and Double-Layer Decussate Graphene Ribbon Arrays - MDPI

nanomaterials Article

Frequency-Reconfigurable Wide-Angle Terahertz Absorbers Using Single- and Double-Layer Decussate Graphene Ribbon Arrays Longfang Ye 1, * , Fang Zeng 1 , Yong Zhang 2 , Xiong Xu 3 , Xiaofan Yang 3 and Qing Huo Liu 4 1 2 3 4

*

Institute of Electromagnetics and Acoustics, Department of Electronic Science, Xiamen University, Xiamen 361005, China; [email protected] EHF Key Laboratory of Fundamental Science, University of Electronic Science and Technology of China, Chengdu 611731, China; [email protected] State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System, Luoyang 471003, China; [email protected] (X.X.); [email protected] (X.Y.) Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA; [email protected] Correspondence: [email protected]; Tel.: +86-592-218-2456

Received: 28 September 2018; Accepted: 12 October 2018; Published: 14 October 2018







Abstract: We propose and numerically demonstrate two novel terahertz absorbers made up of periodic single- and double-layer decussate graphene ribbon arrays. The simulated results show that the proposed absorbers have narrowband near-unity terahertz absorption with ultra-wide frequency reconfiguration and angular stability. By tuning the Fermi level of graphene ribbons, the over 90% absorbance peak frequency of the absorber with single-layer graphene structure can be flexibly adjusted from 6.85 to 9.85 THz for both the transverse magnetic (TM) and transverse electric (TE) polarizations. This absorber with single-layer graphene demonstrates excellent angular stability with the absorbance peaks of the reconfigurable absorption bands remaining over 99.8% in a wide angle of incidence ranging from 0 to 70◦ . The tuning frequency can be significantly enhanced by using the absorber with double-layer graphene structure from 5.50 to 11.28 THz and 5.62 to 10.65 THz, approaching two octaves under TM and TE polarizations, respectively. The absorbance peaks of the reconfigurable absorption band of this absorber for both polarizations maintain over 70%, even at a large angle of incidence up to 70◦ . Furthermore, an analytical fitting model is also proposed to accurately predict the absorbance peak frequencies for this variety of absorbers. Benefitting from these attractive properties, the proposed absorber may have great potential applications in tunable terahertz trapping, detecting, sensing, and various terahertz optoelectronic devices. Keywords: terahertz; graphene; frequency reconfigurable absorber; surface plasmons

1. Introduction Terahertz waves generally refer to electromagnetic waves with a frequency of 0.1–10 THz. Terahertz technology has broad applications in terahertz communication, spectroscopy, detecting, sensing, and imaging [1–4]. THz metamaterial absorbers (MAs) have aroused increasing attention since Landy et al. proposed a perfect MA in 2008 [5]. For many applications, frequency-tunable narrowband MAs would be preferred over typical broadband MAs, owing to their ability to absorb given frequency resonance without influencing neighboring spectrums. For conventional MAs, the absorption characteristics can only be manipulated by changing the resonator geometry or the surrounding medium [6]. Recently, by integrating varactors [7], semiconductors [8], microelectromechanical systems (MEMS) [9], diodes [10], and liquid crystals [11], various tunable MAs with frequency, Nanomaterials 2018, 8, 834; doi:10.3390/nano8100834

