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Abstract
A bifunctional metamaterial is proposed based on a hybrid graphene and vanadium dioxide (VO2) configuration, which can realize a dynamic switch between beam steering and broadband absorption. The structure consists of a VO2 square, graphene patch, topas spacer, VO2 film, topas spacer, and metal substrate. When VO2 is in the metallic state, the structure serves as a coding metamaterial. By engineering different sizes of the top VO2 square and adjusting the Fermi energy level of graphene, the incident wave is scattered in different patterns. When VO2 is in the dielectric state, the structure serves as a broadband absorber. By changing the Fermi energy level of graphene from 0.0 eV to 0.9 eV, absorptance can be gradually changed and working bandwidth widens. There is an absorption band with near 100% absorptance from 0.9 THz to 1.35 THz when the Fermi energy level is 0.73 eV. And the designed broadband absorber is polarization-insensitive within the incident angle of 50°. Our work may show great potential in applications such as terahertz switching and modulation.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterial is a kind of artificial electromagnetic materials composed of subwavelength metallic or dielectric blocks [1,2]. Its permittivity and permeability can be arbitrary in principle. The greatly expanded parameter range provides a significantly improved ability to control electromagnetic wave over a range of different frequencies, leading to many fascinating phenomena, such as negative refraction [3,4], invisible cloak [5,6], and perfect absorption [7,8]. By carefully designing the geometry of the resonant element, one can freely control reflective and transmissive phases and amplitudes of electromagnetic wave. So metamaterials offer a novel way to realize multifunctional materials and devices. But when the structure of metamaterial is set, spectral position and bandwidth are always fixed. Thus, the functionalities of metamaterial cannot be changed. In practical applications, tunable or switchable metamaterials are more attractive due to their flexibility [9,10].
Coding metamaterial is firstly proposed by Cui et al. in 2014 [11]. Their structure is composed of two kinds of unit cells which can realize 0 and π phase response to mimic “0” and “1” elements. By designing “0”and “1” elements in certain sequences, beam control is realized. Such 1-bit coding can also be extended to 2-bit coding with phase responses of 0, π/2, π, 3π/2 to mimic “00”, “01”, “10”, and “11” elements, which have more possibilities in permutations and combinations. Additionally, they proposed a biased diode-controlled structure in subwavelength size by using field programmable gate array. Digital metamaterial can realize “0” and “1” elements without changing individual unit cell. In 2015, Yan et al. proposed and fabricated a novel 2-bit coding non-absorptive metamaterial to redirect electromagnetic energies in terahertz region, which is based on an eightfold symmetric double cross metallic line structure [12]. In 2017, a new coding method is proposed by Ma et al. with orthogonal parameters in the emitting beam [13]. They combined orthogonal polarization and orbital angular momentum to establish a vector beam modulator.
Graphene is a monolayer of carbon atoms in a planar hexagonal lattice and can be considered as a two-dimensional form of graphite [14–16]. Graphene has attracted much attention due to its unique electrical and optical properties, and has become an important platform for the construction of integrated plasmonic devices with a wide wavelength range from near-infrared to terahertz [17,18]. Due to electrostatic tuning properties, graphene has great application potential in the fields of chemistry [19], energy [20], material [21], and physics [22]. In 2017, Rouhi et al. presented a method of real-time manipulation of terahertz waves based on graphene named graphene-based coding metamaterial [23]. “0” and “1” elements are characterized by two graphene squares with equal size but with different Fermi energy levels providing an inverted phase response. They also established a 2D inverse discrete Fourier transform algorithm to predict far-field patterns. In 2020, Jadeja et al. proposed a wideband absorber based on C-shaped graphene metamaterial and studied its absorption performance at visible frequencies between 430 THz and 770 THz [24]. In the whole visible region, the average absorption rate is up to 84%. More recently, Lin et al. proposed a double-layer graphene absorber where pattern hybridization and superimposed effects were investigated [25].
Vanadium dioxide (VO2) is another good candidate for dynamically tunable materials. As a phase change material, dielectric permittivity of VO2 undergoes a reversible dielectric-metal phase transition around 340 K [26–28]. In recent years, tunable metamaterials have been realized at different electromagnetic frequencies based on phase-transition characteristics of VO2 [29–31]. In 2019, Z. Cui et al. designed a multiband terahertz resonator using an anisotropic array [32]. The unit cell contains four pairs of H-shaped resonators of different sizes, and discrete frequency shift and dynamic amplitude tuning can be observed by varying polarization angle. In 2020, J. Huang et al. proposed a controllable terahertz active absorber with dual wideband characteristics [33]. Simulated results show that absorption bandwidths are 0.88 THz at 0.56–1.44 THz and 0.77 THz at 2.88–3.65 THz, respectively.
