Investigation on the tunable and polarization sensitive three-band terahertz graphene metamaterial absorber

A tunable three-band absorber has been proposed and investigated in the terahertz (THz) with graphene strips. Three perfect absorption is elaborately analyzed with the electrical field and the induced surface current distribution. Owing to the unique character of graphene, the position and intensity of three peaks are flexibly regulated with different Fermi energy and chemical potential. Meanwhile, an on to off modulation of the perfect absorption is achieved when the polarization angle varies from 0 to 90°, and the modulation degree of three resonant peaks can simultaneously approach 100%, which are much higher than the previous work. Moreover, the tunable absorption is examined with different geometry parameters and intermediate medium. Such highly tunable absorber with our proposed design has numerous application potential in the controllable optical switchers, filters, detectors, and sensors.


Introduction
Metamaterial absorber (MA) was proposed for the first time in 2008 with a subwavelength design of an electric ring resonator and a split wire [1], which has garnered much attention due to its ability to control electromagnetic waves [2,3]. Since then, much work has been carried out on MA with different unit cell [3][4][5][6][7][8][9], such as trapezoidal array [3], cross ring resonator [4], rotational symmetry resonator [5], crossed-shaped resonator [6] and strip resonator [7] to generate single band, two band, three band, multi-band, or broadband perfect absorption [6][7][8][9]. However, the absorption of the above-mentioned metal-insulator-metal structure is unable to tune once the design is set, which limits its practical applications. Recently, flexibly tunable absorber has been developed through the initiation of external electronic field [10,11], magnetic field [12], temperature [13] or pressure [14]. For instance, Zhang et al suggested a graphene-based terahertz MA with external voltage [10]. Xu et al demonstrated a broadband terahertz MA that is optically adjustable with two split ring resonators [12]. Luo et al showed a thermo-tunable MA with InSb star-shaped structure glued to a gold foil [13]. Among them, graphene is frequently chosen as the unit cell, which is a 2D layer of carbon atoms laid out in a honeycomb lattice. With careful chosen Fermi level, graphene behaves like a thin metal and interacts strongly with the incident light, thereby motivating the surface plasmons along the graphene surface. It can capture and manipulate electromagnetic waves with an external voltage, resulting in surface plasmon manipulation at the graphene/dielectric interface [15,16]. These fascinating properties make graphene an appropriate candidate for tunable and compact terahertz switcher. For example, Cai et al suggested a MA composed of stacked, orthogonal and elliptic graphene layers to achieve eight THz absorption bands [17]. Deng et al presented a polarizationsensitive MA, consisting of an electric resonance structure with periodic patterns and a metallic grounding plane spaced by single-layer graphene and SiO 2 [18]. Cao et al have developed an actively tuned polarization sensitive multi-band absorber in the infrared region, which consists of stacked multiple layers of graphene separated by dielectric layers on a metal mirror [19]. Liu et al studied a terahertz multi-function modulator consisting of toplayer graphene ribbons and a bottom-layer graphene strip, which can produce a Fano resonance for an electrooptic switch and filter [20]. Ye et al presented a sandwiched graphene structure to get strong polarization- Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. dependent optical absorption for transverse electric wave under total internal reflection [21]. Furthermore, the polarization tunable electromagnetic waves response has also been investigated with a slab of in-plane anisotropy black phosphorus [22]. Other optical designs have been carried out to absorb efficiently. Sacks et al presented an alternative approach to derive a perfectly matched layer for mesh truncation by using anisotropic material [23]. Constantinos et al utilized a semi-analytical integral equation to analyze the scattering characteristics of an infinite two-dimensional planar microstrip antenna [24]. However, tunable intensity of three resonant peaks with high modulation depth simultaneously are barely investigated.
