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Abstract
In this paper, we propose an all-solid-state, electrically tunable, and reflective graphene metasurface array that can generate a specific phase or continuous scanning between 0° and 352.5° in the terahertz band. By optimizing the structural parameters of the metasurface, the average reflectivity can reach 68.3%, and the maximum reflectivity variation range is only 30%. We also simulate the results that an electrically tunable terahertz phased array can be achieved by adjusting the Fermi levels of a monolayer graphene resonator. The maximum deflection of the reflected beam is 46.05°, and the resolution can be improved to 1.10°. It should be noted that the sidelobe energy only accounts for 1.06% of the main lobe energy, due to the slight change in reflectivity with the phase gradient.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz phased array (TPA) is an all-solid-state beam control technique, which achieves electromagnetic beam-steering by introducing a phase gradient along the beam path [1–3]. Compared with the mechanical beam control system, TPA has the characteristics of low loss, compact profile, low cross-polarization, and high efficiency. In recent years, due to the wide application of terahertz technology in wireless communication [4,5], security scanning [6–8], biological imaging [9–11], and spectral detection [12,13], it is necessary to develop new active devices for dynamic control of terahertz wave propagation in free space.
To meet this demand, the use of tunable metasurfaces has been investigated. In the initial research, the static metasurface was used to control the amplitude [14–16], phase [17–19], and polarization [20,21] of the incident electromagnetic wave. Moreover, owing to the static metasurface can only achieve the fixed characteristics, it has gradually evolved into an active metasurface [22–25] that can realize free wavefront manipulation. Various tunable materials, such as transparent oxides [26,27], two-dimensional materials [28,29], semiconductor materials [30], phase change materials [31], and liquid crystal materials [32], have been used in the related research.
However, the active metasurface-based TPA often produces unnecessary sidelobes because the phase cannot cover the range of 360° or the amplitude is not uniform across the phase range [33,34]. This problem is quite serious because the extra sidelobes produce extraneous beams, which will produce false positives in practical scanning applications. Forouzmand and Mosallaei [35] designed an electrically tunable reflective array metasurface for beam steering by embedding indium tin oxide (ITO) materials. The designed metasurface array can achieve the expected beam deflection, but with the increase of the deflection angle, the side lobe increases gradually, which had a destructive effect on the beam steering. To extend the phase modulation range under the premise of minimum amplitude change [36]. demonstrated an electrically tunable metasurface array with independent phase and amplitude control by applying a voltage to two layers of ITO, respectively. A wide range of phase control is achieved when the reflectivity is constant in this method. However, the reflectivity of this kind of metasurface is low, only about 1%, and the structure of double-layer ITO increases the process difficulty.
To solve the above problems, we design an electronically controlled reflective metasurface based on monolayer graphene and propose a high reflection, low sidelobe all-solid-state TPA. The metasurface unit cell designed in this paper is composed of a graphene structure layer, a dielectric layer, and a metal substrate. The simulation results show that the phase modulation range can reach 352.5°, and the average reflectivity can reach 68.3%, while the maximum variation range of reflectivity is only 30% at 6.98 THz. In addition, by controlling the applied voltage of the metasurface, the phase gradient distribution of the target can be achieved, and the maximum deflection of the reflected beam is 46.05° in the terahertz band. It is most noteworthy that the maximum sidelobe energy is only 1.06% of the main lobe energy in the process of beam deflection.
2. Structure design and simulation methods
The cell structure and the overall schematic diagram of the metasurface are illustrated by Figs. 1(a) and 1(b), respectively. The unit structure is consisted of a graphene structure layer, an insulating dielectric layer, a lightly doped silicon layer, a SiO2 dielectric layer and a gold substrate from top to bottom.
Fig. 1. Structure of the proposed metasurface. (a) Unit cell of metasurface. (b) Active metasurface array composed of electrically tunable super-pixel period.
