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Abstract
This work designs a graphene/hBN/Al grating anisotropic hybrid structure. Formed by strong coupling between plasmonic Magnetic polaritons (MPs) in the metal grating and phonon-plasmon polaritons, hybrid hyperbolic phonon-plasmon polaritons in the graphene/hBN film have been excited, resulting in three sharp, high absorption peaks, which are 0.75, 0.97 and 0.97, formed at 5.92 μm, 6.32 μm, and 7.64 μm respectively. The absorption mechanisms have been theoretically analyzed. Local electromagnetic field and power dissipation density are depicted for further elucidating the underlying mechanisms. The different structural parameters and chemical potential, which affect the absorption peak were discussed. These numerical results can provide potential application in the field of optical detection and optoelectronic.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nanostructures have critical applications in the field of military and medical industry. Two dimensional (2D) [1–8] materials, which electrons can only move freely in two dimensions, have drawn extensive attention because of their excellent properties. Different kinds of materials like graphene, hexagonal boron nitride (hBN) and phosphorene, have been proven to achieve great application value in aspects of photovoltaic, biosensing, energy harvesting. The enhancement of light-matter interactions through a plethora of dipole-type polaritonic excitations can be observed in 2D materials [9]. With only a single atomic layer thickness, graphene [10–16] is an excellent two-dimensional plasmon material because of its broad-band absorption, high carrier mobility, and high light transmittance, also widely used in solar energy and photoelectric detection. Still, in the field of photodetection, increasing the absorptivity of graphene is an important prerequisite for the better application of graphene. Hexagonal boron nitride(hBN) [17–22], as a two-dimensional layered structure, is similar to graphene, which has a very smooth surface and unique dielectric constant. And it is often used as a substrate material and dielectric material for high-performance devices. Due to its unique phononic characteristics, hBN has great application of devices in the mid-IR band to terahertz band. In the infrared band, the plasmon polariton characteristic of graphene and the phonon polariton characteristic of hBN have been coupled together to form a graphene/hBN heterostructure with plasmon-phonon polarons.
Recently, a promising way to combine graphene and hBN to study the heterostructure optical properties has been generally reported. Kumar et al. [23] theoretically analysed the plasmon-phonon modes coupled by graphene/hBN heterostructures in the mid-infrared optical properties. They found that the graphene plasmon coupled differently with the phonons of the two Reststrahlen bands owing to their different hyperbolicity. Dai et al. [24] fabricated sample which the graphene covered the surface of hBN and placed it on the substrate of SiO2. The experiment results showed that the hyperbolic plasmon-phonon polaritons possessed particular features, which combined virtues of surface plasmon polaritons in graphene and hyperbolic phonon polaritons in hBN. Wu et al. [25] theoretically demonstrated that the perfect absorption by monolayer graphene and hBN in the infrared region and achieved high absorption in wide frequency and large incidence angles. Zhao et al. [26] proposed a structure: the silver grating covered by hBN, which can improve the anisotropic structure absorption characteristics. Magnetic polaritons (MPs) in metal gratings coupled with hyperbolic phonon polaritons in hBN can create hybrid hyperbolic phonon-plasmon polaritons to enhance its absorption.
This paper proposed a graphene/hBN/Al grating anisotropic hybrid structure, which can excite MP in the grating trench to enhance the absorption of graphene/hBN. Based on Finite Element Method (FEM) and Finite Difference Time Domain Method (FDTD), the absorption of anisotropic hybrid structure and characteristics of electromagnetic field have been calculated and the influence of the structural parameters and chemical potential on the absorption characteristics is studied. Also, the correctness of the numerical results is mutually verified by the above two methods. Both graphene and hBN can be grown in large areas by chemical vapor deposition (CVD) techniques and the silver grating can be fabricated by electron beam lithography and transfer the film to the grating. Also, experimental preparation is technically feasible [27–33]. These numerical results can provide potential application in the fields of optical detection and optoelectronic devices.
