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Abstract
Two-dimensional (2D) materials, which have attracted attention due to intriguing optical properties, form a promising building block in optical and photonic devices. This paper numerically investigates a tunable and anisotropic perfect absorber in a graphene-black phosphorus (BP) nanoblock array structure. The suggested structure exhibits polarization-dependent anisotropic absorption in the mid-infrared, with maximum absorption of 99.73% for x-polarization and 53.47% for y-polarization, as determined by finite-difference time-domain FDTD analysis. Moreover, geometrical parameters and graphene and BP doping amounts are possibly employed to tailor the absorption spectra of the structures. Hence, our results have the potential in the design of polarization-selective and tunable high-performance devices in the mid-infrared, such as polarizers, modulators, and photodetectors.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metamaterials, artificial composite materials composed of periodic arrangements of unitary structures, are capable of exhibiting extraordinary physical properties not possessed by natural materials and enabling researchers to adjust their permittivity ($\varepsilon $) and permeability ($\mu $) through physical structure design to achieve new properties that break the limits of natural laws and obtain extraordinary physical properties [1,2]. Early research on metamaterials was dominated by negative dielectric materials and negative magnetic permeability materials, while recent years, hyperbolic metamaterials and near-zero materials have gradually attracted attention as typical representatives of metamaterials. $\varepsilon $-near-zero (ENZ) [3,4] materials have attracted widespread attention from researchers due to their unique properties exhibited by their dielectric constants converging to zero in specific frequency bands in the fields of wide-angle perfect absorption [5], near-perfect bending waveguides [6], just to name a few. With the further of the research on metamaterial, Weyl semimetals [7,8] were added to artificial materials with unconventional electromagnetic properties, demonstrating that ENZ response could be achieved through weyl cone tilt, chemical potential, and electromagnetic wave frequency [9,10]. There are uncoordinated limitations of the ENZ-based metamaterials which are not existing in the emerging two-dimensional (2D) materials, such as graphene and black phosphorus (BP).
Since the first separation of single atomic layer thickness of few-layer graphene in an approach of mechanical exfoliation method suggested by Geim et al. at the University of Manchester in 2004 [11], researchers have found that graphene represents a 2D material with unique optoelectronic effects [12], such as zero band gap, large surface area, ultra-high carrier mobility. Most importantly, graphene can regulate the Fermi level by doping and applying bias voltage gates, wide application in sensors [13], modulators [14], waveguides [15] and photodetectors [16] and absorbers [17–20], and so forth. Researchers found that structures fusing artificial metamaterial with natural 2D materials have greatly enhanced the performance of absorbers; graphene supports surface plasmon over a wide wavelength range from infrared to terahertz (THz) [21–23]. Therefore, a number of approaches have been introduced in this study. Piper et al. [24] proposed a structure composed of graphene and photonic crystal slabs, which achieved complete absorption of near-infrared and visible light at critical coupling. Ke et al. [25] observed a double-layer cross-shaped graphene array structure to realize wavelength-tunable improved infrared absorption materials. Masyukv et al. [26] demonstrated an ability of intercalated few-layer graphene for the development of the optically tunable absorption metasurface. The introduction of graphene in the above mentioned devices increases the tunability of the device, but the zero band gap of graphene limits its application.