www.mdpi.com/journal/nanomaterials

Nanomaterials 2018, 8, 834

2 of 11

bandwidth, and strength adjustability have been achieved. However, such tunable absorbers usually have very limited frequency tuning range and also require large external controls and complicated manufacturing techniques. Graphene is a monatomic carbon layer two-dimensional material that has attracted a great deal of attention in the past decade because of its unique electrical performance, low intrinsic loss, and photonic properties [12]. Since graphene possesses the ability to support long propagation and strongly localized surface plasmon polaritons (LSPPs) in the terahertz and infrared regions, it has become an excellent electromagnetic film material widely used in various terahertz components and devices [13–15]. To date, many graphene-based MAs have been proposed and investigated in a wide frequency spectrum ranging from microwave to ultraviolet light [16–20]. Via the chemical or electrostatic doping of graphene, both strong absorption and flexible tunability can be easily achieved. Especially, as a new type of MAs with broad potential applications in electromagnetic wave sensing, modulation, detection, and stealth, graphene-based frequency reconfigurable absorbers have recently attracted increasing attention. For example, Ning et al. proposed a tunable mid-infrared absorber made up of a graphene–metal nanostructure with angular-insensitive absorption within −12◦ to 12◦ [21]. Meanwhile, by tuning the graphene Fermi level from 0.2 to 0.8 eV, the absorbance peak wavelength (frequency) shifts from 9969 nm (30.1 THz) to 9318 nm (32.2 THz), corresponding to the relative frequency tuning range (RFTR) of 7%, where the RFTR is defined as the absolute absorbance peak frequency tuning range over the lowest absorbance peak frequency, (f H − f L )/f L × 100%. Li et al. demonstrated a tunable mid-infrared narrowband absorber using parallel double-layer graphene ribbons with an RFTR of 18.7% from 22.73 to 27 THz and a wide angular stability of 60◦ [22]. Wu investigated a tunable absorber using a dielectric grating-graphene-Bragg grating structure with an RFTR of 1.1% from 8.92 to 9.02 THz [23]. He et al. presented an active graphene-based terahertz MA with an RFTR of 20.6% from 1.31 to 1.58 THz [24]. Zhang et al. proposed a graphene-based tunable MA with an RFTR of 14.9% from 0.94 to 1.08 THz [25]. An enhanced angular stability up to 70◦ (50◦ ) was achieved in that absorber for transverse magnetic (TM) (transverse electric, TE) polarized terahertz waves at 0.94 THz, but the insensitive angle of incidence was drastically decreased to 25◦ as the absorption band shifted to the higher-frequency end at 1.08 THz. In addition, dual-band tunable terahertz and mid-infrared MAs with RFTRs of 31.4% and 19.5% were also achieved [26,27]. Despite the recent progress in tunable MAs, most of these graphene-based absorbers still suffer from the disadvantages of small angular stability and very limited RFTR range, usually less than 35%. How to achieve tunable graphene-based absorbers with larger RFTR and wider angular stability remains a challenge. To address this issue, we propose a new variety of frequency-reconfigurable narrowband near-unity terahertz absorbers with significantly enhanced RFTR and angular stability using single/double-layer decussate graphene ribbon arrays (S/DLDGRAs). To demonstrate the properties and mechanisms of the absorbers, we present the geometric configurations and study their performance, including terahertz absorbance spectra, effective impedance characteristics, field distributions, frequency reconfiguration, and angular stability of the proposed absorbers. It was found that by tuning graphene Fermi level, the RFTR for the over 90% absorbance peak frequency of the proposed absorber with SLDGRA reached 43.8%, ranging from 6.85 to 9.85 THz for both TM and TE polarizations under normal incidence. The RFRT for the over 90% absorbance peak frequency of the absorber with DLDGRA could be further extended to 105.1% (89.5%), ranging from 5.50 (5.62) to 11.28 (10.65) THz, approaching two octaves for the TM (TE) polarization under normal incidence. The absorbance peaks of the different absorption bands for both absorbers maintained over 70% in a wide range of angle of incidence from 0◦ to 70◦ . Furthermore, we propose a simple analytical fitting model to accurately predict the reconfigurable absorbance frequencies of the absorbers. Finally, we systematically draw the conclusion of the whole work.

Nanomaterials 2018, 8, 834

3 of 11

2. Geometric Configurations of the Absorbers The schematic of the proposed frequency-reconfigurable wide-angle terahertz absorbers with S/DLDGRAs is illustrated in Figure 1. The absorber with a SLDGRA is made up of a periodic graphene ribbon array, a ZrO2 dielectric layer, and a gold (Au) reflection layer from the top to the bottom. The absorber with DLDGRAs can be interpreted as the transformation of the absorber with a SLDGRA by separating two graphene ribbon arrays into different layers with a distance of h1 while keeping the identical thickness of the dielectric layer. Here, we display the top views of the unit cells of the proposed absorbers with S/DLGRAs in Figure 1c,d, respectively. In the terahertz region, the surface conductivity of the graphene is calculated by the Kubo formula as σg = σintra + σinter (Unit: S) [28,29], where the intraband contribution σintra and interband contribution σinter are given by: σintra (ω, µc , Γ, T0 ) =

