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Abstract
Based on the phase-transition property of vanadium dioxide (VO2), a terahertz bifunctional absorber is proposed with switchable functionalities of broadband absorption and multiband absorption. When VO2 is metal, the system is regarded as a broadband absorber, which is composed of VO2 patch, topas spacer, and VO2 film with metallic disks inserted. The system obtains a broadband absorption with absorptance >90% from 3.25 THz to 7.08 THz. Moreover, the designed broadband absorber has a stable performance within the incident angle range of 50°. When VO2 is dielectric, multiband absorption with six peaks is realized in the designed system. Graphene and the metallic disk-shaped array play the dominant role in the mechanism of multiband absorption. Through changing the Fermi energy level of graphene, the performance of multiband absorption can be dynamically adjusted. Because of the switchable functionalities, the proposed design may have potential application in the fields of intelligent absorption and terahertz switch.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterial, an unique kind of artificial electromagnetic materials, has aroused great research interest because of its unnatural electromagnetic phenomena, such as negative refraction [1–3], perfect absorption [4–6], and electromagnetically induced transparency [7–9]. The realization of wave confinement by subwavelength geometry has been one of the hottest research area in recent years. By artificially designing the geometry of “meta-atoms”, effective permittivity and permeability of artificial subwavelength structure can be controlled, causing phase and amplitude of reflected or transmitted waves flexibly adjusted. As an important application of metamaterials, metamaterial absorbers (MAs) gain more attraction than conventional electromagnetic absorbers due to the flexible design and very thin thickness. Based on metal-insulator-metal (MIM) triple-layer configurations, single-frequency or multiband absorption can be achieved in the structures of single or several resonators. The mechanism of absorption is generally based on magnetic resonance and/or electric resonance, but the bandwidth of MA is usually narrow because of the resonant characteristic [10]. To obtain the phenomenon of broadband absorption, different resonators and unique design of the structure are always needed. But spectral response and working performance are usually fixed as the structure of metamaterial is not easy to change. Thus, tunable or switchable metamaterial shows a wider application prospect due to its more flexible control [11,12]. As a result, some active materials whose electromagnetic properties are tunable through external stimuli are introduced in the design of MAs.
Graphene is a one-atom-thick 2D arrangement of carbon atoms in the hexagonal lattice, and it is the fundamental composition of graphite [13,14]. Since the experimental achievement of the first few graphene flakes in micron scale in 2004 [15], graphene has been drawing lots of attention in various fields due to its surface conductivity [16], tunable optical transparency [17], and high electron mobility [18]. Surface conductivity of graphene as a function of Fermi energy level can be controlled by electrostatic doping, magnetic field as well as optical excitation. As a result, graphene has been widely used in the design of tunable electromagnetic absorbers in the wide frequency range from microwave to terahertz [19–21]. In 2012, R. Alaee et al. showed how to use graphene flakes as building blocks for perfect absorbers [22]. The structure only consists of a monolayer graphene placed at an appropriate distance from a metallic ground plate. M. Rahmanzadeh et al. designed an extremely broadband terahertz absorber based on multilayer patterned graphene in 2018 [23]. The spectrum exhibits >90% absorptance in an extremely broad frequency band of 0.55–3.12 THz with the relative bandwidth of 140%. In 2021, Y. Cai et al. proposed a multiband absorber consisting of stacked and orthogonal elliptical graphene layers, which can achieve eight absorption bands in the terahertz frequency range [24]. The spectrum can be changed by geometrical parameter and Fermi energy level for each graphene ellipse. All of these graphene absorbers have excellent adjustable absorption characteristics. Therefore, there is a rapidly emerging interest to add graphene into the design of absorbers to exceed the fixed performance of conventional MAs [25].