In this paper, we have presented a simple and tunable MA absorber comprised of top graphene strips layer, middle dielectric layer, and a gold substrate. It can concurrently achieve three perfect peaks with absorption of 98.6%, 87.8%, and 98.5% at 2.30 THz, 3.41 THz, and 4.2 THz respectively. To reveal the physical origin of perfect absorption thoroughly, the electric field distribution and induced surface current are explored, and excellent agreement is achieved with each other. Tunable absorption peaks are further examined with external gate voltage and chemical potential. Besides, an on to off switch of the MA is realized when the polarization angle is varying from 0 to 90°. Therefore, it is believed that the adjustable structure may find considerable application in optical switchers, filters, sensors, and detectors. Figure 1(a) is a schematic representation of the proposed graphene MA. The top layer consists of a symmetric graphene strips with a thickness of 1 nm. SiO 2 has a high melting point with low permittivity values of 2.25, making it a suitable candidate as the middle dielectric layer. Its thickness is taken as 7.26 μm. The conductivity of the bottom gold layer is 4.09 × 10 7 S m −1 . The thickness is 0.5 μm. It is thicker than the skin depth of metal in THz. By adjusting the external gate voltage between the substrate and Au electrode, the Fermi energy can be altered in figure 1(b). The concrete parameters are indicated in figure 1(c). To obtain the numerical results, we employ the COMSOL Multiphysics. It is a commercial software which divides a complex system into more manageable chunks, which are then combined into a broader set of equations to model the whole structure [25]. The electric and magnetic field components of each point in the grid space are determined using Maxwell's equations and their solution. All of the electromagnetism characteristics for the simulated space are provided in the space grid based on the continuity of the tangential electric field at each boundary. For the sake of simplicity, the computing domain consists of one unit cell. Additionally, the boundaries along the z direction are subjected to the perfect matched layer, and they are periodic conditions along the x and y directions. On the presumption of perfect absorption, we investigated absorption at eight parameters (d 1 , d 2 , l 1 , l 2 , l 3 , w 1 , w 2 and w 3 ) in figure 1(c) by using the gradient optimization algorithm. During our optimization, we set the other parameters unchanged by tuning one parameter. Finally, the periodicity is optimized as P x = P y = 25 μm. The lengths of parallel strips are l 1 and l 3 of 18.7 μm and 7 μm, respectively. The width w 1 and w 3 are set as 1.7 μm and 1.5 μm. The length of

Design and simulation
the vertical strip l 2 is 1.3 μm and its width w 2 is 4 μm. The vertical graphene strips away from the left and middle of the patterned graphene are d 1 and d 2 of 5.4 μm and 2.65 μm.
With the rapid development of photonic technique and metamaterial technology, the fabrication of our proposed metamaterial is feasible. The uniform Au and silica layer can be sequentially deposited on the silicon substrate by electron beam evaporation, and then the graphene sheet grown by chemical vapor deposition can be transferred onto silica [26]. The graphene pattern can be fabricated by e-beam lithography followed by plasma etching [27]. Finally, the gold electrode is deposited by electron beam evaporation [28]. The fabrication of the proposed device and its influence on metamaterial performance needs further investigation. Then, the absorption of the prepared samples can be tested by THz time-domain spectroscopy system [29].
Graphene with flexible tunability and high confinement of light in terahertz region is modeled as a twodimensional sheet [30,31]. Its relative permittivity is given by , where s w ( ) is the graphene surface conductivity. The conductivity of graphene follows Kubo formula, which includes the contribution of inter-band and intra-band transitions [33,34].
where e stands for the electron charge and ω is the angular frequency. Boltzmann constant is k B , the reduced Planck constant is ÿ, and T is the room temperature of 300 K. The relaxation time, τ is given as where E F stands for the Fermi level, the Fermi velocity is v F , and μ denotes the carrier mobility. The inter-band transitions of polarized electrons excited by magnetic or electric fields in the low THz range is disregarded in accordance with the Pauli exclusion principle [35,36]. Thus, in this paper, graphene is treated as isotropic in our numerical calculation. And the conductivity of isotropic single-layer graphene under the assumption of (E F ? ÿω, E F ? k B T) is simplified as [37,38], Figure 2 shows the real and imaginary parts of graphene conductivity at different Fermi level E F and carrier mobility μ. The real part of conductivity decreases at a higher frequency in the THz in figure 2(a). It keeps a constant with different Fermi energy. Figure 2(b) shows that the imaginary part shrinks as the Fermi energy increases, which can be utilized to adjust the position of the absorption peak. The real part of the graphene conductivity is getting smaller at a higher carrier mobility in figure 2(c). However, the imaginary part is rarely altered at various carrier mobility in figure 2(d). The carrier mobility can be well tuned with the gate voltage or the doping concentration. Temperature dependence of electron transport in graphene and its bilayer have been investigated in [39]. The carrier mobilities can reach up to ∼0.4 and 40 m 2 V −1 s −1 ) for characteristic gate voltage between 5 and 50 V (carrier concentration between 3 and 30 ×10 15 m −2 ). Bolotin et al also reported its mobility is larger than 17 m 2 V −1 s −1 in ultraclean suspended graphene at 5 K [40]. Moreover, by reducing the Coulomb interaction between electrons and charged impurities, they can substantially enhance the mobility of graphene up to 54 m 2 V −1 s −1 in monolayer graphene sandwiched between two layers of a CrOCl insulator [41]. Due to its ability to be efficiently controlled by the Fermi level and carrier mobility, graphene has the much potential applications in optical and optoelectronic devices [42].

