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Abstract
A dual-frequency broadband terahertz metamaterial absorber, composed of a periodically ellipse-shaped graphene array placed over a thin SiO2 layer and a lossy polyimide layer backed with a gold ground, is proposed in this article. The numerical simulation results reveal that the effective absorption band (absorption > 0.9) ranges from 0.3 THz to 0.75 THz and 1.57 THz to 1.87 THz, with a favorable independence of incident angle. Furthermore, replacing the gold ground with a frequency selective surface inserted with graphene, another absorbing peak appears between two broad absorbing bands and can be continuously tuned from 1 THz to 1.3 THz by controlling the chemical potential of graphene from 0 eV to 0.5 eV in the FSS. To improve the absorbance of the tunable absorbing peak, a backed cavity is added to the structure, which promotes the absorbance from 0.6 to more than 0.9 with unaffected tunability. These designs overcome limitations of traditional absorbers and have promising applications for filtering, detecting, and sensing.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The terahertz (THz) range (0.1-10THz) of the electromagnetic spectrum, lying between the microwave and far infrared frequencies, has attracted rapidly increasing interests due to their potential applications in wireless communication, imaging, and sensing [1–3]. Various THz devices, such as filters, emitters, detectors, and absorbers, have been developed, among which the metamaterial absorber (MA) is believed to fabricate more powerful modulators, filter, stealth materials, and sensors [4–7]. The absorbers offer a wide variety of practical applications. The absorption in a wide range of frequency region leads to no reflection, which can be used for cloaks and filters. Besides, MAs are tunable with respect to their operational wavelength, they can be used as spectrally sensitive detectors or sensors [8]. Much work has done in both integrating MAs into existing designs and creating novel devices based on MAs to provide detection and sensing throughout the electromagnetic spectrum, such as pyroelectric detector [9], plasmonic sensors [10] and so on. To achieve high absorption, the electromagnetic wave should be restricted to the lossy materials [11, 12]. Graphene, a 2-D lossy material consisting of the carbon atoms arranged in a honeycomb crystal lattice, has become one of the most promising materials in the design of MAs because of its unique properties, including the high carrier mobility, excellent mechanical properties, the capacity to support surface plasmons, and flexibility [13–22]. However, it is rather hard to design the THz MA by a single sheet of undoped graphene layer whose light absorption is close to 2.3% [23]. To enhance the absorption intensity, patterned graphene absorbers with periodic structures have been proposed including cross, micro-ribbons, fishnet and so on [24–26]. Nevertheless, to sustain high absorption, a majority of MAs based on graphene have narrow bandwidth and limited numbers of operating bands, limiting their scope of application. At present, one of the hottest research directions in absorber is to find an effective approach to overcome the limitation of narrowband. Therefore, there is increasing interest to make graphene absorbers with broad bandwidth and dual/multi bands.
In order to expand the bandwidth, various structures have been investigated. An effective method is to take advantage of multiple patterned graphene layers, which are biased at different voltage and backed with dielectric substrates stacked on top of each other [27]. Another typical structure, integrating different multiple resonators within a unit cell, can shape broadband absorption due to the overlap of adjacent resonances [28]. Recently, an absorber based on single-layered graphene ribbons with gradient width has been proposed to reduce the complexity of structure while maintaining broadband absorption performance [29]. A dynamically tunable broadband absorber derived from graphene analog of electromagnetically induced transparency has been also researched [30]. Moreover, a near self-complementary MA with periodically sinusoidally-patterned graphene layer realizes near-unity broadband absorption for both TE and TM polarizations [31]. However, there are some unavoidable limitations on most of the broadband graphene-based MAs mentioned above, such as angle sensitivity, single absorbing band, and poor tunability. Besides, controlling multi-layered patterned graphene or integrating different resonators requires both of the fine fabrication technology and accurate basing voltage, which brings great challenge to the realization of broadband MA. Further, it is rather difficult to add another absorbing peak at specified frequency band once the MA has been designed. It is still a challenge to realize broad bandwidth and multiband in a single structure Hence, the independence of incident angles and multi-frequency broadband MA based on simple graphene structure is still needed to be investigated ulteriorly.