In fact, both metamaterial absorbers and coding metamaterials have been widely studied. However, no one has come up with a structure that combines these two functionalities so far. In this work, we propose a switchable metamaterial based on graphene and VO2. A coding metamaterial and a broadband absorber are integrated in a single structure, and they can be freely switched, opening a new way to realize multifunctional metamaterial devices.
2. Principle and method
At first, we consider a homogeneous coding metamaterial that contains M×N lattices, and each lattice is a small isotropic scatterer. This metamaterial is illuminated by a normally incident plane wave, and its far-field scattering pattern (not normalized) can be expressed as
Fig. 1. The distributions of ${A_{m,n}}$ and ${\alpha _{m,n}}$ (a-c) and their 2D far-field scattering patterns (d-f), where $U = \sin \theta \cos \varphi $ and $V = \sin \theta \sin \varphi $. Each scattering pattern is normalized by the maximum value of the pattern for perfect mirror reflection (d).
3. Analysis and design
3D schematic of the whole design is shown in Fig. 2(a). The proposed coding metamaterial is a chessboard-like structure made up of $6 \times 6$ “0” and “1” lattices with $4 \times 4$ unit cells. Each unit cell is a sandwiched structure composed of six layers, including VO2 square, graphene patch, top topas spacer, VO2 film, and bottom topas spacer. A metallic mirror is placed as a bottom layer. The structure is designed with period $p = 80\; \mathrm{\mu }\textrm{m}$ in x and y directions. In order to realize the desired performance, graphene is designed with a cross shape which is characterized by $l = 78\; \mathrm{\mu }\textrm{m}$ and $w = 29.4\; \mathrm{\mu }\textrm{m}$. The top VO2 square with thickness $t = 1\; \mathrm{\mu }\textrm{m}$ is designed as $b = 32/65.6\; \mathrm{\mu }\textrm{m}$ to realize “0”/“1” element. The thickness of the top topas spacer and the bottom topas spacer are ${t_1} = 28\; \mathrm{\mu }\textrm{m}$ and ${t_2} = 10.9\; \mathrm{\mu }\textrm{m}$, respectively. The thickness of VO2 film inserted in topas is $t = 1\; \mathrm{\mu }\textrm{m}$. Gold is selected as metal substrate with the conductivity of $4.561 \times {10^7}\; \textrm{S}/\textrm{m}$. The dielectric constant of topas is 2.35. Polysilicon is employed as an electrostatic gate with a relative dielectric permittivity of 3. The existence of polysilicon has little influence on the design because its thickness is only 20 nm. The proposed structure is simulated by finite element method (FEM, commercial software-COMSOL Multiphysics). Perfect matched layers (PMLs) are set for far-field calculation (beam steering and RCS reduction) along all directions. Excitation source is a plane wave. For absorption, periodic boundary conditions are set for unit cell along x and y directions and PML is set along z direction. Excitation source is the floquet-mode port. To ensure the convergence of the calculated results, appropriate mesh refinement is adopted. Due to the mono-atomic thickness, graphene can be considered as a 2D infinite-thin layer to improve computation efficiency. The optical response of graphene is characterized by complex surface conductivity, which can be divided into two parts as intraband contribution and interband contribution [34–36].
Fig. 2. Schematic diagram of the proposed structure. (a) The whole 3D structure. (b) Schematic of 3D unit cell. (c) Top view of graphene patch.
In these formulas, relaxation time is $\tau = 0.1\; \textrm{ps}$, and Fermi energy level ${E_F}$ is a tunable parameter. Fermi energy level of graphene is set as 0.0 eV in beam steering and 0.73 eV in broadband absorption. As a typical phase change material, VO2 shows the change from dielectric state to metallic state under the critical temperature of 340 K. The temperature of VO2 can be adjusted by optical pumping. Drude model is used to describe dielectric permittivity of VO2 in terahertz range as
4. Results and discussions
4.1 Tunable multi-beam steering
When VO2 is in the state of metal and Fermi energy level is ${E_F} = 0.0\; \textrm{eV}$, it can be seen that phase response of reflection wave of unit cell in Fig. 2(b) with different VO2 square lengths ($b = 32/65.6\; \mathrm{\mu }\textrm{m}$) are different in Fig. 3(a). In particular, when frequency is 1.279 THz, phase difference reaches $180^\circ $. Coding states “0” and “1” are achieved, and the corresponding reflection amplitudes are ${A_0} = {A_1} = 0.80$. According to (2), electromagnetic properties of graphene can be regulated by frequency and Fermi energy level. Therefore, for the unit cell “0” and “1”, phase of reflection wave will vary with frequency and Fermi energy level. In Fig. 3(b), we can see contour plot of reflection phase difference $\alpha ({f,{E_F}} )$ with the variation of frequency and Fermi energy level. In the frequency range of 0.0–1.4 THz, phase difference $\alpha ({f,{E_F}} )$ gradually increases to 360° as Fermi energy level increases from 0.0 eV to 0.8 eV. When frequency is 1.279 THz, phase difference $\alpha ({{E_F}} )$ can be dynamically regulated by Fermi energy level ${E_F}$.