Vanadium dioxide (VO2), a kind of phase change materials, has been widely studied to achieve dynamical manipulation. As temperature rises to around 340 K, its lattice structure is transformed from monoclinic to tetragonal structures. During this process, VO2 exhibits a reversible transition from the dielectric state to the metallic state [26–28]. Moreover, conductivity of VO2 can be adjusted by 4–5 orders of magnitude within phase-transition process, which can be finished in the order of picosecond by external excitation of electrical or thermal methods [29,30]. Because of these special performances, VO2 has been widely used in tunable optical modulator, switch, and sensor [31–33]. In recent years, VO2-based absorber has attracted much attention [34–36]. In 2019, H. Liu et al. demonstrated a broadband tunable terahertz absorber based on a hybrid VO2 metamaterial [37]. Due to the phase-transition character of VO2, the maximum tunable range of the proposed absorber can be obtained from 5% to 100%. J. Huang et al. obtain a broadband absorber with four identical VO2-based resonators and the corresponding absorption can be dynamically tuned from 4% to 100% [38].
Graphene and VO2 are promising materials for tunable MAs in terahertz range. However, most reported studies have only utilized graphene or VO2 alone, realizing the independent functionality for broadband, narrowband or multiband absorptions. In our work, a bifunctional terahertz absorber is proposed with the combination of graphene and VO2. The design serves as a broadband (multiband) absorber when VO2 is metal (dielectric). And the involvement of graphene makes it possible to adjust absorption bandwidth and intensity. On account of the combination of VO2 and graphene, the proposed multilayer configuration gains the advantages of switchable functionality and flexible adjustability.
2. Design and method
The designed multilayer MA based on VO2 and graphene is illustrated in Fig. 1. VO2 on the top and inserted in the middle are patterned, and are filled with air and metallic disk, respectively. Monolayer graphene is placed underneath VO2-film and metallic disk. Spacers are the dielectric of cyclic olefin copolymer (Topas) with relative dielectric permittivity of 2.35. Topas is an organic substance and easy to grow experimentally. Its dielectric permittivity is small without loss in terahertz frequencies. Metallic plate mirror is made up of gold with the thickness of ${t_3} = 1\,\; \mathrm{\mu}\textrm{m}$. And its conductivity is chosen as $4.561 \times {10^7}$ S/m. As shown in Fig. 1, the whole structure is periodically arranged along x and y directions to simulate the practical usage. The parameters of the top VO2-patterned patches are set a $[w = 6.4\,\mathrm{\mu}\textrm{m}$, $l = 18.8\,\mathrm{\mu}\textrm{m}$, $p = 20\,\mathrm{\mu}\textrm{m}$ and ${t_1} = 0.04/\mathrm{\mu}\textrm{m}$. The thicknesses of the first topas spacer, VO2 middle layer, and the second topas spacer are ${h_1} = 9.5\,\mathrm{\mu}\textrm{m}$, ${t_2} = 1.0\,\mathrm{\mu}\textrm{m}$ and ${h_2} = 58.6\,\mathrm{\mu}\textrm{m}$. The radius and thickness of metallic disk inserted in VO2 film are $r = 6.3\,\mathrm{\mu}\textrm{m}$ and ${t_2} = 1.0\,\mathrm{\mu}\textrm{m}$.
In simulation, finite element method (commercial software-COMSOL Multiphysics) is adopted to obtain reflection parameter ${S_{11}}$ and transmission parameter ${S_{21}}$. Periodic boundary conditions are set along x and y directions. Fine mesh is carefully chosen to ensure the proper convergence. When linear-polarized plane wave is normally incident into the device, transmission and reflection are monitored by two ports in the z direction. Due to the gapless electronic band-structure and mono-atomic thickness, graphene can be considered as a 2D material to improve computation efficiency. Surface conductivity is generally characterized by Kubo formula [39–41]
3. Results and discussions
As the thickness of gold plate is much larger than its skin depth in the terahertz range, incident electromagnetic wave is almost reflected causing transmittance $T = {|{{S_{21}}} |^2} \approx 0$. Therefore, absorptance can be expressed as $A = 1 - R - T = 1 - {|{{S_{11}}} |^2} - {|{{S_{21}}} |^2} = 1 - {|{{S_{11}}} |^2}$, where $R = {|{{S_{11}}} |^2}$ is reflectance. According to this, the realization of minimum reflectance is equal to the best absorptance. And it can be achieved with impedance matching with free space. In order to demonstrate the switchable absorption property of the proposed absorber, absorptance spectra are plotted in Fig. 2. At room temperature, VO2 acts as dielectric. The array of metal disk and the continuous graphene film react together to change the property of incident wave. As a result, six absorption bands (blue solid line) are observed. Absorption peaks are located at 0.72 THz, 2.17 THz, 3.67 THz, 5.28 THz, 6.81 THz, and 9.0 THz, and the corresponding absorptance are 85.1%, 94.9%, 99.3%, 94.9%, 97.4%, and 97.5%, respectively. In the other case, VO2 exhibits a reversible transition to the metallic state under external excitation. The system behaves as a 3-layer VO2-based resonator with broadband absorption (red dashed line). This design can achieve an absorption bandwidth of 3.83 THz from 3.25 THz to 7.08 THz with absorbance >90% and the relative bandwidth 74%. It is unprecedented that the excellent broadband and multiband absorption properties are successfully integrated in a single system by means of phase change material VO2.
