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Abstract
In this paper, we present a novel tunable graphene coding metasurface structure using a circular graphene patch on an uneven substrate. By changing the Fermi level of graphene or the thickness of the substrate, we can achieve obvious phase variation. Firstly, we put forward two construction methods of 1-bit coding metasurface based on this mechanism. The first method is to change the thickness of the substrate when the Fermi levels of the two-unit cells are the same, so that the two-unit cells exhibit different digital states of ‘0’ and ‘1’. Furthermore, we change the working frequency band in real-time by switching the Fermi level from 0.05 eV to 0.85 eV. The second method is to change the Fermi level of graphene on the two-unit cells when the physical structure is fixed, so that the two-unit cells exhibit different digital states of ‘0’ and ‘1’. In this case, we can achieve the regulation of the direction and number of far-field reflected waves in the frequency range of 2.65 THz ∼ 2.85THz. Then, to obtain a single beam of reflected waves deviating from the normal direction, we create a 2-bit method in combination with two 1-bit construction methods. At 1.9 THz, the four-cell structures have a phase difference of approximately 90° and the same reflection coefficient. We also set several coding modes to analyse the control of the reflected wave on the 2-bit coding metasurface. Finally, we realized the real-time regulation of the reflected wave in eight directions from 0° to 360° by controlling the Fermi level of the graphene. Therefore, this article proposes a potentially effective approach to the design of functional devices for beam splitting and beam deflection.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, coding metasurface draws amounts of research interests due to its potential for controlling microwaves and terahertz waves, and the core idea is to design a variety of different coding unit cells to achieve the reflection phase difference in the form of 180° (i.e. 1-bit coding) and 90° (i.e. 2-bit coding), or 45° (i.e. 3-bit coding) [1–3]. An N-bit coding metasurface requires 2N coding unit cells respectively corresponding to a phase response between 0 and 2π. At the same time, by optimizing the coding sequence of the metasurfaces, it is possible to effectively control the electromagnetic waves to exhibit the desired state [4,5]. Coding metasurfaces for microwave and terahertz wave control can be used to make functional components such as beam splitting [6,7], focusing [8], beam deflection [9,10], polarization conversion [11,12], and also can effectively reduce the target radar cross-section (RCS) in the wideband range [13]. However, these designs cannot be dynamically changed because once the device is manufactured, its structure and corresponding phase response are static anyway. Thus, many efforts have been made recently to develop metasurfaces that can be changed dynamically [14]. In 2018, Cui and Cheng proposed “time-domain digital coding metasurface” and provide a way for us to study the real-time adjustable coding metasurface [15–17]. In this method, reflection properties can be varied within different time slots by changing the biasing voltages of varactor diodes in specially designed meta-atoms and solves the defect that the metal cannot be real-time adjusted. However, considering the limitations of material properties and processing capabilities, this method cannot be simply transplanted to the THz range for direct application. Therefore, we combined the unique properties of graphene to achieve beam steering in the terahertz range.
Graphene is an almost completely transparent, zero-bandgap semi-metallic material, which has received widespread attention due to its excellent properties [18–23]. In the study of coding metasurfaces, most metasurfaces achieve phase regulation by changing the size or orientation of the surface of coding unit cells’ metal patch, but once the coding unit cells are fixed, it is difficult to adjust again [24,25]. Graphene can be re-adjusted by applying an external voltage or magnetic field, providing a new method for real-time adjustment [26]. Recently, Kasra Rouhi has achieved real-time control of terahertz waves by using graphene-encoded metasurfaces [27]. In his work, 1-bit coding unit cells are constructed by merely changing the chemical potential of the surface graphene. However, the available frequency band is only one, and the difference in reflection amplitude between the two-unit cells at 2 THz in this frequency band has reached a large value of 0.5. Therefore, the reflected beam from the 1.7 THz to 2 THz normal direction cannot be perfectly eliminated.
