Tunable broadband terahertz absorber based on multilayer graphene

Vol. 26, No. 24 | 26 Nov 2018 | OPTICS EXPRESS 31693

Tunable broadband terahertz absorber based on multilayer graphene-sandwiched plasmonic structure YIJUN CAI1 AND KAI-DA XU 2,3,* 1

Fujian Provincial Key Laboratory of Optoelectronic Technology and Devices, Xiamen University of Technology, Xiamen 361024, China 2 Department of Electronic Science, Xiamen University, Xiamen 361005, China 3 Department of Electrical and Computer Engineering, University of Wisconsin–Madison, Madison, WI 53706, USA *[email protected]

Abstract: We numerically demonstrate a tunable broadband terahertz absorber with nearunity 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, multinarrowband 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 #347809 Journal © 2018

https://doi.org/10.1364/OE.26.031693 Received 10 Oct 2018; revised 6 Nov 2018; accepted 12 Nov 2018; published 15 Nov 2018


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. Reference

a b

Bandwidtha

fc

Type

[18] [27]

0.60 THz 0.52 THz

Tunable 0.79 THz

Single layer Single Layer

[32]

0.46 THz

Tunable

Single Layer

[33] [34]

2.7 THz 2.57 THz

3 THz 1.84 THz

Multilayer Multilayer

[35] This work

6.9 THz 0.76 THz

8.15 THz Tunable

Multilayer Multilayer

Bandwidth of absorption above 90% Angular stability marked with NM means not mentioned in the reference.

Angular Stability b

NM TE up to 58° TM up to 59° TE up to 60° TM up to 60° NM TE up to 40° TM up to 50° NM TE up to 60° TM up to 62°

Fabrication difficulty Easy Easy Not easy Easy Not easy Not easy Easy


2. Modeling g and parame eters

Fig. 1. 1 (a) Perspective view and (b) crross-section view of proposed threee-layer graphene-sandw wiched plasmonic absorber (GSPA). The symbols w1 , w2 and w3 repressent the widths off differeent graphene layeers, respectively. The T symbols t annd d represent thee thickness of thee upperr three Al2O3 layerrs and bottom Al2O3 layer, respecttively. The symbool p represents thee period dicity of the period dic structure.

A schematic drawing of the proposed thrree-layer graphhene-sandwichhed plasmonic absorber hown in Fig. 1.. The structuree consists of thhree graphene nanoribbons oof infinite (GSPA) is sh length sandw wiched between n Al2O3 layers with a relativve permittivityy of ~3.2 [36].. The top dielectric layeer has a neglig gible effect on the absorptionn performancee due to the waavelength much larger than t in th he terahertz reegime, but itt can keep thhe top grapheene from s graaphene-dielectrric structure is mounted environmentaal-induced degrradation. The sandwiched on a full refleective gold mirror. The gold d mirror is thicck enough to bblock the inciddent wave and no energy y is allowed to o transmit throu ugh the absorbber. Furthermoore, the reflecteed energy is suppressed by electromag gnetic losses in n the lossy grapphenes, resultinng in strong abbsorption. nd and tunablle properties of o GSPA are investigated uusing finite inntegration The broadban technique (FIIT) via simulaations using CST C Microwavve Studio, whhich numerically solves Maxwell’s eq quations under periodic boun ndary conditionns in the x andd y directions and open boundary con nditions in the z direction. Ad daptive tetraheddral mesh refinnement is appliied for all simulations. The T plane wav ve is incident downward d from m the top surfaace of the absoorber. The wavelength deependent absorrption rate A(λλ) can be expreessed as A(λ) = 1 − R(λ) − T(λ), where the reflection R(λ) is equal to |S11(λ)|2 an nd transmissionn T(λ) is givenn by |S21(λ)|2. Since the p the do ownward wavee propagation, the transmissiion T(λ) is reggarded as gold mirror prevents zero over the entire waveelength range of interest. C Consequently, A(λ) = 1 − R(λ). In w suppose thaat graphene is an a anisotropic dispersive dieelectric materiaal with an simulations, we = effective relattive permittivitty tensor ε as


0 ε xx (ω ) = ε =  0 ε yy (ω ) 

0

0

0 0  ε zz 

(1)

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) as

ε in (ω ) = ε xx (ω ) = ε yy (ω ) = ε 0 +i

σ (ω ) Hω

(2)

where 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]

σ (ω , μc , Г , T) = σ intra + σ inter σ intra =

∞  ∂f (ξ , μ , T) ∂f (−ξ , μc , T)  je 2 c ξ d − d d ξ  0 ∂ξ ∂ξ π  (ω − j 2 Г )   2

σ inter = −

je 2 (ω − j 2 Г ) ∞ f d (−ξ , μc , T) − f d (ξ , μc , T) 0 (ω − j 2 Г )2 − 4(ξ / )2 dξ π 2 f d (ξ , μc , T ) = (e(ξ − μc )/ kBT + 1) −1

(3)

(4)

(5) (6)

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 is

σ=

ie2 μc π  2 (ω +iτ -1 )

(7)

where 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.


