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Abstract
We numerically demonstrate a tunable broadband terahertz absorber with near-unity absorption by using multilayer graphene ribbons sandwiched in a plasmonic integrated structure. By stacking slightly different widths of graphene ribbons in a sandwiched configuration, the absorption bandwidth can be increased because of the different resonant modes closely positioned together. The absorption spectrum’s center frequency can be manipulated by varying the graphene’s chemical potential, which provides a flexible way to design and optimize absorption property after fabrication. Furthermore, the structure can tolerate a wide range of incident angles, while the improved structure with graphene nanoparticles also shows polarization-independent feature. In this routine, stacking more graphene ribbons or particles with well-designed dimensions can further increase the bandwidth, as long as the metamaterial dimension satisfies the sub-wavelength condition. Therefore, our research provides an important theoretical guide for designing various graphene-based tunable broadband absorbers at terahertz, infrared, and microwave frequencies. This may have promising applications in imaging, sensing, and novel optoelectronic devices.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Efficient incident wave absorption is of great importance in some device applications from microwave to optical frequency [1–5]. Since the first theoretical and experimental demonstration of perfect metamaterial absorber (MA) was presented by Landy et al. in 2008 [6], various kinds of MAs have been proposed and studied [7–9]. In recent years, terahertz MAs have attracted increasing attentions [10], which have diverse applications in sensor [11], thermal emitters [12] and imaging devices [13]. To obtain single narrowband, multi-narrowband or broadband perfect absorption, absorbers with periodic arrays using different shaped resonators such as cross, square rings, circular split rings and all-dielectric metasurfaces [14–17] have been developed.
These above metamaterial or metasurface absorbers consisting of normal metals and dielectric materials have the inherent drawback of non-adjustability after fabrication. Consequently, two-dimensional materials such as graphene [18], black phosphorus [19] and MoS2 [20] are also utilized as lossy materials in novel MAs for ultra-compact devices. Among these materials, graphene has the highest carrier mobility and excellent mechanical properties. Besides, graphene’s complex conductivity depends on the Femi level and can be adjusted by electrostatic doping or chemical doping [21]. Hence, graphene-based MAs (GMA) with tunable absorption properties have attracted rapidly increasing interests [18,22–24]. For instance, Alaee et al. utilizes graphene ribbons to achieve perfect absorption in the THz frequency. Afterwards, the analytical and rigorous analysis of graphene ribbons has been proposed by Khavasi’s group in [25,26], which gives a general, valid, and reliable analysis of interaction between incident wave and graphene ribbons. However, the absorption bandwidths of common GMAs are often narrow since only a single resonance is utilized during the process of absorption, limiting their potential applications in practical engineering. In order to achieve broad bandwidth absorption, various plasmonic structures have been investigated [27–35]. For example, by utilizing a hybrid graphene-gold metasurface on SiO2/pSi/PDMS substrate with an aluminum back, Zhao et al. proposed an excellent absorber in the low-terahertz regime [27]. A GMA composed of four patch resonators with different geometric sizes was developed by Xiong et al., which has its bandwidth tunable through a voltage biasing [28]. Ye et al. demonstrated a broadband GMA with near-unity absorption by using a net-shaped periodically sinusoidally-patterned graphene sheet, in which continuous plasmon resonances can be excited [29].
However, most of the above broad GMAs have the disadvantages of dependence on the incidence angle or polarization, and require extremely complicated fabrication technique. Besides, their center frequencies could not be tuned flexibly by bias voltage after fabrication. Therefore, it is still quite in demand to further investigate new tunable broadband terahertz GMAs with a better polarization insensitivity and omnidirectionality without fabrication difficulties.
In our work, we propose a multilayer graphene-sandwiched plasmonic configuration based on perfect absorption mechanism to achieve tunable broadband terahertz absorber. Numerical results show that the broadband metamaterials graphene absorber can tolerate a wide range of incident angles. Moreover, the center frequency of its absorption spectrum can be linearly tuned by adjusting the chemical potential of graphene. The mechanism of the broadband absorption property is elaborated. In addition, the three-dimensional configuration with nanoparticles is also evaluated for the polarization-insensitive and angle-independent characteristic. To indicate the improvement in the performance of the proposed absorber, the comparisons of main properties between state-of-the-art broadband graphene absorbers are listed in Table 1.
Table 1. Comparisons between broadband absorbers at THz frequencies.