π¯h2 (ω − j2Γ)

σinter (ω, µc , Γ, T0 ) = − 

Z∞

je2

0

je2 (ω − j2Γ)

 −1

π¯h

 ∂ f d (ξ, µc , T0 ) ∂ f d (−ξ, µc , T0 ) − ξdξ, ∂ξ ∂ξ Z∞

2 0

f d (−ξ, µc , T0 ) − f d (ξ, µc , T0 )

(ω − j2Γ)2 − 4ξ/¯h2

dξ,

(1)

(2)

where f d (ξ, µc , T ) = e(ξ −µc )/k B T + 1 is the Fermi–Dirac distribution, ω is the radian frequency, µc is the chemical potential or Fermi level, T0 is the temperature, Γ is the phenomenological scattering rate, Γ = 2τ −1 , τ is the relaxation time, e is the charge of an electron, ξ is energy, h¯ is the reduced Plank’s constant, and kB is Boltzmann’s constant. The relative dielectric constant of ZrO2 was set as εr = 4.41 [30,31] and the relative dielectric constant of Au was obtained by the Drude Model [32]. In the absorber designs, Lx and Ly are the periods of the unit cell, and W x and W y are the widths of the graphene ribbons in x and y directions, respectively. The thickness of the upper and lower ZrO2 spacers, the Au reflecting layer, and the total thickness of the absorbers were set as h1 , h2 , h3 , and h = h1 + h2 + h3 , respectively. In this study, we assumed the parameters as Lx = Ly = 4 µm, W x = W y = 0.9 µm, h1 = 1 µm, h2 = 4 µm, h3 = 1 µm, T0 = 300 K, τ = 0.6 ps [33], respectively. In the numerical simulations, graphene ribbons were modeled as equivalent two-dimensional surface impedance layers with Zg = 1/σg without thickness [34,35] and the finite element method-based frequency domain solver of the commercial software CST Studio was used to study the properties of the absorbers. The absorbance of the absorbers is defined as A = 1−T–R, where reflectance R = |S11 |2 , transmission T = |S21 |2 , and S denotes the scattering parameter, respectively [20]. In addition, the theoretical and experimental available Fermi level µc of graphene can be easily tuned from 0 to 1.0 eV via chemical or electrostatic doping [29,36,37], making it possible to achieve flexible control of the absorbance properties of the absorbers.

Nanomaterials 2018, x, x

3 of 11

Nanomaterials 2018, 8, 834

4 of 11

2. Geometric Configurations of the Absorbers THz Waves

THz Waves

(a)

E

H

z o

x h1

h2 h

Ly

y

h3

Graphene ZrO2 Au

Lx

Wy

Ly

o

Lx

y

(d)

z o

Unit cell

h

o

Lx

Wx

Wy

Ly

x

y

h2 Ly

Wx

E

k

y

Unit cell

h1

(c)

H

k x

h3

(b)

Lx

x

Figure Figure 1. 1. Schematic illustrations of the proposed proposed frequency-reconfigurable frequency-reconfigurable wide-angle wide-angle terahertz terahertz absorbers. absorbers. (a) The absorber absorber with with aa single-layer single-layer decussate decussate graphene graphene ribbon ribbon array array (SLDGRA); (SLDGRA); (b) (b) The The absorber ribbon arrays (DLDGRAs); (c) (c) toptop view of the cell absorber with withdouble-layer double-layerdecussate decussategraphene graphene ribbon arrays (DLDGRAs); view of unit the unit of the proposed absorber with SLDGRA; (d) top view of the unit cell of the proposed absorber with cell of the proposed absorber with SLDGRA; (d) top view of the unit cell of the proposed absorber DLDGRA. The geometric parameters of theof absorbers were set as set Lx =asLL Wxy ==W 0.9 with DLDGRA. The geometric parameters the absorbers were y = 4W µ xm,= W y =µm, 0.9 y x==4Lµm, hμm, h2 = h42µm, h3 =h13 µm. = 1 μm, = 4 μm, = 1 μm. 1 = 1h1µm,