The graphene structure layer is designed as a continuous surface to connect the bias voltage, and the structural parameters per unit period are as follows: p = 5 μm, a = 4 μm, b = 2 μm, c = 0.3 μm. The surface conductivity of single-layer graphene can be obtained by the following Kubo formula, including the intra-band σintra and inter-band σinter parts [37,38]:
The insulating layer between graphene and p-type silicon is polymethyl methacrylate (PMMA), and its thickness is designed to be 0.05 μm. In our work, the lightly doped silicon layer provides the function of grounding. And to minimize the reflection loss, the thickness of this material is designed to be 0.05 μm [39,40]. The dielectric layer material is SiO2, and its thickness is 0.1 μm, and the refractive index is 1.97. The Au layer of the substrate is set at 0.1 μm, which can prevent the incident terahertz waves transmitted through the metasurface. In the simulation, the permittivity of Au in the THz band follows the Drude model as [41]
In subsequent experiments, the graphene film prepared by chemical vapor deposition (CVD) will be transferred to the surface of SiO2 by the wet transfer technology [42]. And gas plasma etching technology will be used to prepare graphene structures [43,44]. To adjust the Fermi level of graphene, zero voltage is connected to the lightly doped silicon layer. Meanwhile, a list of cell structures in the graphene structural layer is combined into one column unit, and three adjacent column units are combined into a metasurface pixel. Then, each metasurface pixel is connected to an equipotential voltage to ensure the consistency of the applied bias voltage. In addition, a 0.5 μm interval is added between the two metasurface pixels to prevent mutual crosstalk, as shown in Fig. 1(b). In addition, in order to avoid the nonuniformity of Fermi level caused by p-Si electrode layer, the metal wire array electrode scheme [45] is also simulated (see Supplement 1, Figs. S1 and S2), and the results of the two schemes are virtually identical.
3. Simulation results and discussions
Firstly, we simulate and analyze properties of reflection amplitude and reflection phase of the metasurface at graphene Fermi level of 0.44 eV when the thickness of SiO2 is h = 6 μm, as shown in the black curve in Figs. 2(a) and 2(b). Under the above conditions, the metasurface produces two low valley values at frequencies 6.54 THz and 6.98 THz of the reflection amplitude curve, which means that there are strong resonance effects at these two frequencies. And affected by the resonance effect, the abrupt phase change occurs at the two frequencies, which is of great significance for realizing phase control on the metasurface. Figure 2(a) shows that the reflectivity is higher when the frequency is 6.98 THz, which is easier to meet the high energy utilization requirements of TPA. Therefore, the subsequent optimization and research are under this resonant frequency. Subsequently, the reflectivity and phase curves of different graphene Fermi levels are also simulated, and the results are shown in Fig. 2. When the Fermi level of graphene increases from 0.44 eV to 0.45 eV, the central wavelength of metasurface increases from 6.98 THz to 7.13 THz. And the phase increases from 104.11° to 177.03° at f = 6.96 THz. If we continue to increase the Fermi level of graphene, the center frequency and abrupt phase position will be blue shifted. By using the phenomenon that the resonance center frequency shifts with the Fermi level of graphene, the phase can be controlled at a fixed frequency.
Fig. 2. (a) Reflectivity of metasurface with different Fermi levels. (b) Phase of metasurface with different Fermi levels.
In addition, the thickness of SiO2 dielectric layer h = 6 μm is the result of a series of optimizations. During metasurface structure simulation and parameter optimization, it is found that the most crucial factor to influence the resonance effect is the thickness of the medium. Therefore, we simulate the reflectivity, the maximum phase difference, and the frequency difference of the different thicknesses of SiO2 at f = 6.96 THz, as shown in Fig. 3. The frequency difference is the frequency range corresponding to a phase change period, determining the Fermi energy differential with adjustable phase. By comparing the three curves, it is found that when h = 6 μm, the metasurface can be endowed with the advantages of high reflectivity (61.7%), large phase difference range (352.5°), and small frequency difference (0.47 THz). In addition, it has the advantage of smooth phase curve change which can be finely controlled by external bias voltage, so we choose the thickness of the SiO2 as h = 6 μm.
Secondly, to explore the phase control ability of the designed metasurface and the consistency of reflection amplitude, the phase change curve and amplitude change curve of different graphene Fermi levels at f = 6.96 THz are simulated as shown in Fig. 4. The phase gradually increases from -119.65° to 177.03°, and then enters the next phase period, in which the phase gradually increases from -170° to 55.83° again when the Fermi level of the graphene increases from 0.3 eV to 0.5 eV. The Fermi level of 0.43 eV ∼0.49 eV graphene is selected as the condition of all phase control because the maximum phase control range of the metasurface can reach 352.5° within this range. Although the reflection amplitude at 6.96 THz will change according to resonant frequency, the maximum reflectivity variation of the optimized metasurface results is only 30%, and the average reflectivity reaches 68.3%. This feature will reduce the sidelobe energy of TPA as much as possible on the premise of ensuring high energy utilization. Besides, the design method of phase control by changing the Fermi level of graphene is not only effective for the center frequency f = 6.96 THz. For other frequencies, the phase control can be achieved by changing the parameter of the graphene Fermi energy level, even the parameters of structure.