3. Results and a discussio ons

Fig. 2. 2 Light absorption n of three-layer GS SPA (a) under TM M and TE incident llight and (b) usingg differeent thickness of lo ower Al2O3 layer, for w1 = 0.155 μm m, w2 = 0.170 μm, w3 = 0.180 μm, p = 0.25 5 μm and t = 0.5 μm, μ under normal incidence.

First, we stud dy the absorptio on properties of o the proposedd three-layer G GSPA under noormal TM and TE incideence with mag gnetic and elecctric fields Hy aand Ey, respecctively, perpenddicular to the x-z planee as shown in n Fig. 2(a). Th he chemical ppotential of thhe graphene iss initially assumed to bee µc = 0.2 eV, while the relax xation time is set as 0.1 ps. T The electric fieeld of TE incidence is parallel p to the graphene g ribbon ns (y-axis), in which conditioon plasmonic rresonance is poorly exciited. In contrast, the electric field f of TM inccidence is alonng the x-axis, w which will excite carriers of graphene to vibrate in the finite widtth and induce the localized graphene mon (GSP). Beecause the tran nsmission is ccompletely supppressed by thhe bottom surface plasm gold mirror, the t maximum absorption of the absorber ccan be achieveed when the bbroadband impedance matching m condiition of the terahertz inciddence is satisffied. The absoorber has broadband absorption with a 90% absorbaance bandwidthh of 0.70 THz,, from 5.78 TH Hz to 6.48 nter frequency fc can be obtaained by fc = (ff- + f+)/2 = 6.113 THz, wheree f- and f+ THz. The cen represent the low and upperr frequency ed dges of 90% abbsorption, resppectively. The ffractional bandwidth, th he ratio of the absolute bandw width to the c enter frequenccy, is about 11.4%. The effects of pollarization depeendence imply a promising ppotential for appplications of polarized light filters. The T properties with w TM incid dent light are foocused on in thhe following ddiscussion because of low w absorption raate of the TE in ncident light. The thick kness of the lower l Al2O3 layer l d affectts the GSPA performance, thus the absorption spectra under diffferent d values are shown inn Fig. 2(b). As d decreases frrom 8 μm a rate and the bandw width drop sharrply. This is atttributed to thee decrease to 4 μm, the absorption of the effectiv ve thickness of o the Fabry-Peerot resonator, which is form med by grapheene layers and the gold mirror. m


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.

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. 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: A(λ ) = 2π

c

λ

ε ''  El dV 2

V

(8)

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 grapheene ribbon is reelatively weakk compared witth the 1st hene ribbons. This is attributed to the resoonance frequenncy of the 3rd graphene and 2nd graph ribbon is arou und 5.86 THz, which w is a littlee away from thhe simulated frrequency 6.38 T THz. In contrasst, for f = 5 TH Hz as presented d in Figs. 4(b) and 4(d), therre is few enhannced near field for absorrption enhanceement in graphene ribbons beecause this freqquency is far aw way from all the plasmo onic resonance frequencies off these three grraphene ribbonns on the spectrrum.

Fig. 4. 4 Simulated averaage electric field intensity distributtions. Figure 4(a)) and 4(b) presentt sectio onal views at the in-plane across thee 1st graphene forr NGL = 3 at the frequency of 6.388 THz and a 5.00 THz resp pectively. Figure 4(c)-4(f) 4 present ccross-section view ws for NGL = 3 att the freequency of 6.38 THz, T 5.00 THz, 6.11 THz and 5.866 THz respectivelyy. Figure 4(g) andd 4(h) present p cross-sectio on views for NGL L = 2 and NGL = 1 at the frequencyy of 6.38 THz. Thee dimen nsions in the GSPA A are w1 = 0.155 μm, μ w2 = 0.170 μm m, w3 = 0.180 μm, p = 0.25 μm, d = 8 μm an nd t = 0.5 μm. Fou ur unit cells are plo otted in the figure.