3. Results and Discussion The schematic of the proposed frequency-reconfigurable wide-angle terahertz absorbers with S/DLDGRAs is illustrated in study Figureterahertz 1. The absorber withspectra, a SLDGRA is made up of a periodic In this section, we first absorbance frequency reconfiguration and graphene ribbon of array, a ZrO2 dielectric layer, a gold Then, (Au) reflection layer from the frequency top to the angular stability the proposed absorbers withand SLDGRA. to demonstrate a wider bottom. The absorber with DLDGRAs can be interpreted as the transformation of the absorber with reconfiguration, we present and investigate the properties of the absorbers with DLDGRA. a SLDGRA bywe separating two graphene ribbon arrays different layers with a distance of h1 while Furthermore, also proposed a simple analytical fittinginto model to accurately predict the reconfigurable keeping thepeak identical thickness the dielectric layer. Here, we display the top views of the unit cells absorbance frequencies of of this variety of absorbers. of the proposed absorbers with S/DLGRAs in Figures 1c,d, respectively. In the terahertz region, the 3.1. The Terahertz Absorption the Absorber a SLDGRA surface conductivity of the Performance graphene is ofcalculated by with the Kubo formula as σg = σintra + σinter (Unit: S) [28,29], where the intraband contribution σ intra and interband contribution inter are given by: First, we investigated the terahertz absorption performance of theσproposed absorber with a SLDGRA under normal incidence. The 2identical in Figure 1a.  f d  , c , T0 parameters f d   , c ,are T0  shown  geometric  je This structure canbe Fabry–Perot-like 2a shows (, c , , Tas  asymmetric  resonant cavity. , (1)    dFigure intraregarded 0 ) an  R for both TE and TM  2 T, and j 2 reflectance 0  polarizations with the simulated absorbance A, transmission µc = 0.3 eV under normal terahertz incidence (θ = 0◦ ). It is clear that excellent narrow-band terahertz je2   peak j 2  approaching f d   , c , T0 100%  f d at, 6.85 absorption was achieved with the absorbance c , T0 THz. Because of the  inter (, c , , T0 )   d , (2) 2 2 2 axisymmetric unit cell, as shown in Figure 1c, this absorber demonstrated polarization independence    j 2Γ   4 / 0 for the TE- and TM-polarized incident terahertz waves under normal incidence. The underlying 1     / k be T absorption by the effective medium theory [38], where the normalized , c , T )   e can interpreted 1 is the Fermi–Dirac where f d (mechanism distribution, μc is the r    ω is the radian frequency,  2 2 2 2 effective givenlevel, by ZT0 = / (phenomenological 1 − S11 ) − S21 . scattering As shown in (1 + S11 ) − SΓ21is the chemical impedance potential or isFermi is the temperature, rate,





c

B

Γ = 2τ−12b, , τ the is the relaxation e iscurves the charge of the an real electron, ξ is energy, ћ isofthe Plank’s Figure blue solid andtime, dashed denote and imaginary parts Z, reduced respectively. We constant, and k B is Boltzmann’s constant. The relative dielectric constant of ZrO 2 was set as ε r = 4.41 observed that for upper green point, Re(Z) = 1.0004, and for the lower green point, Im(Z) = −0.00114, [30,31] and the relative dielectricofconstant of implying Au was the obtained by theofDrude Modelmatched [32]. In the the at the absorbance peak frequency 6.85 THz, impedance the absorber absorber Lx and Lysince are the of the cell, andresulting Wx and from Wy are the widths of the free spacedesigns, well. Therefore, theperiods extremely lowunit reflectance smooth impedance graphene ribbons in x and y directions, respectively. The thickness of the upper and lower ZrO 2

Nanomaterials 2018, 8, 834

5 of 11

A (TE) A (TE) R (TE) R (TE) T (TE) T (TE) A (TM) A (TM) R (TM) R (TM) T (TM) T (TM)