Finally, we simulate the surface electric field distribution and cross-sectional magnetic field distribution at 0.44 eV, 6.98 THz; 0.45 eV, 6.98 THz; 0.45 eV, 7.13 THz, respectively, to further analyze the resonance phenomenon and center frequency control characteristics of the designed structure, as shown in Fig. 5. When μc = 0.44 eV and f = 6.98 THz, the electric field on the graphene surface is obviously enhanced, and the charge forms electric dipole resonance, which shows that the charge is alternately gathered on the central square structure. Moreover, from the magnetic field intensity distribution and direction of the unit structure, we notice a large magnetic field on both the upper and lower surfaces of the graphene structure. And the direction of the magnetic field is parallel to the opposite direction of the structure surface, thus forming a strong magnetic resonance. The results show that when μc = 0.44 eV and f = 6.98 THz, electrical resonance and magnetic resonance occur in the graphene antenna layer, which causes the abrupt change of amplitude and phase at this frequency.
Fig. 5. Surface electric field distribution and cross-sectional magnetic field distribution at (a) 0.44 eV, 6.98 THz; (b) 0.45 eV, 6.98 THz; (c) 0.45 eV, 7.13 THz, respectively.
When the Fermi level of graphene is increased to 0.46 eV, the resonant electric field intensity on the surface of the graphene structure is obviously weakened, and the electric dipole resonance almost disappears. And the magnetic field intensity is significantly reduced, although the magnetic field direction remains opposite to the structure surface. However, when the center frequency is set at 7.13 THz, we find that the strong electromagnetic resonance phenomena are regained on the surface of the graphene structure. This phenomenon reflects that when the Fermi energy level of graphene changes, the resonance does not disappear, but the center frequency shift accompanied by the abrupt phase shift occurs.
4. Terahertz phased array for beam steering
THz phased array is a technology for beam deflection by controlling the phase of the unit. In order to realize the function of the phased array by using metasurfaces, the required phase distribution must be calculated according to the target steering angle. Here we use the relationship between phase and steering angle [36]:
where x is the relative position, k0 is the wavenumber, f0 is the frequency of the incident electromagnetic wave, θ represents the incident angle of the target, and φ represents the phase of the desired position. In order to facilitate the calculation and image representation, the phase gradients with reflection angles of 13.83°, 21.02°, and 45.83° are calculated, respectively, as shown in Figs. 6(a)–6(c). Furthermore, in the design of TPA phase, the phase in Fig. 1 and the control phase of the metasurface need to be converted into a 360° period to facilitate unification. Thus, Figs. 6(d)–(f) shows the phase gradient of 360° cycles corresponding to the selected reflection angle.Fig. 6. Theoretical results of phase corresponding to deflection angles of (a) 13.83°, (b) 21.02° and (c) 45.83°. Theoretical results of phase corresponding to deflection angles of (d) 13.83°, (e) 21.02° and (f) 45.83° according to the period of 360°.
The phase of the metasurface array needs to be set according to the relationship between the phase and the reflection angle. At first, to reduce the difficulty of manufacturing and external bias voltage, three adjacent column elements were used to form a pixel with a period length of 15 μm for each pixel. Secondly, the N-column pixel is set as a super-pixel period, and each super-pixel period is applied to the same phase by adding the same Fermi level. Subsequently, the phase gradient corresponding to all three different reflection deflection angles is selected as 90°. Therefore, the periodic phases of four super-pixel periods can be set as 0°, 90°, 180°, 270°, and extended to the whole TPA metasurface as a large period, as shown in Fig. 7(a, b, c). Finally, N is set to 3, 2, 1 when the reflected beam angles are 13.83°, 21.02°, and 45.83°, respectively. And according to Fig. 4, the Fermi level of graphene is set to 0.430 eV, 0.439 eV, 0.450 eV, and 0.480 eV when the phase is 0°, 90°, 180°, and 270°. And it should be noted that the device is excited by a linearly Ex-polarized plane wave that impinges at normal incidence concerning the surface along the z-direction, as shown in Fig. 1(b).
