrow refers to the direction of propagation, while the blue arrow refers to the direction of polarization. The white virtual box is the location of the gratings and metasurface.
Figure 7(c) gives a photograph of the detection of the metalens. A THz focal plane imaging system is applied, in which a ZnTe crystal is used to image both the intensity and the phase distributions [26]. The metasurface layer is sandwiched by the two grating layers, as shown in Fig. 7(c). The metasurface layer (Slice2) and one of the grating layers (Slice 1) are located face to face and stuck to each other. The electrodes are attached to the graphene and the grating, separately. Slice 3 is behind Slice 2, thus cannot be seen. The gate voltage was applied by the Keithley 4200 semiconductor characterization system. The metalens is fixed 2 mm in front of the ZnTe crystal. And an x-polarized THz wave with a frequency of 0.617THz transmits through the sample.
4.2 Experimental results
The intensity and phase for the structure with and without the gratings under various applied gate voltage are measured by the focal plane imaging system, and then the Huygens-Fresnel principle [37] is used to calculate the far-field distribution of the terahertz wave based on the detected results.
Figure 8 shows the experimental normalized results. It can be observed from Fig. 8(a) that in the case of no voltage and no gratings, the focal length is 3.54mm. After adding the grating, the focal length is increased to 4.44mm as shown in Fig. 8(b). At the same time, the focus intensity is double enhanced. By applying the voltage to 0.7V and 1.4V, the focal length is increased to 4.85mm and 5.05mm, as shown in Figs. 8(c) and (d), respectively. Meanwhile, the focus intensity is decreased with the gate voltage, as demonstrated by the simulation results.
Fig. 8. Experimental results of the metalens at the wavelength of 468µm. (a) Normalized far-field intensity distributions on the x-z plane when the applied voltage is 0 V for the metasurface without the gratings; (b)–(d) Normalized far-field intensity distributions on the x-z plane with a voltage of 0 V, 0.7 V, and 1.4 V, respectively, corresponding to the metasurface with the gratings.
Figure 9 depicts the field intensity distributions at the focal plane calculated by the Huygens-Fresnel principle based on the experimental results when no voltage is applied. It can be seen from Figs. 9(a) and (b) that compared with the metalens without the gratings, a stronger focus is found for the structure with the gratings. The field intensity distribution along the x-axis on the focal plane is plotted in Fig. 9(c). It can be found that the focus intensity of the structure with the gratings is almost 2 times of that of the structure without the gratings. The calculated focusing efficiency based on the experimental results is enhanced 1.8 times by the gratings. Thus, a well-focused and reconfigurable spot is realized, and it can be enhanced by the gratings. We also calculate the corresponding FWHM as 1.72λ and 1.65λ for the structures without and with the gratings, respectively. The ideal diffraction limit is calculated as dW/OG=λf1/D=0.98λ and dWG=λf2/D=1.23λ, respectively, which shows that the experimental focus is larger than the ideal diffraction limit. Thus, this metalens is a diffraction-limited device.
Fig. 9. (a)–(b) Normalized intensity distributions at the focal plane corresponding to the structure without and with the gratings, respectively, when the applied gate voltage is 0 V; (c) Comparison of the focal intensity on the x-axis without and with the gratings when the voltage is 0V; (d) Relationship of the applied gate voltage and the graphene chemical potential. The thickness of the airgap between the two electrodes is assumed to be 2nm.
In order to find the relationship between experiment and simulation results, we estimate the graphene chemicals under different gate voltages. When a gate voltage is applied, the carrier density of graphene n0 can be calculated as [26]:
where ɛ0 and ɛr are the absolute and relative permittivities of the dielectric between the electrodes, respectively. h is the thickness of the dielectric. In our experiment, it is the thickness of the air gap between the grating layer and the metasurface layer. Vg is the applied voltage. e=1.6×10−19C is the elementary charge. And the relationship between the carrier density and chemical potential can be expressed as: where EF is the chemical potential (Fermi level), ћ is the reduced Planck constant, and vF≈106m/s is the Fermi velocity. Because h is difficult to measure, similar to our previous work [26], we assume h=2nm. Then according to Eqs. (4) and (5), the relationship between EF and the gate voltage is calculated as the blue line in Fig. 9(d). It is found that at this thickness, the corresponding graphene Fermi levels of 0.7V and 1.4V are 0.2eV and 0.25eV, respectively. From Fig. 5(d), the corresponding simulated focal lengths are 4.9mm and 5.2mm, while that in the experiment are 4.85mm and 5.05mm, respectively.Conclusion
In conclusion, we demonstrate a graphene-based tunable THz metalens enhanced by two mutually orthogonal gratings for linearly polarized THz plane waves. The focus is shifted by 6.1λ when the chemical potential is increased from 0.1eV to 0.3eV, and the focusing efficiency is enhanced up to 5.6 times by the gratings for the simulations results. In the experiment, the focal length is changed by 1.3λ when the gate voltage is increased from 0V to 1.4V, and the focusing efficiency is enhanced 1.8 times by the gratings. We hope the proposed structure may provide an opportunity for realizing reconfigurable THz metasurfaces with high efficiencies.
Funding
National Natural Science Foundation of China (61875010).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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