BP, with its unique folded structure and in-plane anisotropy, is a direct bandgap semiconductor material from monolayer to bulk. Its direct bandgap is tuned with thickness covering the visible to infrared band from bulk (0.3 eV) to monolayer (2 eV), filling the gap of bandgap of graphene and transition metal dichloride in this band [27]. In addition, the better compatibility of BP with silicon, coupled with the fast carrier migration of BP, displays great potential for anisotropic light absorption, massive outstanding achievements related to this have emerged. The research on the BP-based perfect absorbers usually can be divided into two categories. One is about enhancing the coupling effect of light through the design of material and structure, thus to achieve perfect absorption from infrared to THZ; Liu et al. investigated a structure by monolayer BP sandwiched between polymer (PDMS) and dielectric material (MgF2) with low index contrast [28]. Xiao et al. suggested a BP/dielectric stacking structure [29]. Wang et al. showed the structure of BP sandwiched between dielectric layers [30]. Dong et al. presented a structure consisting of a metallic film, a spacer with a single layer of BP inside, and distributed Bragg reflector [31]. The other is the theoretical demonstration of the perfect absorption properties of anisotropic BP in THZ/infrared, examples can be seen in Alidoust et al. who proposed to control the variation of in-plane strain in BP to achieve perfect absorption. [32,33]. Wang et al. achieved coherent complete absorption in the THz/infrared region [34]. These studies show that BP is widely used in plasma absorption, however, the weak interaction between BP and light remains a challenge for practical applications. Recently, structures combining graphene and BP to enhance the optical response were reported by Nong et al. [35] who investigated the anisotropic absorption properties of graphene surface plasmon and BP local surface plasmon under strong coupling. Cai et al. proposed a multilayer graphene-BP structure sandwiched between dielectric layers to achieve broadband absorption [36]. Most of the above-mentioned cases, the strong anisotropic plasmonic absorption is numerically demonstrated in graphene-BP hybrid structures, however, the mentioned earlier introduction of multilayer structure may increase the complexity of the device fabrication process. Therefore, the device of a simple and more tunable absorber structure by graphene and BP has a wider potentiality and possibility in the future in biology, medicine, communication and imaging.
This study suggests a graphene-BP nanoblock array structure to combine the advantages of graphene and BP supporting surface plasmon excitations with an absorber; and that structure outperforms graphene and BP respectively, demonstrating strong and anisotropic localized surface plasmon resonances. The absorption spectra of x- (transverse magnetic,TM) and y-polarization (transverse electric,TE) were simulated via finite-difference time-domain (FDTD), with maximum absorption of 99.73% and 53.47% respectively. Furthermore, it has been discovered that the structural geometry parameters and doping concentration can efficiently tune the absorption spectra. As a result, our proposed structure has good anisotropic absorption performance and dynamic tunability, providing a new strategy for achieving polarization-dependent anisotropic perfect absorption.
2. Structure and theory
The proposed structure is depicted in Fig. 1(a). It comprises graphene and BP nanosheets separated by a dielectric layer to form a nanoblock, then stacked from top to bottom with the nanoblock, substrate, and gold mirror. In order to facilitate the adjustment of the electron doping concentration of BP here, we designed the intermediate dielectric layer to be of the same size as graphene BP. To investigate the system's absorption properties, numerical simulations are performed using the FDTD method, which utilizes periodic boundary conditions in the x- and y- directions and a perfectly matched layer as the absorption boundary in the z-direction. The plane wave incident on the upper surface of the structure under the action of the magnetic field (${H_y}$) and electric field (${E_y}$) perpendicular to the x-z plane, that is, TM and TE waves. In this paper, the TM wave is defined as x-polarization and the TE wave is defined as y-polarization, the absorption can be expressed as $A = 1 - T - R$, where the transmittance $T = |{S_{21}}{|^2}$, reflectance $R = {|{{S_{11}}} |^2}$, ${S_{11}}$ and ${S_{21}}$ are the scattering parameters related to the reflection and transmission coefficients. Due to the bottom gold mirror effectively suppresses the outgoing wave, the absorption rate can be simplified to A = 1-R.
Fig. 1. (a) Schematic diagram of the graphene and BP nanoblock arrays. (b) x-z cross-section (x-polarization) of the structure. (c) y-z cross-section (y-polarization) of the structure. Total absorption simulated spectra with (d) BP, (e) graphene, and (f) graphene-BP nanoblock, polarization by electric fields along x and y directions in the presence of electron doping ${n_s} = 5 \times {10^{13}}c{m^{ - 2}}$ (${E_F} = 0.5\,eV$), the corresponding structures shown in the inset.