As shown n in Fig. 4(e), at a the resonancce frequency oof the 2nd grapphene ribbon ((f2 = 6.11 THz), the electric field is dramatically d en nhanced and cooncentrated suurrounding the edges of the three graaphene ribbonss, especially th he 2nd ribbonn. This originaates from the fact that resonance freequencies of th hese three grap phene ribbons are not far aw way from the ssimulated frequency 6.1 11 THz. Thereefore, neighborring graphene ribbons are cclose to each oother, the evanescent fieeld scattered by y one graphenee ribbon is connsiderably stronng in the vicinnity of the other graphen ne ribbon comp pared to the excciting field, annd this leads to the intense cooupling of scattered field d from each graaphene ribbon. As a consequuence, the supeerposition of thhe inverse optical fields that are inducced by electric dipole excitedd by the incideent wave contrributes to


the suppressed d reflectance. Therefore, T perffect absorptionn occurs at the resonance freqquency of 6.11 THz as shown s in Fig. 3. 3 When f = 5.86 THz, wh hich is the ressonance frequeency of the 3rrd graphene ribbbon, the incident field ds are mainly focused on the t third graphhene ribbon aas shown in F Fig. 4(f). Moreover, thee electric dipolles placed in th he 2nd and 3rdd graphene ribbbons also conntribute to the third absorption peak at f3 = 5.86 THz, with absorptioon up to 98.7% %. yer of graphenee decreases, as shown in Figss. 4(g) and 4(h)), the total absoorption of As the lay incident wavee is reduced du ue to the lesseened energy loossy inside graaphene at the rresonance frequency. g to Fig. 3 and d Fig. 4, we can n therefore preedict that an ennhanced and bbroadband According absorption spectrum can bee further achiev ved by increassing NGL of thhe proposed G GSPA and mension of each h graphene ribbon. tuning the dim

Fig. 5. 5 Absorption of th hree-layer GSPA under u different inccident angles, for w 1 = 0.155 μm, w2 = 0.17 70 μm, w3 = 0.180 μm, p = 0.25 μm, d = 8 μm and t = 0.5 μm.

The abovee discussion iss only based on o normal inciidence, but thhe robustness oof optical response for non-normal in ncident angless is significantt for terahertzz absorber. Baased on a mulations, the absorption a of three-layer GS SPA is demonnstrated in Figg. 5 as a series of sim function of frrequency and angle a of incideence (keeping tthe wavevectoor in the x-z plaane). The result indicatees that the maaximum absorp ption can mainntain at a high value larger tthan 90% under the inccident angle beelow 63°, and a value largeer than 80% unnder the incident angle below 76°. On O the other hand, h the band dwidth keeps aalmost unchannged under thee incident angle below 58°, 5 which con nsists three obv vious absorptioon peaks show wn in Fig. 5. T Therefore, the absorption n of the three-llayer GSPA sttructure is nearrly independennt of the incideent angle. This can be ex xplained that th he direction off magnetic fieldd for the incideent light remainns almost constant while the angle of incidence is changed, c so thee intensity of m magnetic resonnance can be sufficiently y kept and furrther ensures the t high loss inside graphenne for a wide range of incident anglees. By adjustiing the geomettric dimensionss of the GSPA A configurationn, the absorptioon spectra can be tuned as shown in Fig. F 2(b). It is remarkable r thaat the absorptioon tuning via dd, w1, w2, n designing ann absorber witth specific requuirement. w3 and other dimensions is very useful in p dimen nsions after finnal design andd implementation of the However, varriation of the physical absorber is in nconvenient an nd not feasible. Therefore, ann active tuningg method to coontrol the absorber charracteristics afteer fabrication is indispensablle. By varying the conductivity of the sandwiched graphene g layers, the proposed GSPA is exxpected to achiieve flexible tuunability. As shown in Kubo formulas Eqs. (3)-(6), the surface conductivity of graphene iss directly p μc. Th hus, the perform dependent on the chemical potential mance of grapphene-based deevices can be manipulatted by changin ng the chemiccal potential vvia chemical doping or eleectrostatic doping witho out changing the structure of the devicees. The absorpption tunabilitty 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. 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 th he same way. Besides, they are greatly cooupled with thheir own imagees, which oscillate in antiphase a on th he metallic fillm. Consequenntly, magnetic polaritons [45,46] are formed, whicch induce a sttrong magneticc response annd cause a ressonant dip in the same reflection spectrum. Thus, th he proposed 3D D structure hass a polarizationn- insensitive pproperty.

Fig. 7. 7 (a) Schematics of o the 3D three-lay yer GSPA structuree. (b) Absorption rrate of TM and TE E polariization incident lig ght.

Fig. 8. Absorption of 3D D three-layer GSPA under different incident angles off (a) TM incidencee and (b b) TE incidence, for f w1 = 0.155 μm m, w2 = 0.170 μm, w3 = 0.180 μm, p = 0.25 μm, d = 8 μm an nd t = 0.5 μm.

The stabilities of the inccident angle forr both TM andd TE polarizatioons are revealeed in Fig. 8. For TM polarization, p ass the incident angles increasses, the maxim mum absorptioon of 3D three-layer GSPA maintainss above 90% when w the inciddent angle is less than 62°, w while the bandwidth becomes slightly y narrower. Forr TE polarizatiion, the maxim mum absorptionn 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 polarizationinsensitive and angle-independent broadband terahertz absorber. 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. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

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