Here, we propose new methods for controlling electromagnetic waves in real-time by coding metasurfaces based on graphene. To distinguish the state of the coding particles, we number them as ‘0’ or ‘1’ states. When the two-unit cells’ Fermi levels are the same, only the thickness of the substrate is changed. The substrate with thickness 20 $\def\upmu{\unicode[Times]{x00B5}}{\upmu \rm{m}}$ is set as ‘0’ and thickness 10 ${\upmu \rm{m}}$ is set as ‘1’ to realize the first type of 1-bit coding. We found that the Fermi level of 0.05 eV and 0.85 eV can achieve terahertz wave manipulation in two different frequency bands. For the other case, when the structural parameters of the two-unit cells are the same, only the Fermi level is changed. The Fermi level of 0.4 eV is set to “1”, and the Fermi level of 0.7 eV is set to “0”, thereby realizing the second type of 1-bit encoding.
Subsequently, we combined the above two construction methods and successfully constructed a 2-bit model. By changing the coding, we successfully achieved the eight-direction deflection of the far-field beam 0°, 45°……. 315°.
2. Structural design and theoretical analysis
The proposed unit cells are shown in Figs. 1(a) and 1(b), mono-layer graphene disk is placed the top layer, which radius is 5${\; \upmu }$m. Below the graphene disk, a thin layer of alumina and silicon are sequentially used to increase the nonlinearity of the phase curve. The thickness of substrate polyimide is H, and metallic copper is used as the bottom layer to prevent transmission of transmitted waves. Here, the period P of the unit cell is 12 ${\upmu \rm{m}}$, and the thickness H of the polyimide is 20 ${\upmu \rm{m}}$ and 10 ${\upmu \rm{m}}$ as ‘0’ and ‘1’, respectively. In the simulation, to reduce the unnecessary deviation caused by the coupling between cells and simulate the infinite periodic boundary conditions, M × M unit cells with the same state are formed into super unit cells. In this paper, the period length of the super unit cell composed of M × M unit cells is L = P × M. The state of the super unit cell is consistent with the unit cell, still ‘1’ or ‘0’. Finally, the coding metasurfaces consist of N × N super unit cells, as shown in Fig. 1(c). As shown in Fig. 1(c), in the schematic diagram of the coding metasurface, FPGA provides graphene with a voltage Vg sufficient to change the Fermi level. The ion-gel covers the surface of the super unit cells and uses Pt wires as the gate electrode. When the voltage Vg is applied, an electric double layer (EDL) with extremely high capacitance is formed at the ion-gel / graphene interface, which causes the Fermi level of graphene to change significantly [28,29]. Electromagnetic simulations are performed using CST Microwave Studio. We use the periodic boundary condition in x and y directions. The Floquet port is assigned to the Z direction, and the surface is illuminated by the x-polarized waves.
Fig. 1. (a) 3D diagram of the unit cell. (b) The unit cell consists of five materials, with the graphene disk at the top. (c) The coding metasurface consists of N × N super unit cells, which consist of M × M unit cells in the same digital state. The target position {x, y} is converted into a state matrix by a programmable device such as an FPGA. State matrix can be converted to voltage matrix ${V_g}$ again. In practice, we can use ion-gel to cover the graphene on the surface of the super unit cell, and use Pt wires as the gate electrode to connect to the FPGA.
In the terahertz region, the surface conductivity of graphene can be obtained from Drude model when the condition ${\upmu _c}/{k_B}T \gg 1$ is satisfied at a temperature of 300 K [30,31]:
The total field of far-field radiation can be treated as the superposition of the unit far-fields with different sizes. If the metasurface is composed of N × N elements, the electric far-field region can be expressed as follow in the spherical coordinate system by making an asymptotic of integrals using the stationary phase approximation [33]:
We can use the following two formulas to predict the direction of the reflected wave. The angle between the reflected wave and the normal direction $\theta $ and azimuth angle φ satisfy the following formulas [14]:
3. Results and discussion
3.1 1-bit coding metasurfaces
A 1-bit coding metasurface requires two coding unit cells with a reflection phase difference of 180°, and the two coding unit cells represent two coding states of ‘0’ and ‘1’. Here, there are two methods to achieve the 1-bit coding metasurface, by changing the thickness of the substrate or changing the Fermi level of the graphene. Below, we will analyze the implementation of these two methods and the regulation of terahertz waves.