Figures 1(b) and 1(c) show the schematic diagrams and structural parameters of our designed x-z cross-section and y-z cross-section for separating graphene and BP with a dielectric layer of width $W = 150nm$, length $L = 200nm$, and thickness ${t_m} = 30nm$. The refractive index of the dielectric layer is fixed at 1.5. The same size of graphene and BP nanosheets are placed on their upper and lower surfaces, respectively. The nanoblocks composed of graphene and BP have periods of ${P_x} = 300nm$ and ${P_y} = 400nm$ in the x- and y-direction, respectively. The substrate is non-dispersive and has a fixed refractive index of 1.7. The structure may be achievable with existing technologies, substrate and dielectric spacers can be fabricated by using electron beam lithography, BP can be obtained by mechanical exfoliation or chemical methods, and single-layer graphene can be grown on copper foil using chemical vapor deposition (CVD) and then transferred to the dielectric layer. In the simulation, the thicknesses of BP and graphene are set to 1 nm.
The surface conductivity of graphene can be measured directly [37,38]. The conductivity model of graphene is described by the kubo equation according to the intraband and interband contributions as [39]:
For the terahertz and infrared regions [41,42], the interband part of graphene is negligible compared to the intraband part, so graphene can be expressed with a drude-like surface conductivity as [43]:
The surface conductivity of monolayer BP can be expressed by the semiclassical Drude model [21] as follows:
For monolayer BP [21], we have $\gamma = \frac{{4a}}{\pi }eVm$, $\Delta = 2eV$, ${\eta _c} = \frac{{{\hbar ^2}}}{{0.4{\textrm{m}_0}}}$, ${\upsilon _c} = \frac{{{\hbar ^2}}}{{1.4{m_0}}}$, $\eta = 10meV$ to describe the relaxation rate, $a = 0.223nm$ as the width of the Brillouin zone. We choose electron doping ${n_s} = 5 \times {10^{13}}c{m^{ - 2}}$, ${E_F} = 0.5eV$. These values are experimentally confirmed to be achievable [12,44,45].
The dielectric function for the thin film is (with 2D conductivity) [46]:
The relative permittivity of graphene [41] and BP [46] can be 1 and 5.76, ${\sigma _j}$ is the two-dimensional conductivity, the free-space permittivity ${\varepsilon _0} = 8.854 \times {10^{ - 12}}F \cdot {m^{ - 1}}$, t is the thickness of graphene and BP, which are defined as 1 nm in this paper.
To investigate the anisotropic absorption features of the proposed structure, we first compared its optical response to that of BP, graphene, and graphene-BP nanoblock while computing the polarization of the electric field along the x- (TM) and y-direction (TE). The absorption spectra are plotted in Figs. 1(d)–1(f), with the corresponding structures shown in the insets. As shown in Fig. 1(d), the maximum absorption at x-polarization is 7.63%. In contrast, the absorption intensity at y-polarization is nearly zero, owing to the weak interaction between the light and the monolayer BP sheet and the different absorption due to the anisotropy of the monolayer BP molecular structure. Figure 1(e) demonstrates that the monolayer graphene nanoblocks have anisotropy at both x- and y-polarizations, consistent with the prior results obtained by Freitag et al. [47]. As shown in Fig. 1(f), the combination of graphene and BP exhibits a strong and anisotropic plasmonic resonance, with the absorption of 99.73% at $10.78\mu m$ x-polarization and a maximum of 53.47% at $13.83\mu m$ y-polarization. In fact, when the incident light irradiates the structure with x-polarization, the local surface plasmon structure of graphene is excited and resonance occurs when the in-plane wave vector of the graphene surface plasmon wave matches the diffraction order wave vector scattered by the BP film. The superstructure forms a similar Fabry-Perot (F-P) resonance cavity with the gold mirror, where the local surface plasmon resonance of graphene-BP interacts with the F-P cavity effect of the substrate. Perfect absorption is achieved under critical coupling conditions. This strong and anisotropic resonance facilitates our study of the mid-infrared plasma.
