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Tunable and Anisotropic DualBand Metamaterial Absorber Using Elliptical GrapheneBlack Phosphorus Pairs
Nanoscale Research Letters volume 14, Article number: 346 (2019)
Abstract
We numerically propose a dualband absorber in the infrared region based on periodic elliptical grapheneblack phosphorus (BP) pairs. The proposed absorber exhibits nearunity anisotropic absorption for both resonances due to the combination of graphene and BP. Each of the resonances is independently tunable via adjusting the geometric parameters. Besides, doping levels of graphene and BP can also tune resonant properties effectively. By analyzing the electric field distributions, surface plasmon resonances are observed in the grapheneBP ellipses, contributing to the strong and anisotropic plasmonic response. Moreover, the robustness for incident angles and polarization sensitivity are also illustrated.
Introduction
Graphene is a twodimensional material with carbon atoms arranged in a honeycomb lattice [1, 2]. Various graphenebased photonic devices have been developed in the recent years due to their ultracompact size and unique lightgraphene interaction [3,4,5,6]. As one of its most significant applications, metamaterial absorbers based on graphene have attracted burgeoning amount of interest due to their strong and tunable plasmonic response [7,8,9,10]. However, several applications that require high onoff ratio are restricted due to the zero or nearzero band gap of graphene [11]. As an alternative twodimensional material, black phosphorus (BP), a monolayer of phosphorus atoms arranged in a hexagonal lattice with a puckered structure [12], has also received a surge of research interest recently. It possesses exceptional optical and electronic properties, such as inplane anisotropy, thicknessdependent tunable band gap [13], and high carrier density and mobility [14]. Over the past few years, in the infrared region, researchers have investigated numerous structures to enhance the lightBP interaction strength in the metamaterial based on BP [15,16,17]. Nevertheless, the plasmonic resonance of BPbased absorber is hardly to be tuned flexibly and effectively, and they normally suffer from relatively low absorption rate with moderate doping level. This is attributed to the fact that the resonance strength in monolayer BP is rather weak, limiting its anisotropic potentials. Thus, grapheneBPbased plasmonic absorbers have been proposed utilizing the hybridization of graphene and BP to achieve strong and anisotropic plasmonic absorption [18,19,20]. However, the previous reported grapheneBPbased absorbers generally require relatively complicated fabrication technique or possess single absorption band, impeding their further applications for imaging, biosensing, and communication systems.
In our work, an anisotropic dualband infrared absorber is numerically proposed using periodic elliptical grapheneBP pairs, which is ease of fabrication. The independent tunability of resonance by geometric size and doping level is demonstrated. Electric field distributions are plotted to reveal the physical mechanism. The incident angle tolerance and polarization sensitivity are also illustrated.
Methods
The proposed absorber is made up of transverse and longitudinal elliptical grapheneBP pairs deposited on a SiO_{2} layer as shown in Fig. 1. A hexagonal boron nitride (hBN) layer is inserted between monolayer graphene and BP as an insulating spacer to prevent carrier transport between them and guarantee high carrier mobility. The parameters of SiO_{2} and hBN are obtained from Ref. 21 and Ref. 22 respectively. The simulations are carried out by COMSOL Multiphysics to investigate the dualband properties, which is based on finite element method (FEM) in the frequency domain. We apply Floquet periodicity as the boundary conditions in both x and y directions. A port with infrared wave excitation is set upon the top surface of the computational domain, while perfect electric conductor (PEC) boundary condition is set on the bottom surface. Tetrahedral meshes with usercontroller mesh density are applied for the entire domain.
In the simulation, both graphene and BP are treated as twodimensional surface with surface conductivities instead of bulk materials with permittivity tensors. This assumption solves the problems of thickness definition for ultrathin materials and low computational efficiency [23].
To describe the surface conductivity of graphene σ(ω), we use the wellknown Kubo formulas as below [24]:
According to Eq. 1, σ(ω) consists of the intraband and interband counterparts, namely σ_{intra} and σ_{inter}. ω is the radian frequency, μ_{c} is the chemical potential, Г is the scattering rate, and T is the Kelvin temperature. ħ, e, ξ, and k_{B} are the reduced Planck constant, electron charge, electron energy, and Boltzmann constant, respectively.
In the infrared region, since the incident photon can hardly excite the interband transition, the lightgraphene interaction is dominated by the intraband transition. Particularly, when μ_{c} ≫ k_{B}T, Kubo formulas can be further simplified to Eq. 5:
Thus, the surface conductivity of graphene is dependent on the values of ω, Г, and μ_{c}. Here, Г is assumed as 0.3 meV and μ_{c} is assumed to be 0.7 eV according to the previous work [25, 26].
On the other hand, we calculate the surface conductivity σ_{j} of BP with a simple semiclassical Drude model [27]:
where n_{s} is the carrier density relating with the doping level. We choose n_{s} = 1.9 × 10^{13} cm^{−2} and Г_{BP} = 10 meV according to the previous reference [16]. j is the concerned direction, so σ_{x} and σ_{y} are determined by the electron mass along x and ydirection, respectively. m_{x} and m_{y} can be further calculated by:
where m_{0} is the standard electron mass, and Δ and a are the band gap and scale length for BP monolayer, respectively. By substituting Eqs. 10–12 into Eq. 8 and Eq. 9, one can obtain the electron mass along armchair (x) and zigzag (y) direction. The discrepancy between them contributes to the anisotropic surface conductivity of BP.
Results and Discussion
To illustrate the anisotropic absorption characteristic of the proposed absorber, we first simulate and compare the absorption spectra with individual graphene layer, individual BP layer, and grapheneBP pairs. As can been observed in Fig. 2a, the plasmonic response of graphene is isotropic with two obvious absorption peaks at 9.9 μm and 15.4 μm, independent on the polarization. On the other hand, although the plasmon resonance of BP is anisotropic, its strength is quite weak for either TE (< 12.7%) or TM (< 0.7%) incidence. By combining the advantages of graphene and BP, grapheneBP pairs exhibit both strong and anisotropic plasmonic responses. For TE incidence, the two absorption peaks are located at 8.8 μm and 14.1 μm, with absorption rates larger than 90%. For TM incidence, the wavelengths of maximum absorption are shifted to 9.5 μm and 15.4 μm, respectively. The polarization extinction ratio can be defined as PER = 10 × log(R_{1}/R_{0}), where R_{1} and R_{0} denote the reflectance (R = 1A, A represents the absorbance) of different polarizations at the same wavelength, then the maximum PER of each resonance can reach up to 23 dB and 25 dB at λ = 9.5 μm and λ = 14.1 μm, respectively. Therefore, the proposed absorber can be utilized as a dualband reflective polarizer with high performance.
We next analyze the absorption spectra with different geometric configurations to demonstrate the tunable dualband absorption property in Fig. 2b–d. In Fig. 2b, the first absorption peaks have redshifts as a increases from 42 to 52 nm for both polarizations, while second resonant frequencies are almost unchanged. On the other hand, as shown in Fig. 2c, by increasing the long axis length b, the second resonances are redshifted as well, while the first absorption peaks remain constant for TE and TM polarization. Therefore, the dual absorption peaks can be tuned independently by varying the corresponding axis length in the elliptical grapheneBP pairs. Moreover, the thickness of dielectric layer also plays a critical role in the performance for the proposed device, which acts as a FabryPerot resonator formed by the grapheneBP metasurface and the PEC substrate. Thus, the absorption spectra with different t_{d} are plotted in Fig. 2d. As t_{d} increases from 0.95 to 1.75 μm, the first absorption peaks for TE and TM polarization have a dramatic drop, while the second peaks increase at first then decrease sharply. As a consequence, there is an optimal thickness t_{d} that maximizes the dual absorption peaks of the proposed absorber.
In order to elucidate the physical insight, we further reveal the electric field intensity distributions at different wavelengths in Fig. 3. For TE incidence, the electric field is in the armchair (x) direction. At the first peak (λ = 8.8 μm), the incident infrared light can excite electrons in graphene and BP to oscillate in the transverse direction, leading to the concentration of electric field at the short axis ends of the longitudinal ellipse as shown in Fig. 3a. At λ = 14.1 μm, the localized electric field is enhanced at the long axis ends of the transverse ellipse. On the other hand, TM incidence with electric field in the zigzag (y) direction can excite electrons to vibrate along the longitudinal direction at the absorption peak of 9.5 μm, leading to concentrated field distributions at the short axis ends of the transverse ellipse. Besides, at λ = 15.4 μm, the enhancement of electric field is focused at the long axis ends of the longitudinal ellipse. Therefore, the resonance wavelengths are directly related to the finite oscillation length of the induced dipoles in both transverse and longitudinal elliptical graphene and BP pairs.