The first method is to change the thickness of the substrate. As shown in Fig. 2(b), the thickness of ‘0’ is ${H_0}$ = 20${\; \upmu \rm{m}}$, the thickness of ‘1’ is ${H_1}$ = 10${\; \upmu \rm{m}}$, and the same Fermi level of 0.85 eV is given to the two-unit cells. The phase curves of ‘1’ and ‘0’ are shown in Fig. 2(a), and the amplitude curve is shown in Fig. 2(b). The phase difference is 180° (±30°) in 3.2 THz ∼ 4.2 THz, and the amplitude difference is small in 3.4 THz ∼ 4 THz. In the far-field simulation, we set M = 10, N = 8. For the convenience of explanation, we also design two coding modes. One is a coding mode ${X_1}$ coded only in the x-axis direction, and the other is a coding mode ${X_1}{Y_1}$ coded in the x-axis and y-axis directions. The ‘0’ or ‘1’ we use in the coding mode is a super unit cell composed of M × M unit cells, and these super unit cells are sorted in order. The letter of the coding mode indicates the coding direction, and the number in the lower right corner indicates the number of cycles in the direction. ${X_1}$ owns one cycle in the x-axis direction, so the x-axis direction of coding metasurface is arranged as ‘01010101’. The y-axis direction is arranged as ‘00000000’ or ‘11111111’. ${X_1}{Y_1}$ is coded one cycle along the x-axis direction and one cycle in the y-axis direction. The x-axis direction of coding metasurface is arranged as ‘01010101’, the y-axis direction is also arranged as ‘01010101’. The physical period length of the ${X_1}$ mode in the x and y directions, $ {\mathit{\Gamma _x}}$ = 2L, ${\mathit{\Gamma _y}}$ = $\infty $. The physical period length of the ${X_1}{Y_1}$ mode in the x and y directions, ${\mathit{\Gamma _x}}$ = ${\mathit{\Gamma _y}}\; $ = 2L. The far-field diagrams in ${X_1}$ and ${X_1}{Y_1}$ modes are shown in Figs. 2(c) and 2(d). When the Fermi level is 0.85 eV, the coding metasurfaces can adjust the far-field reflection wave into two and four beams within 3.4 THz ∼ 4 THz. The angles of the reflected wave are shown in Figs. 2(e) and 2(f).
Fig. 2. Changing the substrate thickness of the two-unit cells can construct a 1-bit coding method, in which the Fermi level is 0.85 eV. (a) (b) Phase diagram and Amplitude diagram of unit cells ‘1’ and ‘0’. (c) When the Fermi level is 0.85 eV, the incident wave is reflected in both directions when using the ${X_1}$ coding mode. (d) When the Fermi level is 0.85 eV, the incident wave is reflected in four directions when using the ${X_1}{Y_1}$ coding mode. (e) As the frequency of the incident wave changes, reflected wave angle $\theta $ changes from 21.6 ° to 18.2 ° in the ${X_1}$ coding mode. (f) As the frequency of the incident wave changes, reflected wave angle $\theta $ changes from 31.3 ° to 26.2 ° in the ${X_1}{Y_1}$ coding mode.
Fig. 3. Changing the Fermi level applied to the coding metasurface, we can choose the desired operating frequency band and $\theta $. (a) (b) Phase diagram and Amplitude diagram of unit cells ‘1’ and ‘0’. (c)(d) When the Fermi level is 0.05 eV, the far-field condition using the ${X_1}$ and ${X_1}{Y_1}$ coding modes in the frequency band 6.5 THz ∼ 9 THz is similar to 0.85 eV, and the incident wave is reflected in two and four directions. (e) As the frequency of the incident wave changes, reflected wave angle $\theta $ changes from 10.8 ° to 7.8 ° in the ${X_1}$ coding mode. (f) As the frequency of the incident wave changes, reflected wave angle $\theta $ changes from 15.8 ° to 11.3 ° in the ${X_1}{Y_1}$ coding mode.