A,A,TT&&RR

0.8 0.8

(a) (a)

0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 4 4

5 5

6 6

7 7

8 8

1.0 Re (Z) 1.0 Re(Z) Im((ZZ)) 0.8 Im 0.8 AA

8 (b) 8 (b) 4 4

0.6 0.6

0 0

0.4 0.4

-4 -4

0.2 0.2

-8 -8

9 10 9 10

4 4

Frequency (THz) (THz) Frequency

Absorbance Absorbance

1.0 1.0

Normalized NormalizedImpedance Impedance

matching together with zero transmission enabled by the thick gold layer, the near-unity absorbance of the absorber was achieved. Figure 3a–d display the electric field distributions, |E|, and magnetic field distributions, |H|, for the TM and TE polarizations along the cut-plane on the top graphene layer at 6.85 THz. The localized surface plasmon polaritons (LSPPs) were excited and strongly confined on the graphene ribbons, leading to ultra-high terahertz absorption. As expected from the symmetric configuration and polarization-independent property, the |E| and |H| for TM polarization were exactly 90◦ shifted from that of the TE polarization. Therefore, this absorber with a SLDGRA showed a Nanomaterials 2018, x, x 5 of 11 Nanomaterials 2018, x, x of polarization, which has a significant advantage over the polarization-sensitive 5 of 11 clear independence absorber with single graphene ribbon array.

5 5

6 6

7 7

8 8

0.0 9 100.0 9 10

Frequency (THz) (THz) Frequency

Figure 2. 2. (a) Simulated absorbance (A), transmission (T), and reflectance (R) of of the proposed absorbers Figure (a)Simulated Simulatedabsorbance absorbance (A), (A), transmission transmission (T), (T), and reflectance reflectance (R) (R) the proposed proposed absorbers absorbers 2. (a) and of the with SLDGRAs for both transverse magnetic (TM) and transverse electric (TE) polarizations at μc = with SLDGRAs SLDGRAs for forboth bothtransverse transversemagnetic magnetic (TM) and transverse electric (TE) polarizations (TM) and transverse electric (TE) polarizations at μc at = 0.3 =eV0.3 under normal terahertz incidence; (b) The realThe and imaginary parts of parts the retrieved effective µ eV under terahertz incidence; and imaginary of the retrieved c eV under 0.3 normalnormal terahertz incidence; (b) The(b) real andreal imaginary parts of the retrieved effective impedance (Z) of the absorber for both TMboth and TE and polarization, where the black and red curves effective impedance of the absorber TE polarization, where theand black red impedance (Z) of the(Z) absorber for both for TM and TM TE polarization, where the black redand curves indicate the Re(Z) and Im(Z), respectively, and the vertical green solid cut-line denotes the frequency curves indicate the Re(Z) and Im(Z), respectively, and the vertical green solid cut-line denotes the indicate the Re(Z) and Im(Z), respectively, and the vertical green solid cut-line denotes the frequency of absorbance peak at 6.85 THz. frequency of absorbance peak at 6.85 THz. of absorbance peak at 6.85 THz.

(a) (a)

TM TM

1×108 1×108 V/m V/m

TM TM

0 0 3×104 3×104 A/m A/m

|E| |E| (c) (c)

(b) (b)

TE TE

1×108 1×108 V/m V/m

TE TE

0 0 3×104 3×104 A/m A/m

|E| |E| (d) (d)

|H| |H| 0 0 0 0 Figure 3. 3. (a–d) (a–d) are are the the electric electric field fielddistributions, distributions,|E|, |E|, and and magnetic magnetic field field distributions, distributions, |H|, |H|, for TM Figure 3. (a–d) are the electric field distributions, |E|, and magnetic field distributions, |H|, for TM and TE polarizations of the absorbers with SLDGRAs along the cut-plane on the top graphene layer at and TE polarizations of the absorbers with SLDGRAs along the cut-plane on the top graphene layer and TE polarizations of the absorbers with SLDGRAs along the cut-plane on the top graphene layer 6.85 THz with µc μ =c 0.3 eVeV under normal terahertz incidence, respectively. at 6.85 THz with = 0.3 under normal terahertz incidence, respectively. at 6.85 THz with μc = 0.3 eV under normal terahertz incidence, respectively. |H| |H|