In this paper, we proposed a multi-frequency broadband THz MA, which consists of a periodically ellipse-shaped graphene layer placed over a SiO2 dielectric and a lossy polyimide layer backed with gold ground. The gradient width of elliptic graphene excites continuous resonance so that the broadband absorbing band is formed. By arranging elliptic patches in equilateral triangle, the MA forms not only an absorbing band by electric resonance caused by localized surface plasmon resonance (LSPR) but also another one through magnetic resonance between the graphene array and gold ground. Moreover, a frequency selective surface (FSS) is adopted to substitute the gold ground so as to change the transmission characteristic in the gap of two absorbing bands without affecting the absorption characteristic. Further, by placing a gold reflector at the bottom of the MA backed with the band-pass FSS, a backed reflexible cavity is constituted, thus forming another absorbing band between the original two via the destructive interference of reflected waves. The location of the middle absorbing band, affected by the chemical potential of the graphene inserted in the FSS, can be flexibly tuned. The design scheme is capable to develop various graphene-based broadband absorbers at other frequency region due to the scalablility of metamaterial.
2. Dual-band metamaterial absorber
The structure of the proposed dual-broadband metamaterial absorber, shown in Fig. 1, which is consisted of four layers: a chemically doped graphene layer, a thin SiO2 layer, a lossy polyimide layer, and a gold ground. The top patterned layer is an ellipse-shaped graphene array, arranged in the equilateral triangle. The gap between graphene patches is denoted as g, and the major axis and minor axis of the ellipse are represented by a and b, respectively. It is periodic in the directions of incident electric and magnetic fields with the period of w and l. The SiO2 (εsio2 = 4 [32]) dielectric substrate with thickness tsio2 is conducive to the growth and etching of graphene while the lossy polyimide (εP = 3.5 + 0.02i [33]) with thickness tP1 acts as a spacer in the design. The thickness of the gold ground (conductivity = 4.561 × 107 S/m [34]) tAu is much larger than typical skin depth in low THz so that the transmission wave is suppressed by the gold reflector.
Fig. 1 Schematic geometry of the dual-band MA. The values of the structure parameters are set as l = 312, w = 270.2, a = 150, b = 19.5, g = 6, tg = 0.001, tsio2 = 1, tP1 = 70, tAu = 0.5, unit: μm.
The graphene is numerically modelled by an effective medium with thickness tg, whose permittivity is calculated by εg = ε0 + iσg/(ωtg) [35]. The surface conductivity of graphene σg, which can be measured directly in a wide range of frequencies, consists of interband and intraband transitions according to Kubo formula [36, 37]:
where kB is Boltzmann’s constant, e is the charge of an electron, ℏ = h/2π is the reduced Planck’s constant, EF is the chemical potential (Fermi energy), ω is frequency of the electromagnetic wave, τ is the relaxation time, T is room temperature as 300 K and H(Ω) is defined as:In the THz region, the intraband contribution appears to dominate and the interband conductivity contribution can be neglected. The surface impedance of a graphene monolayer is obtained through the conductivity . Moreover, the frequency dependent conductivity of graphene at the selected values of the chemical potential is shown in Fig. 2. It can be seen that the slope of imaginary and the value of real part are determined by the chemical potential, which can be tuned by controlling the chemical or electrical doping, thus changing the absorption. In this study, the full-wave simulation is conducted in CST Microwave Studio. Perfect magnetic conducting (PMC), perfect electric conducting (PEC) and open boundary conditions have been applied to different boundaries, to mimic the periodic structure. Waveguide ports have been utilized for the excitation. The frequency-domain finite element method (FEM) solver is adopted considering the large contrast in the dimensions of the graphene layer. Adaptive tetrahedral mesh refinement has been used to enhance precision of simulation. The absorbance is calculated by A = 1-R-T (or A = 1-\S11\2-\S21\2), where R and T are the reflectance and the transmittance, respectively [38]. The transmittance T is 0 due to the shielding effectiveness of gold ground, thus the calculation of absorption can be simplified to A = 1-R.
