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Abstract
We report a polarization-insensitive dual-band tunable graphene absorber in the terahertz region, which is composed of a top patterned graphene and a gold ground plane, separated by a silicon dielectric layer. Numerical simulations verify the amplitude of the absorption peaks have reached 98.6% and 98.2% at 0.512THz and 1.467THz, respectively. It exhibits excellent performances with high absorptivity and wide incident angles for both transverse electric (TE) and transverse magnetic (TM) polarizations. The frequency and amplitude of the absorption peaks can be regulated by chemical potential of graphene via bias voltage. These characteristics provide great potential applications in imaging, detecting, and sensing in the terahertz regime.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz wave absorbers have attracted a great deal of attention due to their potential applications in imaging, detecting, and sensing [1–7]. In the last decade, a variety of terahertz wave absorbers have been demonstrated based on matematerial with one band, multi-band, and broad-band [8–10]. For example, Landy et al. [11] proposed a polarization-insensitive terahertz absorber in 2009. Ma et al. [12] designed a metamaterial absorber with dual-band frequencies. Grant et al. [13] reported a terahertz broadband absorber with a polarization insensitive. However, most of the reported absorbers can only operate at a finite range of terahertz wave frequencies or a certain terahertz wave frequency. The dynamic tenability of these terahertz wave absorbers can only controlled by altering of the geometries. In fact, robust tunable terahertz absorbers are important for many of the practical applications. Recently, a kind of two-dimensional material, graphene has attracted remarkable attention due to gate voltage tenability of its surface conductivity [14]. Different tuning schemes for terahertz wave devices based on graphene have been demonstrated [15–16]. It becomes a good candidate scheme to design dynamically tunable terahertz absorbers. More recently, tunable graphene-based terahertz absorbers were investigated. Such as, Andrei et al. demonstrated a graphene-based perfect absorber by changing the graphene surface conductivity [17]. In 2014, Zhang et al. integrated cross-shaped metallic resonator with graphene to realize a polarization independent absorber [18]. Amin et al. created a ultra-broadband graphene absorber by superimposed multilayer patterned graphene layer [19]. Su et al. used multilayer graphene/MgO2 stacked on metallic copper to produce dual-band resonance frequency [20]. Despite great progress have been made, it is still a challenge to obtain high efficiency and wide incidence angle terahertz absorber in a simple structure.
In this paper, we have demonstrated a new design of a flexible dual-band all-graphene-dielectric terahertz absorber with a crossing structure and combination of the ring with four-split shape. The unit cell of the studied graphene absorber composed of a graphene pattern separated by a dielectric silicon located upon a gold ground plane. We have clarified the absorption mechanism and analyzed absorption characteristics of the proposed graphene absorber by various size parameters of graphene pattern, substrate thickness, and incident angle of terahertz waves. The simulation results indicate that the amplitude of the absorption peaks reach 0.986 and 0.980 at 0.512THz and 1.467THz, respectively. The proposed absorber exhibits dual-band absorption, high absorptivity, polarization-insensitivity and wide incident angles. Besides that, by varying the bias voltages, the terahertz absorptivity can be tuned from 68.3% to 98.6%. In addition, graphene atomic thickness can be easily implemented into a chip-scale integrated circuit. Such an absorber in this work show promising potential applications in sensing, detecting, and imaging in the terahertz regime.
2. Device design and simulation
Figure 1 schematically illustrates the structure and geometric parameters of the tunable graphene terahertz absorber, which consists of graphene crossing, graphene ring with four gaps and a gold ground plane, separated by a silicon dielectric layer. A loss free silicon with relative permittivity of εr=11.9 and the thickness of 45µm acts as substrate, which shows high transparency in the terahertz range [21]. The gold film with a conductivity σ=4.56×107S/m and a thickness of 0.5µm will guarantee the complete reflection for the incident terahertz wave. The specific optimized parameters of the all-graphene-dielectric terahertz absorber are as follows: Px=Py=50µm, the outer and inner radii of the graphene ring with four gaps, the width of the graphene crossing and the gap are R = 15µm, r = 10µm, s = 8µm, and g = 3µm, respectively.
Fig. 1. Schematic diagram of the proposed all-graphene-dielectric terahertz absorber (Here, the parameters of the terahertz absorber are set as Px=Py=50µm, R = 15µm, r = 10µm, s = 8µm, g = 3µm, and t = 45µm).