Fig. 7. Phase-gradient profile for the target beam-steering angle of (a) 13.83°, (b) 21.02° and (c) 45.83°, theoretically. Full-wave simulation results of the beam steering for (d) 13.88°, (e) 21.10° and (f) 46.05°. Reflected electric field distribution of the beam steering for (g) 13.88°, (h) 21.10° and (i) 46.05°.
Figures 7(d)–7(f) are the simulations of the metasurface size is 200 μm × 200 μm, the figures show that the beam deflection angles are 46.05°, 21.10°, 13.88°, respectively. While their full width of half maxima (FWHM) is about 2.18°, 1.09°, 0.74°. Furthermore, sidelobe energy of them is very low, which are only 1.06%, 0.82%, and 1.03% of the main lobe energy respectively. In order to show the modulation effect of the beam visually, the distribution of reflected electric field as shown in Figs. 7(g)–(i) and the far-field diagram as shown in Supplement 1, Fig. S3 are also simulated.
It should be noted that the method of changing the beam deflection angle includes not only changing the N value, but also changing the phase gradient. Above simulation results have proved that a series of discrete beam deflection angles can be achieved by changing the N value. If we want to achieve more deflection angles, the two methods above need to be used in combination. For the convenience of illustration, the theoretical beam deflection angle of 28.57° is taken as an example. The black curve in Fig. 8 is a linear phase curve calculated according to Eq. (1). Set N as 1, the periodic phases of four super-pixel periods can be set as 60°, 120°, 180°, 240°, and 300° respectively, which the corresponding Fermi levels of graphene are 0.430 eV, 0.436 eV, 0.442 eV, 0.450 eV, 0.470 eV, 0.485 eV.
The far-field simulation result is shown in Fig. 9. The figure shows that there is an obvious reflection spot at the position of far-field coordinate (180°, 27.49°), and there is no observable sidelobe in the whole far-field. There is a certain deviation between the beam deflection angle obtained by simulation and the target deflection angle, mainly due to the step value of the phase. Therefore, it is necessary to recalibrate according to the results in practical application. In conclusion, since the phase control range of the metasurface is up to 352.5°, we can obtain continuous beam deflection within 45.83° by combining the above two methods. In addition, the TPA can also achieve more than 45.83° deflection angles when the selected phase gradient is greater than 90°, but this will lead to poor beam quality and cannot perfectly meet the actual application requirements.
Besides the maximum beam deflection angle, the resolution should be optimized. Simulation results show that the overall size of the metasurface, that is, the maximum number of column periods, has a significant effect on the FWHM parameters, and is proportional to the resolution.
For this reason, the relationship between different metasurface sizes and FWHM is simulated. The results are shown in Fig. 10: when the metasurface size increases from 120 μm × 120 μm to 1200 μm × 1200 μm, the FWHM first decreases sharply to 1.60° and then slowly reduce to about 1.10°, which also indicates that the angular resolution of the designed metasurface TPA can reach a maximum deflection angle of about 1.10°. The resolution will increase as the size increases, but not as much.
In addition, the above function of beam deflection is only the result of the example when the wavelength is 6.98 THz. In this paper, the working wavelength of the structure can be extended to 5.5∼7.0 THz only through the selection and optimization of the Fermi energy level (see Supplement 1, Fig. S4).
5. Conclusion
We have shown an electrical phase modulation metasurface with a smooth phase tunability range up to 352.5° only by utilizing a monolayer graphene pattern in the THz region. And this metasurface has the advantage of low reflectivity variation under a wide range of phase modulation. We have also numerically accomplished the beam steering based on the proposed metasurface. For the TPA design, the maximum sidelobe energy up to 1.06% of the main lobe is achieved within beam deflection of 46.05°. In addition, for the incident wave of other frequencies, the deflection control can be realized by changing the structure size of graphene. The TPA designed in this paper is to be all-solid-state and allows wide phase control, low reflection change, scalability, and narrow beam divergence. With excellent CVD technology, wetting transfer technology, and gas plasma etching technology, our metasurface design approach can facilitate the development of practical and commercially THz miniaturized elements. In order to further reduce the range of reflectivity variation and improve energy utilization, we will try to use the structure of broadband tunable graphene metasurface to realize the beam deflection function of TPA in future studies.
Funding
National Natural Science Foundation of China (61775048); Shenzhen Fundamental Research Program (JCYJ2020109150808037); National Key Scientific Instrument and Equipment Development Projects of China (62027823).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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