2. Modeling and parameters
A schematic drawing of the proposed three-layer graphene-sandwiched plasmonic absorber (GSPA) is shown in Fig. 1. The structure consists of three graphene nanoribbons of infinite length sandwiched between Al2O3 layers with a relative permittivity of ~3.2 [36]. The top dielectric layer has a negligible effect on the absorption performance due to the wavelength much larger than t in the terahertz regime, but it can keep the top graphene from environmental-induced degradation. The sandwiched graphene-dielectric structure is mounted on a full reflective gold mirror. The gold mirror is thick enough to block the incident wave and no energy is allowed to transmit through the absorber. Furthermore, the reflected energy is suppressed by electromagnetic losses in the lossy graphenes, resulting in strong absorption. The broadband and tunable properties of GSPA are investigated using finite integration technique (FIT) via simulations using CST Microwave Studio, which numerically solves Maxwell’s equations under periodic boundary conditions in the x and y directions and open boundary conditions in the z direction. Adaptive tetrahedral mesh refinement is applied for all simulations. The plane wave is incident downward from the top surface of the absorber. The wavelength dependent absorption rate A(λ) can be expressed as A(λ) = 1 − R(λ) − T(λ), where the reflection R(λ) is equal to |S11(λ)|2 and transmission T(λ) is given by |S21(λ)|2. Since the gold mirror prevents the downward wave propagation, the transmission T(λ) is regarded as zero over the entire wavelength range of interest. Consequently, A(λ) = 1 − R(λ). In simulations, we suppose that graphene is an anisotropic dispersive dielectric material with an effective relative permittivity tensor as
where ω is the angular frequency of light, εzz is assumed as an out-of-plane component of graphene with a constant value of 9.0 [37,38], εxx(ω) and εyy(ω) are in-plane components of permittivity, which can be represented by the surface conductivity of graphene σ(ω) aswhere ε0 is the permittivity of vacuum, and the thickness of graphene H is assumed as 0.5 nm [39]. The surface conductivity of graphene σ(ω) can be expressed by the following equations based on the Kubo formulas as below [40] where σintra and σinter are originated from the intraband and interband transition, respectively, fd (ξ, μc, T) is the Fermi-Dirac distribution, ω is the radian frequency, e is the electron charge, kB is the Boltzmann constant, T is temperature of Kelvin, ħ is the reduced Planck constant, Г = 1/(2τ) is the scattering rate, τ is the electron-phonon relaxation time, μc is the chemical potential, and ξ is the energy of electrons. At room temperature T = 300 K, the Kubo equation is reduced to a Drude-like form, which iswhere the intraband transition is dominant in the terahertz and far-infrared region compared with the interband transition. Therefore, the value of σ mainly depends on τ, μc and ω.
Fig. 1 (a) Perspective view and (b) cross-section view of proposed three-layer graphene-sandwiched plasmonic absorber (GSPA). The symbols w1, w2 and w3 represent the widths of different graphene layers, respectively. The symbols t and d represent the thickness of the upper three Al2O3 layers and bottom Al2O3 layer, respectively. The symbol p represents the periodicity of the periodic structure.
3. Results and discussions
First, we study the absorption properties of the proposed three-layer GSPA under normal TM and TE incidence with magnetic and electric fields Hy and Ey, respectively, perpendicular to the x-z plane as shown in Fig. 2(a). The chemical potential of the graphene is initially assumed to be µc = 0.2 eV, while the relaxation time is set as 0.1 ps. The electric field of TE incidence is parallel to the graphene ribbons (y-axis), in which condition plasmonic resonance is poorly excited. In contrast, the electric field of TM incidence is along the x-axis, which will excite carriers of graphene to vibrate in the finite width and induce the localized graphene surface plasmon (GSP). Because the transmission is completely suppressed by the bottom gold mirror, the maximum absorption of the absorber can be achieved when the broadband impedance matching condition of the terahertz incidence is satisfied. The absorber has broadband absorption with a 90% absorbance bandwidth of 0.70 THz, from 5.78 THz to 6.48 THz. The center frequency fc can be obtained by fc = (f- + f+)/2 = 6.13 THz, where f- and f+ represent the low and upper frequency edges of 90% absorption, respectively. The fractional bandwidth, the ratio of the absolute bandwidth to the center frequency, is about 11.4%. The effects of polarization dependence imply a promising potential for applications of polarized light filters. The properties with TM incident light are focused on in the following discussion because of low absorption rate of the TE incident light.
Fig. 2 Light absorption of three-layer GSPA (a) under TM and TE incident light and (b) using different thickness of lower Al2O3 layer, for w1 = 0.155 μm, w2 = 0.170 μm, w3 = 0.180 μm, p = 0.25 μm and t = 0.5 μm, under normal incidence.