By using the random phase approximation, the graphene surface conductivity including both the intraband process contributed by in-band electron-photon scattering and interband process contributed by the transition between carriers can be expressed as [21–22]
3. Results and discussion
We perform finite element method numerical simulations by commercial software CST Microwave Studio to investigate the absorption performance of proposed terahertz absorber. The periodic boundaries are adopted in both x-direction and y-direction. Floquet plane-wave ports are assigned along z-axis direction. The effective thickness and the relaxation time of graphene are set to be 0.34 nm and τ=0.1ps, respectively. Graphene in the terahertz regime can excite surface plasmons, thereby, it makes sense to utilize the resonant absorption characteristics of graphene surface plasmon polaritons to enhance the absorption of terahertz wave. The absorptivity of the terahertz absorber is described by the formula A = 1−R(ω)−T(ω) = 1-|S11|2-|S21|2, where T is transmission, R is reflectivity, S11 is the reflection coefficient and S21 is the transmission coefficient. Owing to the thickness of the bottom gold plane greater than the skin depth across the entire terahertz region, no terahertz wave can penetrate the structure (i.e. S21 is closed to 0). Then, the absorptivity is simplified as A = 1−R(ω) =1-|S11|2. The absorption spectra for different chemical potential of the all-graphene-dielectric crossing and ring with four gaps composite structure under normal incidence are displayed in Fig. 3. Obviously, there are two distinct absorption peaks at 0.492THz and 1.472THz, whose absorption strengths exhibit evident effect by chemical potential. As the chemical potential changes from 0.9 eV to 0.5 eV, the two absorption peak amplitudes decline and exhibit red shift in the terahertz region [25]. It means that the chemical potential influence both the absorption frequency and absorption strength simultaneously.
To further study the absorption mechanism of the all-graphene-dielectric-based terahertz absorber, we calculated the absorption spectra and the electric field distribution of the terahertz absorber. Figure 4(a) indicates the absorption spectra based on the graphene crossing shaped, ring with four gaps, crossing and ring with four gaps composite structure under normal incidence. From the figure, one sees that there are two distinct absorption peaks at 0.521THz with absorptivity of 0.957 and 1.472THz with absorptivity of 0.412 when the absorber consists of graphene crossing shaped structure. The absorber based on ring with four gaps generates two resonance absorption peaks 0.690 at 0.536THz and 0.978 at 1.511THz. It is clear that the absorber based on crossing and four-split ring shape composite structure gives rise to two perfect absorption peaks at 0.521THz with absorptivity of 0.986 and 1.467THz with absorptivity of 0.98. Figure 4(b) show the surface electric field distributions of the crossing-shaped, ring with four gaps, crossing and ring with four gaps composite structure absorbers, with the chemical potential of the graphene 0.7 eV at the resonant frequencies.
Fig. 4. (a) Absorption spectra based on the graphene crossing shaped, ring with four gaps, crossing shaped and ring with four gaps composite structure under normal incidence, (b) Electric field distribution (color for the intensity) of the all-graphene-dielectric patterns to describe the plasmon hybridization effect in the proposed absorber structure when the grapheme chemical potential is assumed to be 0.7 eV.
The electric field and magnetic field distributions of x-y plane and x-z plane (y = 0) at absorption peak of unit cell are given in order to better understand the mechanism of dual-frequency absorption. Figure 5(a) reveals electric field distribution of the proposed absorber at 0.512THz. The electric field is mainly concentrated on the gaps of the split-ring. For 1.461THz, the electric field is mainly surrounded on the edges of the split-ring, as shown in Fig. 5(b). Due to the wave vector of graphene matching the free space wave vector, the graphene patterns can be excited and confine surface plasma. The two absorption peaks are actually corresponding to the first- and second- order surface plasma resonance modes. The graphene patterns interact with the incident terahertz wave to form an inductive current opposite to the incident electric field, and the bottom metal layer generates the reverse inductive current. The two currents interact with the magnetic field of the incident terahertz wave to produce a magnetic dipole, which induces strong magnetic resonance. Thus, resonant absorption peaks are generated at the resonance frequencies to achieve perfect absorption. From Figs. 5(c-d), one sees that the magnetic field is also distributed in the lossless silicon dielectric layer. The magnetic field distribution strongly proves the existence of the magnetic dipole. The interaction of surface plasmon resonance and magnetic response can produce perfect absorption of double-frequency absorption resonance peaks.
Fig. 5. Side view of electric field (a-b) and magnetic field (c-d) distributions at resonance points of 0.512THz, 1.461THz, respectively.