The absorption spectrums for different relaxation time and chemical potentials (Fermi energies) have been calculated and displayed in Fig. 3. The relaxation time is calculated by τ = EFμ/(eυF2), where υF is Fermi velocity, μ is the carrier mobility. The carrier mobility can be significantly enhanced changing the surrounding environment, thus increasing of relaxation time [39]. With EF = 0.3 eV, the position of absorbing bands remains unchanged while the absorption in the central range of operating bands first increases and then drops as τ increases. When τ = 0.3 ps, the charge carriers make the plasma oscillation absorption reach saturation. Keeping τ = 0.3 ps, two absorbing bands experience slight blue shift and the absorption increases gradually simultaneously when EF changes from 0 eV to 0.5 eV, which is attributed to the decrease of effective index of the graphene [40]. Due to the discrete structure, the ellipse-shaped graphene patches is chemically doped instead of electrical tuning.
Fig. 3 Absorption spectra of the dual-band MA (a) different relaxation time (b) different chemical potentials.
To research the absorbing properties of the proposed structure, the absorption spectra with EF = 0.3 eV and τ = 0.3 ps is simulated under normal incidence. As shown in Fig. 4, there are two broad effective absorption bands (absorption > 0.9) with the central frequencies of 0.53 THz and 1.72 THz, respectively. The underlying physical mechanism of absorption for this structure is related to the electric resonance in the patterned graphene array triggered by localized surface plasmon resonance (LSPR) and magnetic resonance between the graphene array and gold ground. Moreover, the formation of broadband absorption is associated with the continuous resonance caused by gradient width of elliptic graphene patch. To give a further understanding to the absorbing mechanism, the electric field distributions on the front and side of the MA are presented in Fig. 5. The first absorbing band ranges from 0.3 THz to 0.75 THz. It is depicted in Fig. 5(a), (d) that the extremely confined fields are distributed between unit cells at 0.33 THz and 0.68 THz as a result of the electric dipole resonances excited by the incident wave. Besides, on the surface of graphene array, most of the electric fields are confined to the curved edge of elliptic graphene patches arranged sideling due to effects of the LSPR [40]. Especially, different absorbing frequencies correspond to different positions of elliptic graphene patches. The absorption at higher frequency (0.68 THz) occurs at the end of graphene patch with smaller width, while that of the lower frequency (0.33 THz) corresponds to the median width positions, thus forming a wide absorbing band. Moreover, observing the electric field along the propagation direction, the MA traps the field around the top layer of graphene, which results from the LSPR. As for the second absorbing band of 1.57 THz to 1.87 THz, it can be seen in Fig. 5(c), (d) that electric field focuses on the elliptic patches, which are perpendicular to direction of the incident electric field. The larger the width of these patches is, the lower frequency of absorption becomes, which further confirms that a broadband absorber can be achieved by graphene patches with gradient width. Differing from the first absorbing band, the electric fields of 1.6 THz and 1.84 THz oscillate between the graphene array and gold ground instead of being confined to the top layer, which illustrates that the second one is formed by the magnetic resonance between graphene top and gold bottom. From another point of view, this electric dipole is greatly coupled with its own image, which oscillates in antiphase on the other side of the gold film, thus forming a magnetic polariton.
Fig. 5 Electric field distribution of the dual-band MA on the top and side (a) 0.33 THz (b) 0.68 THz (c) 1.6 THz (d) 1.84 THz.
Further, the robustness of the MA under oblique incidence is investigated. The incident angle defined as the angle between the incident wave and the surface normal of the MA. Figure 6 gives the simulated absorption as a function of frequency and incident angle. The red strip on the bottom indicates the angle-independent high absorption of the first operating band, which is a significant characteristic of graphene plasmon resonance [29]. The absorbing frequency of the second operating band exhibits slight blue shift in absorption spectra when the incident angle increases from 0° to 60°. The variation of incident angle changes the propagation direction of electromagnetic wave between the graphene array and gold ground, thus disturbs the magnetic resonance of the second absorbing band. Nevertheless, the impact on the broadband MA is limited, and the proposed structure can still work with 90% absorbance over a wide range of incident angle even up to 60°.
3. Tunable triple-band absorbing metamaterial
As seen in Fig. 6, there is a reflection gap between the two absorbing bands. We replace the gold ground of the MA with a graphene-gold frequency selective surface (FSS), which plays the role of reflector in original absorbing bands while leaves a partial pass band in the gap. Due to the losses of gold and graphene in the THz, most of the energy is absorbed by the unit cell of FSS at the resonance frequency. Furthermore, controlling the chemical potential of the graphene inserted in the FSS via bias voltage, the position of the partial absorption peak can be adjusted flexibly.