3. Results and analysis
The effect of structural parameters on absorption properties is analyzed further in this section by modeling the structure of graphene BP nanoblocks with different W, L and $P$ values. Figure 2 shows the absorption spectra of the two polarizations when W and L are varied, keeping ${P_x} = 300nm$ and ${P_y} = 400nm$. In Fig. 2(a), we plot the absorption spectra for the nanoblock $W$ variations at different polarizations. Due to the anisotropy of the monolayer BP molecular structure and the non-quadruple rotational symmetry of the structure, the optical losses of x- and y-polarization show significant differences. It can be seen that with the increase of W, the absorption peak position of x-polarization shows a redshift, and the absorption peak first increases and then decreases. The redshift of the absorption peak can be considered as an increase in the effective length of the carrier vibration inside the graphene- BP, while the change in the absorption intensity indicates the process of the system from undercoupling, critical coupling, and then overcoupling [24], on the other hand, the optimal $W$ range of the device is $160\mu m$-$180\mu m$ when the critical coupling is reached to achieve perfect absorption. While in the case of y-polarization, the weaker the coupling between nanoblocks as the $W$ decreases, the peak absorption intensity increases monotonically with the increase of W. The absorption spectra of nanoblock $L$ with wavelength are shown in Fig. 2(b), where the x-polarization shows a slight blue shift with increasing $L$, but the absorption peak remains unchanged, the y-polarization shows an increasing and then decreasing absorption characteristic, which is the opposite of the polarization when changing the W. These findings indicate that we can modify the structural parameters of the nanoblocks more easily to tune the absorption spectra.
Fig. 2. Absorption spectra of graphene-BP nanoblock with different (a) $W$ and (b) $L$ in x- and y-polarization.
In addition, the effect of the period on the absorption properties was investigated under different polarization cases with a fixed graphene BP nanoblock $W = 150nm$ and $L = 200nm$, as shown in Figs. 3(a) and 3(b). At x-polarization, the interaction between neighboring nanoblocks gradually weakens as the ${P_x}$ increases. The absorption peak moves to shorter wavelengths, and the absorption peak width gradually becomes smaller. However, the absorption intensity is unchanged. However, the absorption peak intensity gradually decreases with increasing ${P_x}$ at y-polarization. The weakening of the absorption peak intensity is related to the filling factor of the graphene- BP nanoblocks, which becomes smaller with an increasing period, so the electric field intensity inside the graphene-BP nanoblocks is significantly weakened, and therefore the absorption peak intensity is weakened [46]. The absorption spectra with ${P_y}$ are shown in Fig. 3(c) and 3(d). The absorption peak of x-polarization has a slight red shift from $250nm$ to $300nm$, the position of the absorption peak remains the same after greater than $300nm$. While the y-polarization has almost no absorption below $300nm$, above $300nm$ and x-polarization exhibit the same properties, which proves the tunability of our designed structure in terms of period. In addition, the absorption of y-polarization is generally lower, which may be due to the more significant optical loss of the BP layer in y-polarization compared to x-polarization.
Fig. 3. Absorption spectra of two adjacent graphene-BP nanoblock periods (a) ${P_x}$, (c) ${P_y}$ changed in x-polarization and periods (b) ${P_x}$, (d) ${P_y}$ changed in y-polarization.
Next, we investigated the effect of the thickness (${t_m}$) of the dielectric layer between graphene and BP on the absorption spectra. Figure 4 shows the absorption spectra of the two polarizations when the ${t_m}$ varies in the range of $10\sim30\,nm$. When ${t_m} = 10nm$, the absorption peaks of x- and y-polarization are 92.2% and 40.2%, respectively. With the increase of ${t_m}$, the absorption peaks of the two polarizations remain the same. The inset of Fig. 4 plots the electric field distribution at the resonant wavelength at x-polarization. From the electric field distribution, it is known that infrared incidence can excite local surface plasmon resonance in a finite-size graphene-BP [46]. At ${t_m} = 20nm$, a strong local surface plasmon resonance is exhibited between graphene and BP, this local surface plasmon resonance is gradually transferred to the upper graphene layer as ${t_m}$ increases, because the surface conductivity of graphene in the frequency range is more significant than that of BP, the loss of graphene is more vital than that of BP, there is almost no electric field present in the BP layer at ${t_m} = 30nm$.