Fig. 2. Absorptance spectra when VO2 is dielectric (blue solid line) or metal (red dashed line) under normal incidence.
The working mechanism of the proposed bifunctional absorber is investigated and depicted in Figs. 3–5. Electric field of incident wave is polarized along the y axis. For broadband absorption, as the middle VO2 film in the metallic state reflects almost all incident waves, electromagnetic wave is mainly absorbed due to the resonance within VO2 patches. Figure 3 shows field distributions of the top VO2 patches for broadband absorption in XOY plane at two different resonant frequencies. In Fig. 3(a), electric field is strongly enhanced in the gap of adjacent VO2 patches at 4.5 THz. At the resonant frequency of 5.5 THz, electric field in Fig. 3(b) is mainly distributed along the edge of individual VO2 patch with negligible interaction. Therefore, the low-frequency resonance in broadband absorption is attributed to the coupling interaction between neighbouring structures, while the high-frequency resonance is caused by electric dipole mode of individual VO2 patch. The overlap of two resonances leads to broadband performance of the designed absorber. When VO2 is dielectric, two VO2 layers and the top topas spacer have small contribution to absorption. Figure 4 illustrates simulated electric field distribution at the first peak frequency 0.72 THz of multiband absorption. Electric fields are concentrated on the edge of each metallic disk, forming an electric dipole resonance. Incident wave induces localized surface plasmon resonance. Because of different absorption mechanism, simulated electric field distributions at other five resonant frequencies of multiband absorption are illustrated in Fig. 5. Due to Fabry-Perot (FP) resonance, electric field is mainly distributed in the middle dielectric layer. The distributions of electric field are differently concentrated for different resonant frequencies, and show different locations in the optical cavity. Five resonances in the FP cavity excite five narrowband absorption modes of the structure.
Fig. 3. Electric field distributions in the top VO2 patches for broadband absorption at the frequencies of (a) 4.5 THz and (b) 5.5 THz.
Fig. 5. Simulated electric field distributions for multiband absorption at (a) 2.17 THz, (b) 3.67 THz, (c) 5.28 THz, (d) 6.81 THz, and (e) 9.0 THz.
As it is necessary for absorber to perform well under oblique incidence, broadband and multiband absorption spectra of the proposed design are simulated under a wide range of incident angles to investigate angular tolerance. As shown in Figs. 6 and 7, absorptance spectra of transverse electric (TE) and transverse magnetic (TM) polarized waves as a function of incident angle and frequency are numerically calculated. Incident angle is the angle between incident wave vector and negative z direction, which is adjusted from 0° to 80°. For broadband absorption, whether TE polarization or TM polarization, there is a quite weak dependence on incident angle below 50° in Fig. 6. It means that due to the symmetry of structure, broadband absorptions of the system keep good performance within the angle range of 50°. When incident angle is 50°, absorptance remains more than 80% with bandwidth 3.8 THz from 3.45 THz to 7.25 THz for both TE and TM polarizations. This behavior is mainly related to the confined electric field in the top VO2 patches. It can also be observed that absorptance decreases gradually as incident angle increases for both polarizations, and Bragg scattering appears at high frequencies for TM polarization. Moreover, the spectrum has a slight blue-shift for both polarizations, but broadband absorption effect is still stable even at a large oblique angle. As for multiband absorption, absorption intensities of the first 3 peaks become smaller and smaller for TE polarization, while the case is reverse for TM polarization. Electric field of TE polarization is always perpendicular to incident plane. With the increase of incident angle, impedance of the design will gradually lose its match with that of free space. Magnetic field of TM polarization is always perpendicular to incident plane. With the increase of incident angle, the vertical component of electric field (${E_z}$) will increase gradually. It is also observed that resonant frequencies exhibit blue shift for both TE and TM polarization. As the increase of incident angle, higher-order FP resonant modes are seriously affected by Bragg scattering. This behavior is obvious for the third-, fourth-, fifth-order FP resonance (3 absorption modes on the right) in Fig. 7.