To demonstrate the properties of wide frequency reconfiguration and angular stability, we To demonstrate the properties of wide frequency reconfiguration and angular stability, we studied the dependence of Fermi level μc and angle of incidence θ on the absorbance spectra. Figure studied the dependence of Fermi level μc and angle of incidence θ on the absorbance spectra. Figure 4a depicts the absorbance spectra for both TM and TE polarizations under normal incidence with 4a depicts the absorbance spectra for both TM and TE polarizations under normal incidence with various μc. It was found that changing the μc of the graphene ribbon had a significant influence on various μc. It was found that changing the μc of the graphene ribbon had a significant influence on

Nanomaterials 2018, 8, 834

6 of 11

To demonstrate the properties of wide frequency reconfiguration and angular stability, we studied the dependence of Fermi level µc and angle of incidence θ on the absorbance spectra. Figure 4a depicts the absorbance spectra for both TM and TE polarizations under normal incidence with various µc . It was found that changing the µc of the graphene ribbon had a significant influence on the absorption frequency band. As µc increased from 0.2 to 0.8 eV, the absorbance peak frequency band red-shifted accordingly from 5.58 to 11.32 THz. Especially, good frequency reconfiguration characteristics6were Nanomaterials 2018, x, x of 11 clearly observed. As µc increased from 0.3 to 0.6 eV, the over 90% absorbance peak frequency varied fromdisplay 6.85 tothe 9.85simulated THz, demonstrating wide absolute frequency tuningangle rangeand of 3operating THz withfrequency the RFTR 4b,c absorbance aspectra as a function of incidence of 43.8%, which was larger than the recently reported works [21–27]. Figure 4b,c display the simulated with μc of 0.3 and 0.6 eV, for the first and the last absorption bands with over 90% peak absorbance, absorbance spectra as a function incidence angle and withangular µc of 0.3 and 0.6for eV, respectively. The results showedof that the absorber also operating possessedfrequency an excellent stability for the first and the lastabsorption absorptioncharacteristics. bands with over 90% peak The results narrowband terahertz Owing to theabsorbance, wide-anglerespectively. localized resonance of showed that the absorber also possessed an excellent angular stability for narrowband terahertz SPPs in the SLDGRA structure, the peak absorbance remained over 99.8%, even at a large oblique absorption characteristics. Owing toThis the wide-angle localized resonancereconfiguration, of SPPs in the SLDGRA incidence angle of 70° for both cases. absorber with wide frequency absolute structure, the peak absorbance remained over 99.8%, even at a large oblique incidence angle of 70◦ for polarization independence, and excellent angular stability may have significant potential both cases. This absorber with wide frequency reconfiguration, absolute polarization independence, applications in the terahertz regime. and excellent angular stability may have significant potential applications in the terahertz regime. 1.0 90%

Absorbance

0.8

0.2 eV 0.3 eV 0.4 eV 0.5 eV 0.6 eV 0.7 eV 0.8 eV

0.6 0.4 0.2

(a)

0.0 4

6

8

10

12

14

70 60

1.0

(b) 0.8

50 40

0.6

30

0.4

20 10 0

0.2

μc = 0.3 eV 0.0

2 4 6 8 10 12 14

Frequency (THz)

Incidence angle  (deg)

Incidence angle deg

Frequency (THz)

70 60

1.0

(c) 0.8

50 40

0.6

30

0.4

20 10 0

0.2

μc = 0.6 eV 0.0

2 4 6 8 10 12 14

Frequency (THz)

Figure4.4.(a) (a)Simulated Simulatedabsorption absorptionspectra spectrafor forboth bothTM TMand andTE TEpolarizations polarizationsunder undernormal normalincidence incidence Figure with μµcc ranging ranging from 0.2 to are the spectra as a function incidence angle and with to 0.8 0.8eV; eV;(b,c) (b) and (c) absorbance are the absorbance spectra as a of function of incidence operating frequencyfrequency with µc fixed andas 0.60.3 eV,and respectively. angle and operating withasμ0.3 c fixed 0.6 eV, respectively.