When the coding metasurfaces of ${X_1}$ are used and the Fermi level is 0.85 eV, the normal reflection of the reflected wave is mainly eliminated and two reflected waves of $\varphi {\; }$ = 0° and $\varphi {\; }$ = 180° can be obtained in 3.4 THz ∼ 4 THz. With the increase of frequency, $\theta $ decreases from 21.6° to 18.2° gradually tending to the normal direction, as shown in Fig. 2(e). When the Fermi level is changed to 0.05 eV, the frequency band is altered to 6.5 THz ∼ 9 THz and θ is varied from 10.8° to 7.8°, as shown in Fig. 3(e).
When the coding metasurfaces of ${X_1}{Y_1}$ are used and the Fermi level is 0.85 eV, θ decreases from 31.3° to 26.2° as the frequency increases, as shown in Fig. 2(f). When the Fermi level is changed to 0.05 eV, the reflected wave exhibits a four-beam state similar to the Fermi level of 0.85 eV. $\varphi $ is 45°, 135°, 225°, 315°, and θ can vary from 15.8° to 11.3° with frequency enhancement, as shown in Fig. 3(f). These simulation results are consistent with the predictions of Eqs. (5) and (6). So, by changing the Fermi level applied to the coding metasurfaces, we can select the desired operating frequency band which reflects the adjustable performance that metal does not have.
In order to study the influence of the periodicity of the 1-bit coding metasurface we proposed on the far-field reflected wave, we change the number of cycles in the x-axis and y-axis directions and establish a new coding mode ${X_1}{Y_2}$, $ {X_2}{Y_1}$, $ {X_2}{Y_2}$. Similar to the two coding modes defined above, the subscript still indicates the number of cycles. Taking 3.7 THz as an example, the far-field stimulation effect of different coding modes is shown in Figs. 4(a) to 4(d). The specific directions of the reflected waves in the four modes are as follows: $\; {X_1}{Y_1}:({\theta ,\varphi } )= ({28.1^\circ ,45^\circ{/}135^\circ{/}225^\circ{/}315^\circ } ),\; {X_1}{Y_2}:({\theta ,\varphi } )= 21.8^\circ ,26.6^\circ{/}153.4^\circ{/}206.6^\circ{/}333.4^\circ ,\; {X_2}{Y_1}:({\theta ,\varphi } )= 21.6^\circ ,63.4^\circ{/}116.6^\circ{/}243.4^\circ{/}{\; }296.6^\circ ,\; {X_2}{Y_2}:({\theta ,\varphi } )= 13.8^\circ ,45^\circ{/}135^\circ{/}225^\circ{/}315^\circ $. First, we compare the two coding modes ${X_1}{Y_1} $ and ${X_2}{Y_2}$. When the number of cycles in the x-axis and y-axis directions becomes larger at the same time, the reflected wave $\varphi $ does not change, and θ becomes smaller. The far-field top view is shown in Figs. 4(a) and 4(d), and the 2D map is shown in Figs. 4(e) and 4(h). When ${X_1}{Y_1}$ is compared to ${X_1}{Y_2}$, the number of cycles in the x-axis direction is constant, and the number of cycles in the y-axis direction is increased. Currently, the reflected wave θ becomes smaller and closes toward the x-axis. The far-field top view is shown in Figs. 4(a) and 4(b), and the 2D map is shown in Figs. 4(e) and 4(f).
