Based on graphene tunable dual-band terahertz metamaterial absorber with wide-angle
Introduction
Metamaterial absorber (MMA), as a subclass of metamaterials (MMs) can effectively absorb electromagnetic (EM) wave, which has been attracted a large amount of interest due to its potential applications of thermal emission, imaging and sensing [[1], [2], [3]]. The discovery and verification of MMs, combining the application of terahertz (THz) spectroscopy, have opened a new research hotspot [[4], [5], [6], [7]]. Since it is hard to search an efficient absorption material at THz region in nature, the design of THz MMA is extra important. Recent years, there have been numerous studies of MMAs that were reported and applied for EM stealth, detection, modulation, imaging and so on [[8], [9], [10], [11], [12]]. In addition, various MMA structures for THz waves have been proposed and investigated intensively from narrow to multi or broad band, and fixed to tunable frequency [[13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27]]. However, the methods of designed multi-band or broadband THz MMA generally were realized by integrating multiple resonators, which would be relative complex to fabricate [[3], [14], [16]]. The methods of tunable MMA mainly include machine [19], laser [[20], [21], [22], [23]],temperature [[24], [25]] and voltage modulation [[26], [27]]. Although aforementioned methods for tunable MMAs have been demonstrated theoretically and experimentally lately, they usually operated well in a single-band frequency range. Besides the voltage modulation method for tunable MMA, the other methods have some limitations, such as particular condition and complex structure. The external bias voltage modulation method is widely used to design dynamic tunable devices from microwave, THz to optical frequency.
These days, a new method based on graphene with external bias voltage for tuning absorption properties of the THz MMA has been proposed and investigated theoretically [[28], [29], [30], [31], [32], [33], [34], [35], [36], [39], [37], [38], [40]]. Graphene as a two-dimensional (2D) mono-layer carbon atom material has drawn intense attention due to its exotic properties [[41], [42], [43], [44]], when its experimental preparation has been realized and verified by Novoselov [45]. The conductivity of graphene sheet can be continuously and visibly tuned by changing the chemical potential (), which may be potentially tuned from −1 to 1 eV by chemical doping or external bias voltage [46]. Thus, the graphene could be a good candidate for designing and engineering some tunable devices due to the above mentioned modulated properties. Moreover, graphene can strongly interact with incident EM waves over a wide frequency range from THz to infrared regions. Ke et al. presented tunable absorber composed of periodically patterned cross-shaped graphene arrays on the dielectric substrate [29]. The MMA performed enhancement absorption of graphene sheet by exciting surface plasmon polaritons (SPPs) resonances. The absorption level and working frequency could be tuned by modulating the sizes of structure, relaxation times and chemical potential. However, the absorption peak of the designed MMA only achieved 25%. Andryieuski et al. proposed and demonstrated a perfect absorber based on graphene [30], which could only tune the narrow and broad band absorption magnitude, but not the working frequency. Xing et al. presented a tunable perfect absorber composed of graphene ribbon-array coupled with a sheet sandwiched between two dielectric spacers with different thicknesses on the metal film [31], which could achieve tunable absorption properties via modulating chemical potentials. However, it only performed single band absorption. Faraji et al. proposed a tunable THz absorber consisting of two patterned graphene layers separated by Al2O3 [32], which could achieve tunable four bands absorption. However, the relative modulation bandwidth was narrow. In addition, the double layers graphene sheet increased the difficulties of fabrication and modulation.
For the purpose of designing a dual-band THz MMAs based on a simple structure, we presented a structure based on the square graphene patch (SGP) on dielectric substrate placed on metal film. Since the higher-order plasmon resonance was effectively excited in the SGP for THz waves [34], the dual-band absorption could be achieved by inducing fundamental and second higher-order SPPs, which was demonstrated by the electric field and power loss distributions of SGP and unit-cell of MMA. The numerical simulation results showed that the designed MMA performed great absorption (over 70%) and achieved slight and obvious frequency modulation in the lower (0.85 THz to 1.01 THz) and higher frequency region (2.84 THz to 3.37 THz) via changing chemical potential from 0.4 eV to 0.8 eV. Moreover, the relative modulation bandwidth and absorption depth were 17.20% and 10.66% in the lower frequency region, and 17.07% and 21.84% in the higher frequency region, respectively. The further simulation results indicated the proposed MMA was wide-angle absorption for the incident waves.
In this paper, firstly, the conductivity model of the SGP was investigated theoretically. Then, the unit-cell structure of the designed MMA was proposed and simulated individually. In the next section, the simulation result and absorption mechanism were specifically illustrated by analyzing the electric field and power loss density distributions at resonance frequencies. In addition, the tunability of the proposed MMA was demonstrated. Finally, the wide-angle absorption property of the designed THz MMA was clearly shown by the further simulations.
Section snippets
Theoretical model of the SGP
The conductivity of the SGP is derived by well-known Kubo formula [[47], [48]]: In addition, where , , and are radian angular frequency, chemical potential, relaxation time and environmental temperature, respectively. And is an electron charge, is the reduced Planck’s constant, is the Boltzmann’s constant, () is Fermi–Dirac distribution. Since the
Structure design and simulation
Fig. 2 shows the unit-cell structure of our design includes three functional layers: a SGP on the top, a dielectric layer in the middle, and a continuous metallic gold film on the bottom. In addition, metal wires (Au) placed on the SGP provide the bias voltage to modulate the chemical potential of SGP. Obviously, the unit-cell structure of the designed tunable THz MMA is extremely simple, which means that it can be easily fabricated and tuned. For unit-cell structure of the MMA, the length of
Results and discussions
Firstly, to investigate the function of the SGP in our design, we design two MMA models with the SGP and non-SGP. As shown in Fig. 3 (a), the simulation results demonstrates that the MMA based on the SGP has noticeably dual-band absorption at 0.90 THz and 3.12 THz, and the corresponding absorbance is 98.2% and 91.5%, respectively, when . When the designed unit-cell structure is no SGP, there only exists one absorption peak, and the maximum absorbance is only 28.5%. In addition, loss and
Conclusion
In conclusion, we have proposed and demonstrated a tunable MMA based on the SGP for THz waves, which yields dual-band and wide-angle absorption properties. The unit-cell structure of the designed MMA is consisted of a single-patterned SGP and a loss dielectric layer on the backed continuous metallic film. The simulation has shown that this MMA achieves absorption in the lower and higher frequency regions. Since the external bias voltage can be provided by the metal wires on the SGP, the
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61605147 and U1435209), the Natural Science Foundation of Hubei province (Grant No. 2017CFB588) and the Graduate Innovation Fund of Wuhan University of Science and Technology (Grant No. JCX2016012).
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