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Abstract
A multi-band terahertz (THz) absorber based on graphene sheet and nanoribbons is proposed and investigated. In the studied frequency range, five absorption peaks are observed, with four originate from lateral Fabry-Perot resonance (LFPR) and one originates from guided-mode resonance (GMR). The LFPR and GMR peaks behave differently when geometric parameters are adjusted, which makes independent tuning possible. When period increases, the GMR peak red shifts and the frequencies of LFPR peaks remain almost unchanged. On the contrary, as nanoribbon width increases, the frequency of GMR remains almost unchanged while that of LFPRs decrease significantly. With increasing top dielectric layer thickness, the LFPR peaks blue shift while the GMR peak red shifts. In addition, the absorber has the merit of multi-band high absorptivity and frequency stability under large angle oblique incidence. The proposed terahertz absorber may benefit the areas of medical imaging, sensing, non-destructive testing, THz communications and other applications.
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1. Introduction
The field of terahertz (THz) science and technology has great potentials in medical imaging [1], non-destructive testing [2], communications [3] and etc. THz absorbers [4–13] have been research hot spots in recent years. As key materials of THz absorbers, graphene [14,15] has the advantages over noble metals [16,17] in dynamic control, quality factor and modulation depth. Graphene based single band [18,19], dual-band [20,21] and multi-band [22–31] absorbers have been proposed or demonstrated. Graphene-based rectangular gratings [22], several layers of different size graphene square rings [23], combination of graphene nanoribbon and graphene ring [25], square graphene ring with Jerusalem cross graphene sheet [27], multilayer metal-graphene metamaterials [30], ellipse-shaped graphene array [32] have been employed as key structures to implement dual or multi-band absorption. Despite the efforts, some limitations still exist, such as complicated device structures and inability to achieve independent tuning of certain resonant frequencies.
In this paper, we propose a multi-band THz absorber based on graphene with independent tunability and simple structure. Unlike proposed multi-band THz absorbers by other groups with complicated graphene or metal structures, the device presented here simply includes periodic graphene nanoribbons and a continuous graphene sheet, which facilitates the fabrication processes. The multiple absorption peaks in the investigated 3 THz to 60 THz range originate from two kinds of resonant modes, which are lateral Fabry-Perot resonance (LFPR) and guided-mode resonance (GMR). The absorption peak frequencies from different modes follow different laws when geometric parameters are adjusted. This characteristic makes it possible to tune one or several absorption peaks independently without significantly change the frequencies of the rest absorption peaks. Moreover, the multi-band high absorption property remains at large incident angle up to 70$^{\circ }$. The multi-band working frequencies, independent tunability and wide operating angles indicate that the proposed THz absorber has potential applications in the areas relate to medical imaging, sensing, non-destructive testing and THz communications.
2. Structure and simulation method
The device is schematically shown in Fig. 1. A continuous single-layer graphene sheet is embedded in the dielectric layers, which are sandwiched between an array of periodically aligned graphene nanoribbons and the back reflecting gold film. The geometric parameters are as follows unless otherwise stated: device period $p=500\mathrm {\ nm}$, graphene nanoribbon width $w=300\mathrm {\ nm}$, top dielectric layer thickness ${d}_{1}=10\mathrm {\ nm}$, substrate layer thickness ${d}_{2}=1350\mathrm {\ nm}$, gold layer thickness ${d}_{3}=50\mathrm {\ nm}$.
Fig. 1. (a) 3D schematic view of the proposed absorber based on graphene sheet and nanoribbons. (b) 2D schematic view of the proposed absorber.
The electric field of incident THz wave is parallel to the incident plane (TM polarization). As the gold thickness is much larger than the penetration depth of THz waves in gold, the transmittance of THz waves through the absorber can be neglected and the absorption $A=1-R$, where $R$ is the reflectivity of the absorber.