The thickness of the lower Al2O3 layer d affects the GSPA performance, thus the absorption spectra under different d values are shown in Fig. 2(b). As d decreases from 8 μm to 4 μm, the absorption rate and the bandwidth drop sharply. This is attributed to the decrease of the effective thickness of the Fabry-Perot resonator, which is formed by graphene layers and the gold mirror.
Next, we investigate the relationship between the absorption rate and the number of graphene layers (NGL) in the GSPA structure as shown in Fig. 3. When NGL = 1 [only 1st layer graphene is left in Fig. 1(b)], the resonant frequency is 6.45 THz while the absorption rate is 90.1%. As demonstrated in [41], the bandwidth of the absorption can be increased by using a multilayer structure supporting several resonant modes closely positioned in the absorption spectrum. Moreover, the resonant frequency of the absorption caused by the magnetic polariton is primarily determined by the width of graphene ribbons. Thus, we design graphene ribbons of slightly different widths in different layers to ensure that the resonance frequencies of magnetic polaritons could be close to each other. As NGL increases to 2, two closely positioned resonances with absorption up to 95.7% are clearly observed. Owing to these two resonant peaks, we obtain a relatively wide frequency band of absorption, where nearly perfect absorption occurs. Furthermore, we demonstrate a broader bandwidth absorption in a three-layer GSPA structure as shown in Fig. 1. By stacking one more layer, additional magnetic polariton is introduced to this absorber device. Accordingly, three closely located resonances are observed at frequencies f1 = 6.38 THz, f2 = 6.11 THz and f 3 = 5.86 THz, with absorption up to 97.2%, 100% and 98.7%, respectively. The perfect absorption occurs by optimizing the dielectric separation thickness of each layer, thus the three-layer GSPA structure can be impedance-matched to the free space at each resonant frequency. Meanwhile, the thickness of the three-layer structure is still quite thin compared to the incident wavelength, satisfying the sub-wavelength condition.
Fig. 3 Absorption spectra for various layers of graphene, for w1 = 0.155 μm, w2 = 0.170 μm, w3 = 0.180 μm, p = 0.25 μm, d = 8 μm and t = 0.5 μm.
To better understand the physical mechanism of broadband absorption in the multilayer GSPA, the average electric field intensity distributions are plotted in Fig. 4. At the resonance frequency, f1 = 6.38 THz, of three-layer GSPA, Figs. 4(a) and 4(c) clearly show that the incident fields are trapped on the rims of the 1st graphene ribbon as the guided gap-plasmon mode [42] and induce the effects of near field enhancement and energy concentration. The optical loss inside graphene can be evaluated by the following equation:
where V is the volume of graphene, c is the speed of light in vacuum and El is the electric field inside graphene. ε” is the imaginary part of graphene permittivity. The effects of optical saturation and non-linear response are not taken into account in the physical model. Thus, the enhanced fields penetrating graphene ribbon dissipate in the lossy dielectric and contribute to the enhanced absorption inside graphene. In addition, the confinement of electric field energy density inside the 2nd graphene ribbon is also remarkable. However, the strength of concentrated energy inside the 3rd graphene ribbon is relatively weak compared with the 1st and 2nd graphene ribbons. This is attributed to the resonance frequency of the 3rd graphene ribbon is around 5.86 THz, which is a little away from the simulated frequency 6.38 THz.Fig. 4 Simulated average electric field intensity distributions. Figure 4(a) and 4(b) present sectional views at the in-plane across the 1st graphene for NGL = 3 at the frequency of 6.38 THz and 5.00 THz respectively. Figure 4(c)-4(f) present cross-section views for NGL = 3 at the frequency of 6.38 THz, 5.00 THz, 6.11 THz and 5.86 THz respectively. Figure 4(g) and 4(h) present cross-section views for NGL = 2 and NGL = 1 at the frequency of 6.38 THz. The dimensions in the GSPA are w1 = 0.155 μm, w2 = 0.170 μm, w3 = 0.180 μm, p = 0.25 μm, d = 8 μm and t = 0.5 μm. Four unit cells are plotted in the figure.
In contrast, for f = 5 THz as presented in Figs. 4(b) and 4(d), there is few enhanced near field for absorption enhancement in graphene ribbons because this frequency is far away from all the plasmonic resonance frequencies of these three graphene ribbons on the spectrum.