3.2.Terahertz Terahertz Absorption Absorption Performance Performance of of the the Absorber Absorber with with DLDGRAs DLDGRAs 3.2. To further further enhance enhance the the absorbance absorbancepeak peakfrequency frequencytuning tuningrange, range,we wepropose proposethe theabsorber absorberwith with To DLDGRAs, as shown in Figure 1b,d. The ZrO separation (h ) of the double-layer decussate graphene 2 1 DLDGRAs, as shown in Figures 1b,d. The ZrO2 separation (h1) of the double-layer decussate graphene ribbonarrays arrayswas wasset setas as11µµm whilethe therest rest of of the the geometric geometricparameters parametersof ofthis thisabsorber absorberwere werefixed fixed ribbon m while to be be the the same same as as the the absorber absorber with with aa SLDGRA. SLDGRA. The The simulated simulated absorbance absorbance spectra spectrafor for TM TM and and TE TE to polarizations with different µ at normal terahertz incidence are displayed in Figure 5a,b, respectively. c polarizations with different μc at normal terahertz incidence are displayed in Figures 5a,b, Clearly, ultra-wide frequency tuning of the narrowband absorption was obtained by varying respectively. Clearly, ultra-wide frequency tuning of terahertz the narrowband terahertz absorption was obtained by varying μc. For TM polarizations, the reconfigurable over 90% absorbance peak frequency significantly switched from 5.50 to 11.28 THz, corresponding an enhanced RFTR of 105.1%, as the μc increased from 0.2 to 0.8 eV. For TE polarization, the reconfigurable over 90% absorbance peak frequency switched from 5.62 to 10.65 THz, corresponding to a RFTR of 89.5%, as the μc varied from 0.3 to 1.0 eV. Compared with the RFTR of the absorber with a SLDGRA, ultra-wide frequency

upper and lower graphene plane are shown in Figures 6b,d. The LSPPs were strongly excited and concentrated around the lower graphene ribbons, leading to strong terahertz absorption. Clearly, the absorption is largely dependent on the localized resonance of SPPs in the individual layer of graphene ribbons rather than the interplay of SPPs between upper- and lower-layer graphene ribbons. The different field distributions of LSPPs determine the different terahertz absorbance spectra of the Nanomaterials 2018, 8, 834 7 of 11 proposed absorber with DLDGRAs under TM and TE polarizations. Furthermore, we also investigated the angular stability of the proposed absorber with DLDGRAs. Here, for example, we present the simulated absorbance spectra as a function of incidence µc . For TM polarizations, the reconfigurable over 90% absorbance peak frequency significantly angle θ and operating frequency with μc of 0.2 and 0.8 eV for TM polarization in Figures 7a,c, and switched from 5.50 to 11.28 THz, corresponding an enhanced RFTR of 105.1%, as the µc increased from with μc of 0.3 and 1.0 eV for TE polarization in Figures 7b,d, respectively. These results show that the 0.2 to absorbance 0.8 eV. Forcould TE polarization, reconfigurable peak 7a–d frequency still maintainthe above 71.7%, 82.7%, over 88.9%,90% andabsorbance 96.9% for Figures over a switched wide from 5.62 to 10.65 THz, corresponding to a RFTR of 89.5%, as the µ varied from 0.3 to 1.0 eV. Compared c angle of incidence ranging from 0 to 70°, respectively. Therefore, the proposed absorber with with the RFTR of the absorberultra-wide with a SLDGRA, ultra-wide frequency reconfiguration 2× more DLDGRAs demonstrated angular stability, which can be mainly attributed towith the wideproperty ofinlocalized resonance SPPs in individual graphene ribbons. RFTRangle was achieved the absorber withofDLDGRAs. 1.0 90%