The refractive index of the dielectric $n$ is set to be 1.6 [33]. The relative permittivity of gold ${\varepsilon }_\mathrm {Au}(\omega )$ can be derived as [34]:
where $\omega$ is the angular frequency of THz wave, plasma frequency in gold $\omega _\mathrm {p}=1.37 \times 10^{16}\ \mathrm {rad} / \mathrm {s}$, electron collision frequency $\gamma =1.21 \times 10^{14}\ \mathrm {rad} / \mathrm {s}$ [34,35].The dielectric tensor of graphene can be expressed as [36]:
The finite element method (FEM) simulations are carried out in COMSOL Multiphysics [37]. Periodic boundary conditions are applied at both $x$ and $y$ directions. TM polarized THz wave incidents from above with incident angle $\theta$. Perfect Matching Layer (PML) boundary conditions are applied at both ends of the simulation region in the $z(-z)$ directions. The meshes are fine enough to ensure the convergence of simulation results.
3. Results and discussions
Firstly, the absorber performance under normal incidence is investigated. The absorption spectrum in 3 THz to 60 THz frequency range is shown in Fig. 2(a). Five absorption peaks with absorption maximum frequency at 8.9 THz, 23.3 THz, 36.8 THz, 39.6 THz and 48.3 THz are labeled as M1, M2, M3, M4 and M5 respectively. Accordingly, the maximum absorptivity of the five peaks are 76.1%, 85.7%, 84.5%, 73.8% and 33.9%, and the corresponding Q factors are 21.2, 51.8, 73.6, 28.3 and 130.5. Like graphene, gold is also a lossy material which absorbs part of the incident light. For clarity, the absorption spectrums contributed by graphene or gold are calculated additionally and shown in Fig. 2(a) by dotted or dashed lines respectively. In the whole frequency range investigated, the absorptivity contributed by gold is less than 2%, which indicates that graphene rather than gold dominates the light absorption.
Fig. 2. (a) Absorption spectrum of the absorber (solid line) at 1.0 eV graphene Fermi energy. The dotted and dashed lines indicate the absorption contributed by graphene or gold respectively. Five absorption peaks are labeled as M1, M2, M3, M4 and M5 respectively. (b)-(f) Z component of electric field distributions of 8.9 THz, 23.3 THz, 36.8 THz, 39.6 THz and 48.3 THz in the vicinity of graphene respectively. The dashed lines highlight the regions with both graphene nanoribbons and graphene sheet. The plus and minus signs indicate the charge distributions on the graphene sheet.
To discover the absorption mechanisms, $z$ component of the electric field distributions in $x$-$z$ plane at absorption peak frequencies in the vicinity of graphene are plotted in Fig. 2(b)-2(f). To be intuitive, the charge distributions on graphene sheet are indicated by plus and minus signs. From the electric field distributions in Fig. 2(b)-2(f), it can be seen that the five absorption peaks originate from different electromagnetic modes.
In Fig. 2(b), the $E_z$ field distribution at the left edge of the two graphene layers region (dashed line region) indicates a TM$_{0}$ mode exists between two graphene layers [38]. Due to the impedance mismatch at the two boundaries between two graphene layers region and one graphene layer regions (left and right edges of the dashed line region), the TM$_{0}$ mode propagates in the $+x$ direction and reflects back and forth at the two boundaries, forming a standing wave localized below the graphene nanoribbon. The standing wave in the dashed line region can be called a lateral Fabry-Perot resonance (LFPR). The LFPR in Fig. 2(b) is the fundamental mode, while the LFPRs in Fig. 2(c), 2(d) and 2(f) are high-order modes. The mode order of a LFPR can be labeled by an integer $K$ counting the electric field nodes, which is equal to multiples of half-wavelengths. For normal incidence, only odd $K$ modes can be excited since the effective charge dipole provides the restoring force for collective oscillating waves, which is similar to a single graphene nanoribbon excited under normal incidence [39]. For even $K$ modes, the induced charge density has even symmetry, thus zero mode moment, which forbids direct excitation by normal incident light. The frequencies of LFPR modes can be written as [40]:
where $w$ is the nanoribbon width, $c$ is the speed of light, $n_\mathrm {M}$ is the effective modal index of the standing wave.Unlike the electric fields of LFPRs in Fig. 2(b), 2(c), 2(d) and 2(f), the electric fields in Fig. 2(e) mainly concentrate outside the dashed line region. The electric field profile demonstrates a surface plasmon polariton (SPP) forming around the graphene region. Without periodic graphene nanoribbons, the excitation of SPP on graphene sheet is hard to realize due to the momentum mismatch between light in free space and SPP on graphene. The periodic graphene nanoribbons act as a grating that compensates the momentum mismatch and enables the excitation of guided mode resonance (GMR). For normal incidence ($\theta =0$), the GMR can be excited when the nanoribbon period $p$ matches wavelength of the SPP.