Results and discussions
Graphene is a fascinating alternative to metal due to its flexible tunability and low losses in the terahertz region. Figure 3(a) shows the absorption in our designed graphene metamaterials under normal incidence. Fermi level E F is taken as 1.1 eV. Three absorption peaks (peak I, peak II, and peak III) at 2.30 THz, 3.41 THz, and 4.27 THz can be clearly observed in the red line. Their intensity is 98.6%, 87.8%, and 98.5% respectively. The absorption in our design is also examined under the incidence of circularly polarized light in figure 3(a). It can concurrently achieve three peaks with absorption of 74.9%, 96.5%, and 75.4% at 2.30 THz, 3.41 THz and 4.27 THz, respectively. Compared with linearly polarized light, positions of three peaks keep the same but the intensity of peak I and III decrease, while that of peak II increases. In the following discussion, the incident light is linearly polarized by default. The distribution of the electric field is shown in figures 3(b)-(d). It is evident that the electrical field mainly distribute around both corners of the graphene strip in figure 3(b). Peak I is caused by the interaction between neighboring unit cells, indicating two pairs of antiparallel dipoles are formed in the  patterned graphene structure. It is analogous to the bonding modes in a hybridized-molecular system [43]. The electric field is mainly concentrated on the lower corner of short graphene strips at resonant peak II, where two pairs of parallel dipoles exist in figure 3(c). Similarly, electric field mainly concentrates at upper graphene strip at peak III in figure 3(d). The entire structure of graphene strips acts as a dipole-dipole coupling plasmonic resonator [44], and three perfect resonant peaks are induced due to the confinement of the incident electromagnetic waves.
To explore the physical origin of the perfect three-band absorption, we examine the surface current distribution on the upper and lower surface of the middle SiO 2 layer in figure 4. The directions of surface currents on the bottom layer are observed to be antiparallel with those on the top layer. At the frequency of 2.30 THz, the surface currents induced on the top layer are predominantly concentrated on the left and right sides of the top strip. This is compatible with electrical field distribution in figure 3(b). Two pairs of strong antiparallel local current loops are generated at each resonance frequency, revealing the excitation of the magnetic resonance mode [45,46].
To further examine the tunable absorber, the impact of Fermi energy and carrier mobility on the absorption is analyzed in figure 5. Three resonant peaks shift into the high-frequency region as the Fermi energy ranges from 0.9 eV to 1.3 eV. It moves from 2.09 THz to 2.47 THz, 3.12 THz to 3.68 THz, and 3.88 THz to 4.62 THz, specifically. It is well known that graphene behaves as a Drude-type material at lower frequencies, which encourages the generation of surface plasmon in the THz region [47]. The formula k f E c 2 is employed to describe the wave vector of surface plasmon polaritons along the graphene, f r is the resonant frequency and 0 a is the fine structure constant [18]. Thus, the resonant position is inverse to the Fermi energy as f E .