Fig. 6. Angular dependence of broadband absorptance for (a) TE polarization and (b) TM polarization.
Fig. 7. Angular dependence of multiband absorptance for (a) TE polarization and (b) TM polarization.
Except for the switchable functionality in our design, multiband absorption is also actively tunable. Actually, absorption can be tuned by geometric parameter. But these parameters are inconvenient to adjust once the structure is fabricated. Herein, absorptance can be flexibly modulated by adjusting the electromagnetic property of graphene. Hence, multiband response is tuned by adjusting Fermi energy level of graphene as depicted in Fig. 8. It can be seen that change of Fermi energy level affects bandwidth and intensity of absorption. For the first absorption peak at 0.72 THz, absorption intensity gradually decreased to ∼75%. It is easy to explain that as Fermi energy level is 1.0 eV, the increased surface conductivity of graphene influences localized surface plasmon on metallic disks, causing weaker absorption intensity. With regard to other five peaks, the increased conductivity of graphene affects FP resonance. As a result, absorption bandwidth is widened and central frequencies exhibit slight blue shifts. Therefore, it is possible to obtain tunable multiband absorption with unchanged geometric configuration.
We further analyze how absorption depends on structure parameters. Figure 9(a) shows the influence of w value from 2 µm to 12 µm when other structure parameters are kept at the optimized value under normal incidence. Absorption bandwidth will gradually narrow, and absorption intensity increases first and then decreases. When l gradually increases in Fig. 9(b), absorption bandwidth slowly increases, and absorption frequency has a little red shift. Figure 9(c) shows absorptance when ${h_1}$ is modified from 3 µm to 13 µm. Absorption peak increases and absorption bandwidth narrows. This trend reaches an optimum state at ${h_1} = 9.5$ µm. Figure 10(a) shows the change of absorptance when radius value of metal disk is changed from 2.0 µm to 8.0 µm keeping other parameters fixed. Around 0.72 THz, absorption peak decreases and absorption bandwidth increases. Around 2.17 THz, 3.67 THz, 6.81 THz, and 9.0 THz, absorption peak increases first and then decreases. Around 5.28 THz, absorption peak increases gradually. Figure 10(b) shows absorptance spectra varying with different thickness ${h_2}$. With the increase of ${h_2}$, the number of absorption peak will increase accordingly, and absorption frequency will shift to low frequency. According to the influence of geometric parameters, geometric parameters with the best absorption performance are obtained after optimization.
4. Conclusion
To summarize, a bifunctional absorption modulator is designed based on a hybrid VO2 and graphene configuration. The design serves as a six-band absorber when VO2 is dielectric. The multiband absorption property is attributed to the combination of localized surface plasmon resonance at 0.72 THz and five FP resonances for other absorption peaks. As phase transition happens in VO2 by external excitation, broadband absorber is obtained with absorptance >90% in the frequency range of 3.25 THz to 7.08 THz. Absorption mechanism is caused by the interaction between adjacent VO2 patches and individual VO2 electric dipole resonance. Absorptance of the proposed multiband absorber can be greatly tuned by changing Fermi energy level of graphene from 0.0 eV to 1.0 eV. The design has strong polarization independence and works well in a wide range of incident angles, and it could be regarded as an important component in terahertz modulating and filtering applications [45–51].
Funding
National Natural Science Foundation of China (11974294); Guangdong Basic and Applied Basic Research Foundation (2020A1515010375).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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