3.1 Frequency selective surface
As illustrated in Fig. 7, the FSS is consisted of two periodic layers divided by a thin dielectric layer of lossy polyimide. The first layer is composed of a square loop aperture structure and graphene patches placed between the gaps of the inner patch and outer grid, while the second one is formed by gold strips. Applying a DC bias in the two layers, the chemical potential of graphene can be tuned flexibly, thus changing the surface impedance [41, 42]. All the material parameters are the same as those of dual-band MA in section 2. To explore the physical mechanism, the equivalent circuit model of the FSS is given in Fig. 8 according to the equivalent circuit theory [43–45]. From the Fig. 2, we can see that the real part of the surface impedance remains almost constant while the imaginary part increases linearly with the rise of frequency at low-terahertz region, which behaves as a typical LR series model. The graphene patches in the gaps can be modeled as the series model of Rg and Lg. In first layer, the patch inserted with graphene is modeled as the parallel of split capacitance Cf and equivalent circuit of graphene patches, in series with the inductance Lf of external gold grid. The lossy polyimide is regarded as a transmission line. In the second layer, the gold strips are viewed as a paralleled inductance Lb. The equivalent circuit constructs a typical bandpass filter, but part of the energy in the pass band is dissipated by Rg. Regulating the voltage between the layers, the chemical potential of graphene changes rapidly, so does the surface impedance. As a consequence, the position and transmission characteristics of resonant point of the FSS can be controlled.
Fig. 7 Schematic geometry of the FSS. The values of the structure parameters are set as l1 = 78, w1 = 67.55, a1 = 62.4, b1 = 47.28, a2 = 14.04, b2 = 10.81, d1 = 6, tg = 0.001, tP2 = 2, tAu = 0.5, unit: μm.
The simulated spectrum response of the FSS is shown in Fig. 9(a). As the chemical potential varies from 0.1 eV to 0.5 eV, the fluctuation of absorption and bandwidth is relatively small while the central frequency blue-shifts from 1.34 THz to 1.65 THz obviously. The Fig. 2 shows a negative correlation of the chemical potential and the slope of the imaginary part of the surface impedance, which has direct proportion with the equivalent inductance Lg. Meanwhile, the resonance frequency of the equivalent circuit is inversely associated with total inductance, which reduces with the decrease of Lg. Therefore, the resonant point moves to higher frequency with the increase of chemical potential. Except 60% energy absorbed by the graphene and gold, the rest part is reflected or transmitted by the FSS. When replacing the gold film of the dual-band MA with FSS, a polyimide layer with thickness tP1 will be placed above the FSS. Adding dielectric slab with finite length to the one side of the periodic structure not only changes the shape of resonant curves, but also shifts the resonance frequency f0 to somewhere between f0 and , where εr represents the relative permittivity of the dielectric slab [46]. The simulation results of the FSS integrated with polyimide layer of the MA are presented in Fig. 9(b). The resonance frequency decreases about 0.3 THz compared with that of FSS without the polyimide layer and the bandwidth narrows as well, which is consistent with of Ref [46]. These changes ensure that the FSS plays the role of reflector in the two broad absorbing bands of the MA effectively, and make the operating band of FSS fall into the absorbing band gap.
Fig. 9 Reflection, transmission and absorption through the FSS (a) without polyimide layer (b) with polyimide layer.
3.2 Triple-band absorbing metamaterial
The structure of the triple-band absorbing metamaterial (AM) is shown in Fig. 10. As a substitute for the gold film, the FSS is attached to the electrodes so as to control the chemical potential of graphene inserted in the gap of the square loop aperture flexibly. The transmission and absorption characteristics are clearly identified in the spectra provided in Fig. 11 when EF = 0.1 eV. There are two broad absorbing bands ranging from 0.3 THz to 0.75 THz and 1.61 THz to 1.87 THz, and a partial absorption peaking at 1.15 THz. As the two broad absorbing bands are almost coincident with absorber backed with gold film, their physical mechanism is the same as that of the dual-band metamaterial absorber. At 1.15 THz, the absorption reaches 0.6 since the photons excited by resonance are dissipated in the graphene and lossy gold while others are reflected and transmitted, accounting for almost 0.2, respectively. In other words, the absorption of triple-band absorbing metamaterial is the superposition of absorption of dual-band metamaterial absorber and FSS.