One can tune the anisotropic dualband absorption performance effectively by varying the geometric dimensions as demonstrated in Fig. 2b–d. Meanwhile, the surface conductivities of graphene and BP can also be manipulated by varying μ_{c} and n_{s} according to graphene and BP model formulas as mentioned above. μ_{c} and n_{s} represent the doping level of graphene and BP that can be altered after geometric fabrication. Thus, performances of the proposed absorber with different μ_{c} and n_{s} are depicted in Fig. 4. Considering the practical situation, μ_{c} is chosen between 0.4 and 0.8 eV from the previous work verified by experiments [28]. In the previous reported work [29], the maximum theoretical value for n_{s} of BP was demonstrated to be 2.6 × 10^{14} cm^{−2}, so a moderate n_{s} is chosen between 10^{13} cm^{−2} and 10^{14} cm^{−2} in the simulation. In Fig. 4a, when μ_{c} = 0.4 eV, the first absorption peak is located at 10.9 μm and the second one is located at 17.1 μm. As μ_{c} increases to 0.8 eV, the two resonant wavelengths are blueshifted to 8.4 μm and 13.4 μm. Similarly for TM polarization, the dual absorption peaks are blueshifted from 12.4 and 19.8 μm to 8.9 and 14.4 μm, respectively, with μ_{c} increasing from 0.4 to 0.8 eV as shown in Fig. 4b. For individual patterned BP, the resonance wavelength λ_{p} can be calculated as \( {\lambda}_p\propto \sqrt{L/{n}_s} \), where L is the effective oscillation length [27]. Thus, if L is fixed, the absorption spectra exhibit an obvious blueshift as n_{s} increases for TE polarization as plotted in Fig. 4c. For TM polarization, the absorption peaks are also slightly blueshifted as n_{s} increases from 10^{13} cm^{−2} to 10^{14} cm^{−2} as demonstrated in Fig. 4d.
In the practical applications, tolerance of wide incident angles is preferred for infrared absorbers. Therefore, absorption spectra under oblique incidences are elaborated. In Fig. 5a, it is observed that, for TE polarization, the first absorption peak remains larger than 80% when θ increases to 52°, while the second absorption peak maintains above 80% even when θ increases to 80°. When θ > 46°, the second resonant wavelength is redshifted gradually as θ becomes larger. For TM incidence, when θ is less than 62°, the absorption rate at the first peak maintains larger than 90%, while the resonant wavelength keeps constant at λ = 9.5 μm as shown in Fig. 5b. Besides, for the second resonance, the peak absorption remains larger than 80% with θ up to 60°, then drops slightly with the increase of θ. The excellent angular stability originates from the common feature of FabryPerot resonators, which are robust for oblique incident angles [30].
Absorption spectra under normal incidence with different polarization angles φ are presented in Fig. 5c to investigate the polarization dependence of the proposed absorber. We assume the polarization angle of TE polarization to be 0°. One can see from Fig. 5c that, as φ increases from 0 to 90°, the absorption spectrum turns out to be the same as the TM polarization in Fig. 2a. When 0° < φ < 90°, the incidence will excite electrons in BP to oscillate in both armchair and zigzag directions due to its x and y components of the incident electric field. Consequently, surface plasmon resonances can be induced simultaneously in armchair and zigzag directions of BP.
Conclusions
In conclusions, we have proposed an anisotropic dualband infrared absorber consisting of periodic transverse and longitudinal grapheneBP ellipses. The maximum PER at each resonance can reach up to 23 dB and 25 dB. The dual anisotropic resonances are attributed to the induced electric dipoles located at the ends of short and long axes. By adjusting the lengths of short axis and long axis, the first and second absorption peaks can be independently tuned, respectively. Moreover, the resonant absorption bands can also be tuned by changing the corresponding doping level of graphene and BP. Besides, high absorption rates at both peaks can be achieved under oblique incidence for any polarization. The proposed absorber can be utilized as a tunable reflective polarizer and novel infrared sensor.
Availability of Data and Materials
All data are fully available without restriction.
Abbreviations
 BP:

Black phosphorus
 FEM:

Finite element method
 hBN:

Hexagonal boron nitride
 PEC:

Perfect electric conductor
 TE:

Transverse electric
 TM:

Transverse magnetic
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Funding
This work was supported by the National Natural Science Foundation of China (51702271), the Young and Middleaged Teachers Education and Scientific Research Foundation of Fujian Province, China (JAT170407), and the High Level Talent Project of Xiamen University of Technology, China (YKJ16016R).
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CY and LS conceived the idea and wrote the manuscript. ZY and WX undertook the simulations. XK analyzed the data. GR and JW supervised the project. All authors read and approved the final manuscript.
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Cai, Y., Li, S., Zhou, Y. et al. Tunable and Anisotropic DualBand Metamaterial Absorber Using Elliptical GrapheneBlack Phosphorus Pairs. Nanoscale Res Lett 14, 346 (2019). https://doi.org/10.1186/s1167101931829
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Keywords
 Metamaterial absorber
 Twodimensional material
 Dualband absorber
 Surface plasmons