For GMR in monolayer graphene on diffractive grating, the resonant frequency $\omega _\mathrm {GMR}$ can be expressed as [36]:
Compare Eq. (4) with Eq. (5), one can discover that the frequency of a LFPR is inversely proportional to graphene nanoribbon width $w$, while the frequency of GMR is inversely proportional to the square root of $p$. In principle, we can tune the LFPR or GMR frequencies independently by altering $w$ or $p$ individually.
To confirm the speculation, we simulate the performance of device with period $p$ varying from 400 nm to 1000 nm while keeping the graphene nanoribbon width $w$ to be 300 nm unchanged. The results are shown in Fig. 3. One can clearly see that as $p$ increases, the GMR peak red shifts significantly while the frequencies of LFPRs remain nearly constant. We list the frequencies of GMR and LFPR modes at certain $p$ values in Table 1. When the period increases from 400 nm to 800 nm, the LFPR ($K$=1) and LFPR ($K$=3) peaks red shift 0.8 THz and 0.6 THz respectively, while the LFPR ($K$=5) peak blue shifts 0.2 THz due to the coupling of GMR and LFPR ($K$=5) at $p=550\ \mathrm {nm}$. In contrast, the GMR peak red shifts as large as 13.1 THz as $p$ increases from 400 nm to 800 nm. By adjusting period, the GMR frequency can be independently tuned in a wide range with little affect on frequencies of LFPR peaks. Besides, the obvious absorption spectrum on the right side of GMR and LFPR ($K$=5) originates from higher mode of GMR with larger frequency and half SPP wavelength. The absorption peak frequency of the higher GMR mode shows similar red shift trend as $p$ increases.
Table 1. Absorption peak frequency (THz) at different periods.
On the other hand, we also do simulations with graphene nanoribbon width $w$ varying from 50 nm to 400 nm while keeping $p$ to be 500 nm constant. As shown in Fig. 4, the LFPR peaks red shift dramatically with $w$ increasing, while in contrast the GMR peak moves slightly, particularly in the $w=200 \ \mathrm {nm}$ to $w=350\ \mathrm {nm}$ range. The frequency gap (about 2 THz) of GMR spectrum at $w=170\ \mathrm {nm}$ is due to the mode coupling between LFPR ($K$=3) and GMR, and the coupling is stronger than that between LFPR ($K$=5) and GMR at $w=270\ \mathrm {nm}$. We list the absorption peak frequencies at different $w$ values in Table 2. One can see that the frequency decreases of LFPR ($K$=1), LFPR ($K$=3) and LFPR ($K$=5) are 4.5 THz, 12.1 THz and 17.6 THz respectively as $w$ increases from 200 nm to 350 nm. In sharp contrast, the frequency of GMR only decreases 0.1 THz in the same circumstance. Therefore, the LFPR peaks can be independently tuned in wide frequency ranges by adjusting nanoribbon width, while the GMR peak frequency is almost unaffected.
Table 2. Absorption peak frequency (THz) at different nanoribbon width.
Besides period and nanoribbon width, the thickness of top dielectric layer can also be changed to tune the absorber. The absorption map of the THz absorber at different top dielectric layer thicknesses ($d_\mathrm {1}$) is shown in Fig. 5. As $d_\mathrm {1}$ increases, the frequencies of LFPRs and GMR show opposite trends. The LFPR absorption peaks blue shift while the GMR absorption peak red shifts when $d_\mathrm {1}$ increases. It can be calculated from Table 3 that as $d_\mathrm {1}$ increases from 5 nm to 30 nm, the frequencies of LFPR ($K$=1), LFPR ($K$=3) and LFPR ($K$=5) increase 7.8 THz, 16.9 THz and 19.3 THz respectively, while the GMR frequency decreases 3.4 THz. By adjusting the top dielectric layer thickness, the LFPR and GMR absorption peaks can be tuned along different trends.