Fig. 3. (a) Reflection phase and phase difference of “0” and “1” elements with a fixed Fermi energy level (0.0 eV). (b) Contour plot of reflection phase difference with the variation of frequency and Fermi energy level.
Based on the above analysis, we design a tunable multi-beam steering by checkerboard-like coding metamaterial with coding sequence “010101/101010…”. Each “0” (“1”) lattice is composed of $4 \times 4$ “0” (“1”) unit cells. In this condition, (1) can be expressed as
Beam-point angle ${\theta _{max}}$ and ${\varphi _{max}}$ of $\max [{f({\theta ,\varphi } )} ]$ can be illustrated
where $D = 4p$ is the lattices’ periodical length of coding sequence along x axis and y axis, and ${\theta _{max}}$ and ${\varphi _{max}}$ are the solutions of $\textrm{max}[{f({\theta ,\varphi } )} ]$. According to (7) and (8), quad-beam pointing angles are ${\varphi _{max}} = \arctan ({ \pm 1} )= 45^\circ ,135^\circ ,225^\circ ,\; 315^\circ $ and ${\theta _{max}} = \arcsin \left( {\sqrt 2 \pi /4{k_0}p} \right) = 31.2^\circ $. As shown in Fig. 4(a), based on (6), far-field distribution is calculated by Matlab. Simulated result from FEM is in great agreement with that from Matlab. Reflection waves of checkerboard-like coding metamaterial propagate along four directions: elevation angle is $31.2^\circ $ and azimuth angles are $45^\circ ,135^\circ ,225^\circ ,\; and\; 315^\circ $. Furthermore, as we increase Fermi energy level of graphene, phase difference between code states “0” and “1” will gradually diminish. Far-field pattern will change from quad-beam to single-beam. Figure 4 shows the evolution of multi-beam states. As Fermi energy level increases, reflected wave will undergo quad-, penta-, and single-beam states in turn. The working efficiencies (${\propto} \;{|E |^2}$) of the device are 58%, 22%, and 34% for quad-, penta-, and single-beam states. In the process of switching from four beams to single beam, five beams with the equal amplitude at 0.24 eV is an intermediate state. When Fermi level is less than 0.24 eV, the energy of diagonal four beams is stronger than that of the middle beam. When Fermi level is greater than 0.24 eV, the energy of the middle beam is greater than that of diagonal four beams. If we need to have diagonal four beams and middle single beam simultaneously in some application scenes, this function can be adopted.Fig. 4. Calculated (a-c) and simulated (d-f) far-field scattering patterns of the proposed coding metamaterial at 1.279 THz with different Fermi energy levels.
4.2 Tunable broadband absorption
A totally different functionality is realized when VO2 is in the state of dielectric. Absorptance is calculated by $\textrm{A} = 1 - \textrm{R} - \textrm{T} = 1 - {|{{\textrm{S}_{11}}} |^2} - {|{{\textrm{S}_{21}}} |^2}$ in simulation, where $|{{\textrm{S}_{11}}} |$ is reflection and $|{{\textrm{S}_{21}}} |$ is transmission. Skin depth is much smaller than the thickness of gold substrate, so $|{{\textrm{S}_{21}}} |$ is zero. As shown in Fig. 5, whether we use b=32 µm or b=65.6 µm, the results of absorptance are the same. Absorption depends on the responses of graphene when VO2 is in the dielectric state. With the optimized Fermi energy level of ${E_F} = 0.73\; \textrm{eV}$, above 90% absorptance is obtained at the frequency from 0.74 THz to 1.57 THz and near 100% absorptance is obtained in the range of 0.90–1.35 THz. The influence of Fermi energy level on absorptance can be clearly seen from Fig. 5. Due to plasmonic resonance of doped graphene, the centering frequency has a slight blue shift with rising of Fermi energy level. By adjusting Fermi energy level of graphene from 0.0 eV to 0.9 eV, absorptance at lower frequency (0.74 THz) is dynamically tuned from 10% to 90%. Absorptance at higher frequency (1.57 THz) is tuned from 7% to 90%. Thus, a tunable broadband absorber is achieved.