As shown in Fig. 4(e), at the resonance frequency of the 2nd graphene ribbon (f2 = 6.11 THz), the electric field is dramatically enhanced and concentrated surrounding the edges of the three graphene ribbons, especially the 2nd ribbon. This originates from the fact that resonance frequencies of these three graphene ribbons are not far away from the simulated frequency 6.11 THz. Therefore, neighboring graphene ribbons are close to each other, the evanescent field scattered by one graphene ribbon is considerably strong in the vicinity of the other graphene ribbon compared to the exciting field, and this leads to the intense coupling of scattered field from each graphene ribbon. As a consequence, the superposition of the inverse optical fields that are induced by electric dipole excited by the incident wave contributes to the suppressed reflectance. Therefore, perfect absorption occurs at the resonance frequency of 6.11 THz as shown in Fig. 3.
When f = 5.86 THz, which is the resonance frequency of the 3rd graphene ribbon, the incident fields are mainly focused on the third graphene ribbon as shown in Fig. 4(f). Moreover, the electric dipoles placed in the 2nd and 3rd graphene ribbons also contribute to the third absorption peak at f3 = 5.86 THz, with absorption up to 98.7%.
As the layer of graphene decreases, as shown in Figs. 4(g) and 4(h), the total absorption of incident wave is reduced due to the lessened energy lossy inside graphene at the resonance frequency.
According to Fig. 3 and Fig. 4, we can therefore predict that an enhanced and broadband absorption spectrum can be further achieved by increasing NGL of the proposed GSPA and tuning the dimension of each graphene ribbon.
The above discussion is only based on normal incidence, but the robustness of optical response for non-normal incident angles is significant for terahertz absorber. Based on a series of simulations, the absorption of three-layer GSPA is demonstrated in Fig. 5 as a function of frequency and angle of incidence (keeping the wavevector in the x-z plane). The result indicates that the maximum absorption can maintain at a high value larger than 90% under the incident angle below 63°, and a value larger than 80% under the incident angle below 76°. On the other hand, the bandwidth keeps almost unchanged under the incident angle below 58°, which consists three obvious absorption peaks shown in Fig. 5. Therefore, the absorption of the three-layer GSPA structure is nearly independent of the incident angle. This can be explained that the direction of magnetic field for the incident light remains almost constant while the angle of incidence is changed, so the intensity of magnetic resonance can be sufficiently kept and further ensures the high loss inside graphene for a wide range of incident angles.
Fig. 5 Absorption of three-layer GSPA under different incident angles, for w1 = 0.155 μm, w2 = 0.170 μm, w3 = 0.180 μm, p = 0.25 μm, d = 8 μm and t = 0.5 μm.
By adjusting the geometric dimensions of the GSPA configuration, the absorption spectra can be tuned as shown in Fig. 2(b). It is remarkable that the absorption tuning via d, w1, w2, w3 and other dimensions is very useful in designing an absorber with specific requirement. However, variation of the physical dimensions after final design and implementation of the absorber is inconvenient and not feasible. Therefore, an active tuning method to control the absorber characteristics after fabrication is indispensable. By varying the conductivity of the sandwiched graphene layers, the proposed GSPA is expected to achieve flexible tunability. As shown in Kubo formulas Eqs. (3)-(6), the surface conductivity of graphene is directly dependent on the chemical potential μc. Thus, the performance of graphene-based devices can be manipulated by changing the chemical potential via chemical doping or electrostatic doping without changing the structure of the devices. The absorption tunability of the proposed three-layer GSPA is studied in Fig. 6. From a practical point of view, we choose the graphene chemical potential between 0.20 eV and 0.30 eV, because the chemical potential can be easily tuned from 0 to 0.8 eV in experiments by the electrostatic doping [43,44]. The center frequency of three-layer GSPA can be easily controlled between 6.13 THz and 9.30 THz by tuning the chemical potential of graphene as shown in Fig. 6. Moreover, the relationship between the center frequency of GSPA absorption spectrum and the chemical potential of graphene is almost linear, which makes it easier to realize in practical. Therefore, the proposed 2D GSPA is an excellent tunable broadband terahertz absorber with almost omnidirectionality.
Fig. 6 Center frequency of three-layer GSPA versus graphene chemical potential, for w1 = 0.155 μm, w2 = 0.170 μm, w3 = 0.180 μm, p = 0.25 μm, d = 8 μm and t = 0.5 μm, under normal incidence.