Fig. 4. Changing the coding period of the x-axis or y-axis direction, the angle of the reflected wave changes. (a) (e) Far-field top view and 2D map of ${X_1}{Y_1}$. (b) (f) Far-field top view and 2D map of ${X_1}{Y_2}$. Compared to ${X_1}{Y_1}$, the reflected waves are close to the x-axis and $\theta $ is slightly smaller. (c) (g) Far-field top view and 2D map of ${X_2}{Y_1}$. Compare with ${X_1}{Y_1}$, the reflected waves are close to the y-axis. (d) (h) Far-field top view and 2D map of ${X_2}{Y_2}$. Compare to ${X_1}{Y_1}$, $\varphi $ is unchanged and $\theta $ is obviously smaller. The reflected wave is close to the normal direction.
When ${X_1}{Y_1}$ is compared to ${X_2}{Y_1}$, the number of cycles in the x-axis direction increases, and the number of cycles in the y-axis direction is constant. At this time, the reflected wave θ becomes smaller and closes toward the y-axis. The far-field top view is shown in Figs. 4(a) and 4(c), and the 2D map is shown in Figs. 4(e) and 4(g).
The second method is to change the Fermi level, as shown in Fig. 5(b). The thickness of both unit cells is 20 ${\upmu }$m and the only difference is the Fermi level of graphene in their surface. The unit cell with a Fermi level of 0.4 eV is ‘1’, the unit cell with a Fermi level of 0.7 eV is ‘0’, and their phase and amplitude curves are shown in Figs. 5(a) and 5(b). The phase difference is 180° (±30°) in 2.45 THz ∼ 2.9 THz, and the amplitude difference is small in 2.65 THz ∼2.85 THz. It is worth mentioning that at 2.7 THz, the phase difference is 180° and the amplitude difference reaches a minimum. In far field simulation, we set M = 10 and N = 8. After the super unit cells are arranged in order, the ${X_1} $ and ${X_1}{Y_1}$ coding modes are used to simulate the far-field reflected wave at 2.7 THz, as shown in Figs. 5(c) and 5(d). This method is similar to the method of changing the thickness to change the wave number and the angle. So, the effect of the method of changing the Fermi level is not specifically analyzed here.
Fig. 5. The thickness of the two unit cells is constant, and only the Fermi level of the surface graphene is changed to construct ‘1’, ‘0’. (a) The phase of the unit cell ‘1’ and ‘0’. (b) The amplitude of the unit cell ‘1’ and ‘0’. (c) At 2.7 THz, the reflected wave is reflected in two directions when using the ${X_1}$ coding mode. (d) At 2.7 THz, the reflected wave is reflected to four directions when using the ${X_1}{Y_1}$ coding mode.
3.2 2-bit coding metasurfaces
The 2-bit coding metasurface requires four unit cells with different states. The phases reflected by these unit cells are normalized to 0°, 90°, 180°, and 270°. Combining the two construction methods of 1-bit coding metasurfaces, we successfully constructed four 2-bit unit cells with the Fermi level and thickness as variables. As shown in Table 1 and Fig. 6(a), we choose ${H_{1\; }}$=20 µm, ${H_{0\; }}$=10 µm, and apply four different Fermi levels to the unit cells. Finally, the phase difference between the unit cells of ‘0’, ‘1’, ‘2’, and ‘3’ can be realized by 90°. In Figs. 6(b) and 6(c), we find that the phase difference at 1.9 THz is approximately 90°, and the amplitude difference is the smallest here. It satisfied the conditions of destructive interference, so we simulate the far-field at 1.9 THz.
Fig. 6. (a) Schematic diagram of 2-bit unit structure. (b) Phase curve of four unit structures. (c) Amplitude curve of four unit structures.
Table 1. Four units corresponding parameters.