µ / Namely, the resonant frequency is getting larger with an increased Fermi energy, which is consistent with our numerical results in figure 5(a). Additionally, the carrier mobility is taken from 4 to 20 m 2 V −1 s −1 at room temperature to analyze the tunable absorption in figure 5(b). It is discovered that the positions of three peaks keep invariant at different carrier mobility but the intensity decrease at a larger carrier mobility, which can be easily found in equation (4). Therefore, we can get the desired resonant absorption with carefully chosen carrier mobility in the lab. Figure 6 investigates the impact of dielectric layers on the absorption. Three resonant frequencies move into the lower frequency range when the refractive index n rises from 1.3 to 1.7. The resonant absorption change from 2.53 THz to 2.10 THz, 3.76 THz to 3.12 THz, and 4.70 THz to 3.90 THz. The relationship between the resonance frequency and the refractive index can be understood by the equation f LC l n The inductance L of graphene strip is roughly defined as L = 0 m (l·t)/w, where w stands for its width, l is the strip's length, and t is the separation distance between the strip and the gold plate. Two-plate capacitor formula C = l w t 4 r 0 e e ( · )/ is taken to calculate the capacitance C. r e stands for the relative dielectric constant of the middle dielectric layer and 0 e is permittivity in vacuum. Thus, the resonant frequency is roughly expressed as f l n 1 . µ ⋅ Namely, the refractive index is inverse to the resonance frequency. The sensitivity of the refractive index (S) can be defined as the ratio of the frequency variation (Δf) with the deviation of the refractive index (Δn), which can be given as S = Δf/Δn. The ratio of sensitivity to FWHM is referred as the figure of merit (FOM) [49]. The performance of our absorber with other work is shown in table 1. It is evident that our designed absorber has a high FOM of 46.32 and a maximum peak sensitivity of 2000 GHz/RIU. Tunable optical response with different Fermi energy and carrier mobility are elaborately investigated in the above discussion. The effect of various geometrical factors on the absorption is further considered in figure 7.   figure 7(a). It can be well understood with the LC circuit [48]. Namely, the equivalent inductance is inversely proportional to its area. Therefore, blueshift of the resonant frequencies is due to the increased distance d 1 . A linear fit of the resonance position with d 1 is shown in figure 7(b). And the slope for peak I is 0.146, which is higher than that of peak II (0.095) and peak III (0.022). Similarly, three resonance peaks move to lower frequency with larger d 2 in figure 7(c) figure 7(d), which is highly desired in the application of molecule detection. Finally, the absorption at various polarization angles is discussed in figure 8. θ is defined as the angle between the polarization direction and x axis. Obviously, the intensity of three absorption peaks gradually decreases when θ varies from 0 to 90°with an interval of 10°, but their resonant positions remain unchanged. In detail, three perfect absorption peaks of 98.6%, 87.8% and 98.5% at 2.30 THz, 3.41 THz and 4.2 THz absorption can be clearly found while the polarization is along the x-axis. The intensity of the absorptance is reduced to 0.25 when θ is 60°. It almost disappears when θ equals to 90°, namely, the electric field polarization direction is along y axis.  To estimate the extent of modulation of the absorber at a different polarization angle. The absorption amplitude B 0 of the absorption peaks indicates that the absorption loss is 2.4%, 13.2% and 2.5% under the normal incidence. The absorption amplitude B 1 are 0.394%, 0.281% and 0.222% when the polarization angle is 90°. Thus, the modulation degree MD of amplitude is 99.60%, 99.68% and 99.77% according to the equation MD = | B 0 -B 1 |/B 0 [20]. The comparison of MD with other work is shown in table 2. A higher MD is achieved. Therefore, our polarization sensitive absorber with a larger MD at three resonant positions can be easily achieved in a noncontact way, which has a useful application in the field of optical modulation.

Conclusions
To sum up, we have demonstrated a tunable three-band MA with graphene strips. The resonant position and intensity of the transmitted terahertz wave can be dynamically adjusted with different chemical potential, Fermi energy and polarization angle. In addition, the distribution of the electric field and the induced current flow are calculated to examine the physical origin of three perfect absorption. An on to off switch of the absorption is realized when the polarization angle is varying from 0 to 90°. And the modulation degree at three positions is almost approaching 100%. Thus, our work can open up a new way in developing high-performance compact and integrated graphene-based terahertz devices, such as filters, controllable optical switches, sensors and so on.