4. Further evaluation for three-dimensional GSPA
The interaction between incident light and nanoribbons pattern is highly sensitive to the polarization of incidence. When the incident electric field is parallel to the graphene ribbons, localized plasmonic resonance in graphene ribbons is poorly excited. On the contrary, if the incident electric field is parallel to a finite length, the incidence will induce the localized plasmonic resonance. In order to further overcome the limitations of polarization of incidence, we investigate the 3D integrated structure as shown in Fig. 7. Figure 7(a) indicates the perspective view of the 3D three-layer GSPA structure consisting of graphene nanoparticles, Al2O3 layers and gold reflector. The geometry of the 3D configuration is described by the same symbols w1, w2, w3, t, p and d as depicted in Fig. 1. The nanoparticle has a same finite length in x-axis and y-axis directions.
Fig. 7 (a) Schematics of the 3D three-layer GSPA structure. (b) Absorption rate of TM and TE polarization incident light.
As we know, the optical properties of plasmonic configuration based on Fabry-Perot resonator with nanoparticle pattern are highly sensitive to the geometry dimensions of the structure, including nanoparticle width, period and the thickness of the spacer layers. In order to satisfy the perfect absorption conditions, the final parameters of the configuration are taken as: w1 = 0.155 μm, w2 = 0.170 μm, w3 = 0.180 μm, p = 0.25 μm, d = 8 μm and t = 0.5 μm. The chemical potential of graphene is taken as μc = 0.2 eV. The absorption spectra of the structure under normal incidence with TE and TM polarization are plotted in Fig. 7(b). As can be seen, for both TM and TE polarization, the absorber has broadband absorption with a 90% absorbance bandwidth of 0.76 THz, from 4.80 THz to 5.56 THz, while the center frequency fc is 5.20 THz. The fractional bandwidth is about 16.0%. The three closely located resonances are observed at frequencies f1 = 5.48THz, f2 = 5.21 THz and f 3 = 5.02 THz, with absorption up to 93.1% and 100.0%, 100.0%, respectively. The polarization-insensitive absorption property is mainly attributed to the axisymmetric geometry of nanoparticles, whose edge lengths in both x- and y-axis directions are finite and equal. Therefore, for both TM and TE incidence, the electric dipoles formed by the accumulation of charges with opposite signs oscillate in the same way. Besides, they are greatly coupled with their own images, which oscillate in antiphase on the metallic film. Consequently, magnetic polaritons [45,46] are formed, which induce a strong magnetic response and cause a resonant dip in the same reflection spectrum. Thus, the proposed 3D structure has a polarization- insensitive property.
The stabilities of the incident angle for both TM and TE polarizations are revealed in Fig. 8. For TM polarization, as the incident angles increases, the maximum absorption of 3D three-layer GSPA maintains above 90% when the incident angle is less than 62°, while the bandwidth becomes slightly narrower. For TE polarization, the maximum absorption remains larger than 95% as the incident angles increases up to 80°. Besides, the bandwidth starts to decline when the incident angle is larger than 60°. Hence, the 3D GSPA can tolerate a wide incident angles for both TM and TE polarization, which can be utilized as a polarization-insensitive and angle-independent broadband terahertz absorber.
Fig. 8 Absorption of 3D three-layer GSPA under different incident angles of (a) TM incidence and (b) TE incidence, for w1 = 0.155 μm, w2 = 0.170 μm, w3 = 0.180 μm, p = 0.25 μm, d = 8 μm and t = 0.5 μm.
5. Conclusions
In summary, we have theoretically and numerically demonstrated a broadband and omnidirectional terahertz absorber based on multilayer graphene in a sandwiched plasmonic configuration. With slightly different widths of graphene ribbons stacked together, the absorption peaks of different resonant modes could be close to each other, resulting in a broadband absorption spectrum. By increasing the chemical potential of graphene, the center frequency of absorption spectrum shows an obviously blueshift, which provides great flexibility compared with metallic-based metamaterials absorbers. In addition, the 3D GSPA configuration with graphene nanoparticles is also investigated with polarization-insensitive and angle-independent properties. The proposed absorber could be used in many promising applications, such as broadband spatial amplitude modulators, sensors, and detectors in the terahertz region.
Funding
National Natural Science Foundation of China (NSFC) (No. 61601390), the Young and Middle-aged Teachers Education and Scientific Research Foundation of Fujian Province (No. JAT170405), the High Level Talent Project of Xiamen University of Technology (No. YKJ16011R).
Acknowledgments
Technical advices from the program managers Dr. Zhiping Cai and Dr. Qing Huo Liu are greatly appreciated. Extra supports are acknowledged for Dr. Y. Zhou. The authors also thank Mr. Liu for language check.
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