2. Method and analysis
The geometrical schematic of the graphene/hBN/Al grating anisotropic hybrid nano-structure is illustrated in Fig. 1. Hybrid structure is composed of the Al grating periodic structure and the graphene/hBN heterostructure. The hybrid structure is periodic along the x direction and infinitely extended in the y direction, where P is period, θ is incidence angle, b is trench width and h is grating height. The thickness of the covered hBN film is denoted as d. In this study, the geometric parameters are P = 5.5 μm, b = 0.4 μm, h = 1.0 μm and d = 50 nm. The aluminum substrate is assumed to be thick enough so that the photons cannot transmit through the substrate, and the optical constant of aluminum can be gained from the Palik [34].
Fig. 1 (a) Schematic of the graphene/hBN/Al grating anisotropic hybrid structure, where the structure the period, incidence angle, trench width, grating height and hBN thickness are P, θ, b, h, d.
The optical conductivity of graphene includes both the interband and intraband (Drude-like) contributions [35–37].
where . Here, σs is the monolayer conductivity, ε0 is the vacuum permittivity, ω is the angular frequency, e is the electron charge, ℏ is the reduced Planck constant, and kB is the Boltzmann constant. In this work, chemical potential μ = 0.3 eV, electron relaxation time τ = 10−13 s, temperature T = 300 K, and graphene thickness Δ = 0.34 nm.The two kinds of infrared Reststrahlen active optical phonon modes: 1) in-plane phonon mode ( = 1370 cm−1, = 1610 cm−1) and 2) out-plane phonon mode ( = 780 cm−1, = 830 cm−1) are connected with hyperbolicity, where the lower frequency Reststrahlen band corresponds to type-I hyperbolicity (ε∥<0, ε⊥>0), and the higher frequency Reststrahlen band corresponds to type-II hyperbolicity (ε∥>0, ε⊥<0). The hBN permittivity is calculated by (5) and (6) [23,26].
where , The other parameters are , , cm−1, cm−1.The electromagnetic responses and the absorptivity of the anisotropic hybrid structure are computed by the commercial Finite Element Method software (COMSOL Multiphysics) and Finite Difference Time Domain software (FDTD Solutions, Lumerical) respectively. The advantage of FDTD is its quickness of calculating Maxwell's equations in a wide band, and FEM can accurately solve Maxwell's equations at each frequency point. Two methods verify each other to prove the accuracy of the results. Periodic boundary conditions are used to simulate an infinite area. The perfectly matched layer (PML) boundary condition was an absorbing tangential wavevector. The x and z directions of the silver grating are meshed 10 nm a node. Graphene and hBN are 5 nodes in the z-direction to ensure the accuracy of the calculation. The absorptance can be calculated by the ratio of the total power dissipation density w(x,y,z) (W/m3) within a volume V (m3) to the incoming power through the exposed surface area A (m2) by (7) [26,38]. Also the power dissipation density of graphene and aluminum can be calculated by (8), meanwhile the hBN is calculated by (9). The results were consistent with previous studies [39–43].
where E is electric density, Einc is incident electric density, Ex, Ey, Ez is x, y, z electric density, respectively.3. Results and discussion
Figure 2 shows the absorption curve and the incident wave is TM. From 4 to 20 μm, as Fig. 2(a) shows, black curve illustrates the absorptivity of hybrid structure for FEM, red curve is the absorptivity of plain grating and blue curve is the absorptivity of graphene/hBN/Al grating anisotropic hybrid structure for FDTD. Figure 2(b) is a partially enlarged absorption curve at 4-9 μm. Figure 2(c) demonstrates the absorption of aluminum, graphene and hBN, which are calculated by FEM.
Fig. 2 Absorptivity spectra as normal incidence for the hybrid structure. The parameters are P = 5.5 μm, b = 0.4 μm, h = 1.0 μm, μ = 0.3 eV and d = 50 nm. (a) Absorptivity of hybrid structure by FEM and FDTD, and plant grating. (b) Partial enlarged detail in Fig. 2 (a) at 5-9μm (c) The absorption of aluminum, graphene, and hBN calculated by FEM.