Here, we set M = 10, N = 8, and perform far-field simulation according to the coding mode of $ X_1^{\prime}$, $X_{ - 1}^{\prime}$, $ Y_1^{\prime}$ and $Y_{ - 1}^{\prime}$, as shown in Fig. 7. The ‘0’, ‘1’, ‘2’, and ‘3’ we use in the coding mode are super unit cells composed of M × M unit cells, and those super unit cells are sorted in order. To distinguish 1-bit, a symbol is added in the upper right corner to mark. The letter still indicates the coding direction, the lower right corner indicates the number of cycles, and the positive and negative signs indicate the order of the cell array. For example, ‘01230123’ indicates a positive sign, and ‘32103210’ indicates a negative sign. We define $X_1^{\prime}$, $X_{ - 1}^{\prime}$, $ Y_1^{\prime}$ and $Y_{ - 1}^{\prime}$ as gradient coding sequences. The coding modes are as follows:
Fig. 7. The single-beam reflected wave with different deflection directions in four different encoding cases of 2-bit model. (a) (e) Far-field 3D and 2D plots in $X_1^{\prime}$ coding mode and the angle is (19.2°, 0°). (b) (f) Far-field 3D and 2D plots in $X_{ - 1}^{\prime}$ coding mode and the angle is (19.2°, 180°). (c) (g) Far-field 3D and 2D plots in $Y_1^{\prime}$ coding mode and the angle is (19.2°, 270°). (d) (h) Far-field 3D and 2D plots in $Y_{ - 1}^{\prime}$ coding mode and the angle is (19.2°, 90°).
The far-field map and the angle map are shown in Fig. 7, and the four coding modes correspond to four different far-field patterns, respectively. In a 2-bit coding metasurface, the reflected waves exhibit a single beam state with the same θ, and the reflected waves in different coding modes have different azimuth angle φ.
Since the electric field distribution and far-field scattering pattern are Fourier transform pairs on the coding surface, and the addition of any coding mode and gradient coding mode satisfies the following equation [25]:
We choose $X_1^{\prime}$ and $Y_{ - 1}^{\prime}$ as examples for specific analysis. As known in Figs. 7(e) and 7(h) that the $X_1^{\prime}$ and $Y_{ - 1}^{\prime}$ coding modes ${\theta _{x\; }}$=$\; {\theta _y}\; $ = 19.2°. We calculate the gradient coding mode $X_1^{\prime}$ and the gradient coding mode $Y_{ - 1}^{\prime}$ from modulus calculation, as shown in Fig. 8(a). The calculation process is as follows:
Fig. 8. By superposition of gradient coding modes, the deflection direction of the reflected wave can be changed in the far-field, and the original four directions are expanded into eight directions. (a) ${\; }X_1^{\prime} + Y_{ - 1}^{\prime} = {\; }$ (27.7°,45°). (b) ${\; }X_1^{\prime} + Y_{1{\; \; }}^{\prime}$ = (27.7°,315°). (c) ${\; }X_{ - 1}^{\prime} + Y_{ - 1}^{\prime}$ = (27.7°,135°). (d) $ X_{ - 1}^{\prime} + Y_1^{\prime}$ = (27.7°,225°). (e)-(h) Calculated 2D maps correspond to (a)-(d).
4. Conclusion
Tunable graphene-coding metasurfaces on the uneven substrate were theoretically designed and studied. The results show that the use of metasurfaces with the uneven substrate can bring a wider operating band and increase the frequency band selectivity. For the 1-bit unit cells constructed by changing the thickness of the substrate, when the Fermi level of the surface graphene is changed from 0.85 eV to 0.05 eV, the frequency band is changed from 3.4 THz ∼ 4 THz to 6.5 THz ∼ 9THz. In the study of the 1-bit coding modes, we found that the reflected waves can be simultaneously regulated in two or four directions. Changing the coding period in the x or y direction can bring the regularity of the far-field reflected wave closer to the axis. In the 2-bit modes’ study, we found that the coding metasurfaces can produce a single beam of the reflected wave and regulate the direction of the reflected waves. Simulation results show that different gradient coding modes can generate four directions of 0°, 90°, 180° and 270°. Using the convolution theorem, the modulus addition of the gradient coding mode can extend the single beam of the deflected wave from four directions to eight directions. This work supplies a new way to design functional devices of beam separation and beam deflection.
Funding
Natural Science Foundation of Zhejiang Province (No.LY16F010010); Zhejiang Province Public Welfare Technology Application Research Project (No.2015C34006).
Disclosures
The authors declare no conflicts of interest.
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