It is shown in Fig. 12 that the frequency of the narrow absorbing band increases gradually without changing the frequency range and absorbance of two bands on both sides with the growth of the chemical potential of graphene of the FSS. As it varies from 0 eV to 0.5 eV, being consistent to the change rule of resonance frequency of the FSS, the middle absorbing peak blue shifts from 1 THz to 1.3 THz, moving towards to the second broad absorbing band. Meanwhile, absorbance increases gradually due to the superposition effects of the FSS and the original MA. This AM with flexible tunability may be used as a tunable attenuator or spatial modulator at THz frequencies. In order to further improve the absorbance of the tunable band, a backed reflexible cavity can be added to the structure, which is detailedly discussed in the next section.
4. Controllable triple-band metamaterial absorber
As shown in Fig. 13, a lossy polyimide layer backed with gold film is placed behind the AM of section 3.2 to enhance its absorption. It is present in Fig. 12 that the position of the narrow resonant point approaches 1 THz when EF = 0 eV, therefore, the length of the additional polyimide is chosen as tP3 = 40 μm, about a quarter wavelength of 1 THz with this substrate. Except the absorbed waves, the others are reflected and transmitted by the FSS at resonant frequency. Transmitted waves are reflected back by the gold reflector, and some of them come out of the FSS with a phase difference of 2βPtP3 = π, where βP represents the propagation constant of polyimide. This process is repeated many times so that these partial reflected waves destructively interfere with each other, suppressing the reflection and improving the absorbance.
To research the performance variation, Fig. 14 compares the absorptions of the dual-band MA, the tunable triple-band AM, and the controllable triple-band MA when the chemical potential of graphene in FSS is tuned to 0.1 eV. In 1.1 THz, the absorbance increases from 0 to 0.6 to 0.97, the variation trend of which is consistent with the excepted theoretical analysis. The first wide absorption band is almost not changed while the second one moves to higher frequency after the substitution of FSS. It is because the thickness of FSS has little effect on LSPR while causes perturbation to the magnetic resonance between the ellipse-shaped graphene array and FSS, which is the source of the second absorption band.
As the chemical potential of graphene of the FSS increases from 0 eV to 0.5 eV via controlling DC voltage, the absorption spectra is given in Fig. 15. Compared with Fig. 12, the variation trend of the absorption is mostly the same, except the absorbance of the narrow tunable absorbing band, which is greatly enhanced. The absorbance of the narrow band keeps more than 0.9, but it decreases slightly with the growth of the chemical potential since tP3, designed under the condition of EF = 0 eV, deviates from quarter wavelength of resonant point slowly.
5. Conclusion
In conclusion, a dual-frequency broadband terahertz metamaterial absorber based on ellipse-shaped graphene array has been designed and demonstrated theoretically. Two absorption bands are realized by the electric resonance in the patterned graphene array caused by localized surface plasmon resonance and magnetic resonance between the graphene array and gold ground, respectively. The gradient width of elliptic graphene patch excites the continuous resonances of the absorber, thus expanding the operating band. Besides, another tunable absorption peak appears in the gap of two absorption bands via substituting a gold-graphene FSS for the gold ground. Additionally, absorbance of the tunable absorption peak is greatly enhanced with the introduction of a lossy polyimide layer backed with gold film due to the destructive interference of partial reflected waves. This work offers a new perspective on the design of multi-band terahertz broadband absorbers and can be scalable to other terahertz region for various promising applications.
The designed triple-band metamaterial absorber can be realized experimentally by the following procedures [47, 48]: monolayer graphene grown by chemical vapor-phase deposition on copper foil is transferred to SiO2, and then processed to ellipse-shaped patches by the e-beam lithography and oxygen plasma etching; processing graphene patches on the substrate spacer with similar method; patterning the gold-polyimide-gold structure to construct the FSS; placing the SiO2 on the smooth side of the spacer while placing the FSS on the graphene-etched side; adding a polyimide layer backed with gold film at the bottom to enhance absorption.
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