In addition, the x-y plane of power loss density distribution at resonance frequencies of 0.512THz, and 1.461THz are shown in Figs. 6(a) and 6(b), respectively. From the Figure, one sees that the terahertz energy is mainly dissipated along the longitudinal direction of the crossing-shaped structure at 0.512THz and distributed in the left and right sides of the ring with four gaps structure at 1.461THz. Figures 6(c) and 6(d) manifest the surface current intensity distribution for all grapheme dielectric based crossing-shaped and ring with four gaps composite structure at different frequencies. When the crossing and ring with four gaps are composite, the dipole resonances of both the crossing and the ring with four gaps are excited. In this case, the crossing dipole plasmon can interact with the plasmon of the ring with four gaps, producing low energy (bonding mode) and high energy (anti-bonding mode) hybridized states, which is shifted to 0.512THz (1.461THz). The surface current density distribution further illustrates that the dual-band absorption is mainly due to the first and second order surface plasmon resonance. At the frequency of 0.512THz, there is a strong resonance at the crossing-shaped structure and the surface current intensity is mainly distributed in the longitudinal direction of the crossing-shaped structure. It is a symmetric hybridization of localized spoof surface plasmon resonance. At the frequency of 1.461THz, the left and right sides of the ring with four gaps structure have strong resonance. The induced currents oscillate with the same amplitude and phase, resulting in a high-order localized spoof surface plasmon resonance.
Fig. 6. Top view of power loss intensity distribution (a-b) and surface current distributions (c-d) for all grapheme dielectric based crossing-shaped and ring with four gaps composite structure. The according resonant frequencies are of 0.512THz and 1.461THz.
In addition, we simulate the influence of various size structure parameters of the graphene pattern on the absorption, as given in Fig. 7. Figure 7(a) indicates that the thickness change of the dielectric layer will not affect the absorptivity but only affect the second resonance frequency. As the thickness of the dielectric layer (t) increases from 43µm to 45µm, the second absorption peak has red-shift. As shown in Fig. 7(b), one can see that the change of the outer radii of the graphene ring size (R) have a significant impact on the amplitude of the first and second absorption peak. When the R increases in the range from 13µm to17µm, it exhibits that the absorptivity of the proposed absorber increases gradually. From Fig. 7(c), one can conclude that the variety of the graphene crossing (S) in the range of 6µm-10µm cause the absorption amplitude of the first absorption frequency to decrease and a great change in absorptivity. But the change of S size has little impact on the absorptivity of the second absorption peak. In this work, we consider not only normal incidence of terahertz wave, but also extend to an oblique incidence with the TE and TM wave polarizations. Figure 8 gives the absorption efficiencies versus the operating frequency and as a function of incident angle for both TE and TM wave polarizations. From the figure, it can be noted that the absorber sustain more than 98% absorptivity at 0.521THz and 1.461THz while the incident angle varies from 0 to 40 degree for both polarizations. It is worth mentioning that there has a minor difference between TE polarization (see Fig. 8 (a)) and TM polarization (see Fig. 8 (b)) case. For the TM polarization, the absorption rates decrease a bit near the incidence angle of 40°. It is necessary to compare our results with previously reported dual-band terahertz absorbers (see Table 1). The comparison shows although our absorption is not the highest, the presented absorber can still be considered as high absorption strengths with relatively simple structure.
Fig. 7. Absorption characteristics for the proposed terahertz absorber for various substrate thickness t (a), various the outer radius of the graphene ring with four gaps values of R (b), various width of the graphene crossing structure values of s (c).
Fig. 8. Absorption spectra under different polarization angles for (a) TE- and (b) TM-wave polarization incidence
Table 1. Compared the proposed absorber with some others in terahertz region
4. Conclusions
To sum up, we proposed and investigated a dual-band tunable absorber based on all-graphene-dielectric in terahertz regime. It consists of the patterned graphene and a gold ground plane spaced by SiO2 dielectric layer. The amplitude of the absorption peaks is larger than 98% at 0.512 and 1.467THz, respectively. Both amplitude and center frequencies of the absorption peaks can be controlled by chemical potential via external applied bias voltage. Our proposed absorber can operate at a wide range of incident angles (larger than 40°) under both TE- and TM- polarizations. We believe that our device can be applied in terahertz regime with the advantage of simplicity and flexible tunability.
Funding
National Natural Science Foundation of China (NSFC) (61871355, 61831012); Natural Science Foundation of Zhejiang Province (LY18F010016).
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