Fig. 4. Absorption spectra for (a) ${t_m}\textrm{ = }10\,nm$, (b) ${t_m}\textrm{ = }15\,nm$, (c) ${t_m}\textrm{ = }20\,nm$, (d) ${t_m}\textrm{ = }30\,nm$, when polarization along x and y-directions. Inset shows the electric field distribution at the resonant wavelength at x-polarization, where $W = 150\,nm$, $L = 200\,nm$, ${P_x} = 300\,nm$ and ${P_y} = 400\,nm$.
We may efficiently alter the absorption spectra using the above approach by adjusting the geometric dimensions. Furthermore, the surface conductivity of graphene and BP can be changed by ${E_F}$ and ${n_s}$ using the model equation of Eq. (5) for graphene and BP. The plasmon frequency varies with the carrier concentration, which is characteristic of massless Dirac electrons [48,49]. The Fermi energy level of graphene can be dynamically changed by applying an external gate voltage [50], the carrier concentration of the material can be changed by applying a bias voltage [51] or electron doping [45] to BP for tunable purposes. Therefore, we can manipulate the performance of the designed absorber by ${E_F}$ and ${n_s}$ as shown in Fig. 5. We choose ${E_F}$ between 0.4 eV and 0.8 eV, which has been experimentally demonstrated previously [19]. The maximum theoretical carrier density was shown to be ${n_s} = 2.6 \times {10^{14}}c{m^{ - 2}}$ [52,53], we choose ${n_s}$ to be between ${10^{13}}c{m^{ - 2}}$ to ${10^{14}}c{m^{ - 2}}$. As shown in Figs. 5(a) and 5(b), the absorption spectra of both x- and y-polarization exhibit a significant blue shift, with the x-polarized absorption peak blue-shifted from 11.63$\mu m$ to 9.58$\mu m$ and the y-polarization absorption peak blue-shifted from 14.23$\mu m$ to 13.51$\mu m$. In fact, for monolayer BP, the resonance wavelength ${\lambda _p}\mathrm{\ \propto }\sqrt {{W / {{n_s}}}} $, $W$ is the width of the nanoblock [21]. Therefore, when W is kept constant, the resonance wavelength decreases with the increase of ${n_s}$. On the other hand, a similar property is exhibited as shown in Figs. 5(c) and 5(d) with the increase of ${E_F}$. The absorption peak at x-polarization changes from 12.03$\mu m$ to 8.97$\mu m$ and y-polarization from 15.53$\mu m$ to 11.17$\mu m$, which can be explained by the higher conductivity of graphene with the increase of ${E_F}$, which leads to the loss and absorption of electromagnetic energy.
Fig. 5. Absorption spectra as doping levels in x and y polarization: (a) and (b) for different ${n_s}$ of BP, (c) and (d) for different ${E_F}$ of graphene, where $W = 150\,nm$, $L = 200\,nm$, ${P_x} = 300\,nm$, ${P_y} = 400\,nm$, and ${t_m} = 30\,nm$.
4. Conclusion
In summary, we propose a graphene-BP nanoblock array structure, demonstrated by FDTD calculations, which combines the advantages of graphene and BP localized surface plasmon and exhibits strong and anisotropic perfect absorption in two different polarization directions, reaching a maximum absorption of 99.73% for x-polarization and 53.47% for y-polarization. Furthermore, we found that changing the geometrical parameters of the structure and the doping concentration can modulate the absorption spectra, and the electric field distribution was analyzed by varying the thickness of the dielectric layer in order to better understand the absorption mechanism in the structure. With high efficiency absorption, the remarkable anisotropy, flexible tunability, and easy-to-fabricate advantages, the proposed structure shows promising prospects in the design of polarization-selective and tunable high-performance devices in the mid-infrared, such as polarizers, modulators and photodetectors.
Funding
National Natural Science Foundation of China (61765004, 62165004); the Innovation Project of Guangxi Graduate Education (2021YCXS040, 2022YCXS047).
Acknowledgments
We thank the National Natural Science Foundation of China (Grant no., 62165004, 61765004), and the Innovation Project of Guangxi Graduate Education (Grant no. 2021YCXS040, 2020YC) for partial funding.
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.
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