In this model, the geometric parameters are as follow: P = 5.5 μm, b = 0.4 μm, h = 1.0 μm, μ = 0.3 eV and d = 50 nm. According to the previous study, the plain Al grating can generate excitations of MP in the infrared region [44,45]. The peak absorption of this structure parameter is 0.71 at 5.90μm. When the grating is covered by the graphene/hBN heterostructure, three absorption peaks are excited. And calculated by FEM, the peak absorption of 5.92 μm, 6.32 μm, and 7.64 μm is 0.75, 0.97 and 0.97, respectively. By comparing with the FDTD method, it shows the peak position and the size of the curve basically coincide with FEM. The conclusion can be drawn that the results obtained by two algorithms are the same. It can be seen from the Fig. 2(c) that the absorption peak of the aluminum grating increases from one to three, and also the hBN exhibits two absorption peaks. The hBN film is particular thin, so it is difficult for it to achieve high absorption independently. However, this designed hybrid structure can excite MP resonances leading to three absorption peaks to achieve high absorption.
In order to thoroughly comprehend the absorption mechanism, Fig. 3 demonstrates the magnetic field, Poynting distributions and power dissipation density calculated by FEM. Figure 3(a), 3(b) and 3(c) show that the direction of electric field vector is opposite on the two sides of the grating groove, and then the electric field forms a loop around the groove. This excitation mode is caused by the MP resonance. Figure 3(d), 3(e) and 3(f) illustrated that the enhancement of local power dissipation density along the surface of the grating. The incident energy is absorbed mostly by the graphene/hBN film. The intense enhancement occurs at the interface of hBN and grating and the interface of hBN and graphene above the trough. In Fig. 2, the position where the enhancement of power dissipation density occurs can be explained by the internal mechanism of high absorption in Al grating, graphene and hBN. Thus, these resonances are excited by hybrid hyperbolic phonon-plasmon polaritons formed by strong coupling between plasmonic MP in the metal grating and phonon-plasmon polaritons in the graphene/hBN film.
Fig. 3 Magnetic field (color maps) and Poynting vectors (arrows). (a) 5.92μm. (b) 6.32μm. (c) 7.64μm. Local power dissipation density of the hybrid structure. The first colorbar is overall structure, the second is the interface between graphene and hBN, the third is the interface between the hBN and Al grating. (d) 5.92μm. (e) 6.32μm. (f) 7.64μm.
Figure 4 illustrates that absorption distribution is determined by changing only one parameter when other variables are fixed. The basic parameters are based on Fig. 2. As the hBN thickness increases, the absorption intensity of the hybrid structure remains essentially unchanged and the absorption position slightly redshifts. When the height of the grating increases, the original polarization mode is destroyed and only one peak could remain highly absorbing. However, that peak no longer remains sharp. When changing the period and the width of the hybrid structure’s groove, the position and size of absorption peak mainly contributed by hBN are almost unchanged. It only affects the MP polarization generated by the Al grating.
Fig. 4 Absorptivities for various geometric parameters for normal incidence using the parameters given in Fig. 2 as the base case. (a) hBN thickness. (b) Grating period. (c) Trench width. (d) Period.
Figure 5 shows that the position of absorption peak blueshifts when the chemical potential of graphene increases from 0.2 eV to 0.8 eV. The result indicates that the graphene/hBN film not only can enhance the hybrid structure absorptivity but also can control the position of absorption peak. The chemical potential of graphene can be affected by the external voltage, so it can be dynamically adjusted by externally connecting the graphene electrodes to control the performance of the entire device.
4. Summary
In summary, we have theoretically demonstrated that the graphene/hBN/Al grating anisotropic hybrid structure can enhance the graphene/hBN film absorption. Two numerical methods are applied to verify each other's accuracy. It is found that the MP mode and plasmon-phonon polaritons mode can be excited by metal grating in the groove. Three absorption peaks are excited, the peak absorption of 5.92 μm, 6.32 μm, and 7.64 μm is 0.75, 0.97 and 0.97, respectively. The local electromagnetic field and power dissipation density are depicted to further elucidate the underlying mechanisms. In particular, how different structural parameters affect the absorption peak has been discussed. The graphene/hBN film cannot only enhance the hybrid structure absorptivity but also control the tunable position of The absorption peak. By applying a voltage to both ends of the graphene/hBN/Al grating (conductor/insulator/conductor) structure, the electric potential of the graphene layer can be changed. Further changing its chemical potential makes the dynamic regulation theoretically feasible. These numerical results can facilitate the design of optoelectronic device and provide potential application in the field of optical detection.
Funding
National Natural Science Foundation of China (No. 51522601); Chang Jiang Young Scholars Program of China (No. Q2016186); Program for New Century Excellent Talents in University (No. NCET-13-0173).
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