Fig. 5. Dependence of absorptance on different Fermi energy levels of graphene under the conditions of (a) b=65.6 µm and (b) b=32 µm. (c) Absorptance of “01/10” lattice is the same as “0” lattice and “1” lattice When Fermi energy level is 0.73 eV. (d) RCS reduction of the whole structure. The bandwidth of RCS reduction with −20 dB is almost same as 99% absorptance bandwidth of “0” lattice, “1” lattice, and “01/10” lattice.
In order to better explain the physical mechanism of the proposed broadband absorber, electric field distributions are calculated at 0.73 eV. Figure 6 shows electric field distributions in the xoy plane at 1.04 THz and 1.25 THz. Color map represents the intensity of electric field. Electric field of incident wave is polarized along x direction. At 1.04 THz, as shown in Fig. 6(a), electric field is strongly enhanced in the gap between two graphene squares. It indicates that the resonance at lower frequency is mainly caused by the coupling interaction between graphene squares. At 1.25 THz, as shown in Fig. 6(b), electric field is mainly localized at the edge of individual graphene square. It indicates that the resonance at higher frequency is mainly caused by electric dipole resonance. The merging of two resonances in the adjacent frequency range eventually contributes to the realization of broadband absorption.
Fig. 6. Electric field distributions in the graphene patch at 1.04 THz (a) and 1.25 THz (b) in the xoy plane.
Furthermore, it is necessary to calculate absorption under oblique incidence which is very important in practical applications. For this reason, angular dependence of absorption is calculated with transverse electric (TE) and transverse magnetic (TM) waves under different incident angles. For TE polarization, as shown in Fig. 7(a), high performance (over 90% absorptance from 0.74 THz to 1.57 THz) can survive with incident angle up to $60^\circ $. If incident angle increases, absorption will degrade. For TM polarization, as shown in Fig. 7(b), absorption intensity is still at a high level when incident angle is $60^\circ $. The above results show that the designed absorber is insensitive to incident angle.
Fig. 7. Broadband absorptances as a function of incident angle and frequency of the illuminating waves for TE (a) and TM (b) polarizations.
5. Conclusion
To summarize, a bifunctional terahertz metamaterial is proposed based on a hybrid structure of graphene and VO2. This isotropic metamaterial can not only achieve beam steering with the change of Fermi energy level of graphene, but also achieve broadband absorption after the switching of the state of VO2. When VO2 is in the state of metal, the design is a checkerboard-like coding metamaterial with coding sequence “010101/101010…” and serves as a multi-beam steering device. As Fermi energy level of graphene increases from 0.0 eV to 0.8 eV, phase difference of “0” and “1” elements will degrade. Reflected waves can be switched from quad-beam to penta-beam and then single-beam. As a result, a multi-beam coding metamaterial is designed which has dynamic beam steering. When VO2 is in the state of dielectric, the design turns into a broadband absorber, which has >90% absorptance from 0.74 THz to 1.56 THz and ∼100% absorptance in the range of 0.90–1.35 THz. By changing Fermi energy level of graphene, absorption intensity and bandwidth will change as well. Absorption is polarization-insensitive and it works well in a large range of incident angle. Compared with the previous works based on graphene and VO2 that only involve absorption [40,41], the present work uniquely describes the switching between beam steering and absorption. Graphene can control not only the number of beams, but also absorption bandwidth and intensity. Quad-beam and single-beam real-time switching is the most important function for monopulse radar that can be used in the fields of fast target tracking. Furthermore, the proposed multi-beam steering is desired for multi-beam terahertz reflector antenna and multi-angle electromagnetic sensor. But, there are still some challenges in the micro/nano fabrication of such hybrid configuration. Gold film is fabricated by high-vacuum electron beam evaporation onto a quartz substrate. Bicycloheptene experiences ring-opening ectopic polymerization under the action of a metallocene catalyst, and then experiences a hydrogenation reaction to form an amorphous homopolymer. After catalyst separation and devolatilization, topas can be obtained. VO2 is deposited by the pulsed-DC magnetron sputtering technique from a pure vanadium target and a well-controlled O2 gas mixture. X-ray diffraction and micro-Raman spectroscopies are carried out to characterize VO2 films. Chemical vapor deposition method can be employed to gain graphene. As our design can realize multiple functionalities in a single structure, it could be used in the fields of terahertz switching, modulating, and anti-stealth radar [40–45].
Funding
National Natural Science Foundation of China (11974294), Guangdong Basic and Applied Basic Research Foundation (2020A1515010375).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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.
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