Fig. 5. Absorptivity as a function of top dielectric layer thickness and incident THz wave frequency.
Table 3. Absorption peak frequency (THz) at different top dielectric thickness.
The above discussions are limited to normal incidence. From practical point of view, the absorber performance under oblique incidence is an important issue worthy of further investigations. Absorptivity map of the absorber under THz incidence at incident angles ranging from 0$^{\circ }$ to 81$^{\circ }$ is shown in Fig. 6. The frequencies of LFPR peaks stay almost stable under oblique incidence, while the GMR frequency shows small increase under oblique incidence. When $\theta =60^{\circ }$, the frequency shifts compared with $\theta =0^{\circ }$ are 0.1 THz, 0 THz, $-0.1$ THz and 0.3 THz for LFPR ($K$=1), LFPR ($K$=3), LFPR ($K$=5) and GMR respectively. Under oblique incidence, the new absorption spectrum between LFPR ($K$=5) and GMR is LFPR ($K$=6), which is excited due to the excitation of GMR and the coupling between GMR and LFPR ($K$=6). The multiple absorption peaks maintain high absorptivity at incident angle up to 70$^{\circ }$.
Given the above, an independently tunable multi-band THz absorber is proposed with incident angle-insensitive and wide angle high absorption characteristics. For comparison, the device performances are list in Table 4 together with performances of multi-band tunable absorbers presented by other groups. Among the absorbers, our absorber has the most absorption bands and the largest tunable frequency range, which is a magnitude higher than that in Ref. [29] and [30]. Although the tunable frequency range of absorber in Ref. [28] can reach approximately 10 THz, the absorption peaks can not be tuned independently and the absorptivities of four peaks are all below 40%. Besides, employing graphene instead of gold (as in Ref. [30]) as the key absorbing material enables much larger Q factors, which facilitates many applications. To the best of our knowledge, the independent tuning mechanism of the absorber has not been found in other publications yet. What’s more, the independent tuning strategy proposed here may also be applied to other 2D materials, such as transition metal dichalcogenides (TMDCs), black phosphorus and etc. The proposed absorber shows broad prospects of applications in a variety of fields, including medical imaging, sensing, non-destructive testing and THz communications. Although independent frequency tuning of LFPR modes individually has not been realized by now, it is an interesting research target which is worthy of further investigations.
Table 4. Comparison of different multi-band tunable absorbers.
4. Conclusions
In summary, a multi-band THz absorber based on periodic graphene nanoribbons and graphene sheet is proposed and investigated. The multiple absorption peaks originate from LFPRs and GMR, which follow different function relationships with device geometric parameters. Through altering device period or nanoribbon width individually, one can independently tune the frequencies of absorption peaks based on GMR or LFPRs. When device period increases from 400 nm to 800 nm, the GMR frequency decreases from 43.9 THz to 30.8 THz, while the LFPR peaks shift less than 1 THz. In contrast, as the nanoribbon width increases from 200 nm to 350 nm, the frequency increase of LFPR ($K$=1), LFPR ($K$=3) and LFPR ($K$=5) are 4.5 THz, 12.1 THz and 17.6 THz respectively, while the GMR frequency shifts less than 0.2 THz. By increasing top dielectric layer thickness, one can simultaneously increase the LFPR frequencies while decrease the GMR frequency. The tunable frequency range is a magnitude larger than reported multi-band absorbers. At large incident angles, the absorber maintains high absorptivity with absorption peak frequencies almost unchanged. The independently tunable multi-band and incident angle-insensitive graphene THz absorber with simple structure shows promise in the application areas of medical imaging, sensing, non-destructive testing, THz communications and other applications.
Funding
National Natural Science Foundation of China (11664020, 61665004); Project for Distinguished Young Scholars of Jiangxi Province (20171BCB23098); Natural Science Foundation of Jiangxi Province (20202BABL201020).
Disclosures
The authors declare no conflicts of interest.
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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