0.2 eV 0.3 eV 0.4 eV 0.5 eV 0.6 eV 0.7 eV 0.8 eV 0.9 eV

Absorbance

0.8 0.6 0.4 0.2

(a) TM

0.0 4

6

8

10

12

14

Frequency (THz) 1.0 90%

0.2 eV 0.3 eV 0.4 eV 0.5 eV 0.6 eV 0.7 eV 0.8 eV 0.9 eV 1.0 eV

Absorbance

0.8 0.6 0.4 0.2

(b) TE

0.0 4

6

8

10

12

14

Frequency (THz) FigureFigure 5. Simulated absorbance spectra absorberwith withDLDGRAs DLDGRAs with different 5. Simulated absorbance spectraofofthe theproposed proposed absorber with different μc µ c normal terahertz incidence. Absorbance spectra spectra for with μc ranging fromfrom underunder normal terahertz incidence. (a)(a) Absorbance forTM TMpolarization polarization with µc ranging 0.9(b) eV;absorbance (b) absorbance spectra polarization with with μ 0.20.2 to 1.0 eV.eV. 0.2 to 0.2 0.9to eV; spectra forfor TETEpolarization µccranging rangingfrom from to 1.0

Next, it is remarkable that this absorber was no longer polarization-independent because of the non-axisymmetric DLDGRA structure. To better understand this characteristic, we depict the simulated electric field distributions for TM and TE polarizations along the cut-planes on upper and lower graphene layers with µc = 0.3 eV under normal incidence. For TM polarization, |E| distributions of the LSPPs at the absorbance peak frequency of 6.81 THz along upper and lower graphene plane are shown in Figure 6a,c, respectively. It was clearly observed that |E| were mainly confined around upper-layer graphene ribbon edges. Therefore, the terahertz absorption for the TM polarization was mainly caused by LSPPs located at the upper-layer graphene ribbons. Similarly, the electric distributions for the TE polarization at the absorbance peak frequency of 5.62 THz along upper and lower graphene plane are shown in Figure 6b,d. The LSPPs were strongly excited and concentrated around the lower graphene ribbons, leading to strong terahertz absorption. Clearly, the absorption is largely dependent on the localized resonance of SPPs in the individual layer of graphene ribbons rather than the interplay of SPPs between upper- and lower-layer graphene ribbons. The different field distributions of LSPPs determine the different terahertz absorbance spectra of the proposed absorber with DLDGRAs under TM and TE polarizations. Furthermore, we also investigated the angular stability of the proposed absorber with DLDGRAs. Here, for example, we present the simulated absorbance spectra as a function of incidence angle θ and operating frequency with µc of 0.2 and 0.8 eV for TM polarization in Figure 7a,c, and with µc of 0.3 and 1.0 eV for TE polarization in Figure 7b,d, respectively. These results show that the absorbance could still maintain above 71.7%, 82.7%, 88.9%, and 96.9% for Figure 7a–d over a wide angle of incidence

Nanomaterials 2018, 8, 834

8 of 11

ranging from 0◦ to 70◦ , respectively. Therefore, the proposed absorber with DLDGRAs demonstrated Nanomaterials 2018, x, x 8 of 11 ultra-wide angular stability, which can be mainly attributed to the wide-angle property of localized resonance of SPPs graphene ribbons. Nanomaterials 2018,in x, individual x 8 of 11 6×107 6×107 (a)

y

(a)

y o

|E|

o

TM

V/m 6×107 V/m

TM

(b)

TE

(b)

TE

V/m 6×107 V/m

x x

|E|

Upper graphene plane |E|

Upper graphene plane |E|

0

0

(b)

7

Upper graphene plane (c) TM (c)

6×10 0 V/m 6×107 V/m

TM

|E|

Upper graphene plane (d) TE (b) (d)

TE

6×107 0 V/m 6×107 V/m

|E|

Lower graphene plane |E|

Lower graphene plane |E|

0

0

graphene plane Lowerfield graphene plane of the absorberLower Figure 6. Electric distributions with DLDGRAs at μc = 0.3 eV under normal 0 0 incidence, where (a) and (c) are respectively the |E| for the TM polarization along the upper and

Figure 6. Electric field the absorber with atat μc µ=c(d) 0.3 eVthe under normal Figure 6. Electric field distributions ofofthe absorber with DLDGRAs = are 0.3 eV under normal lower graphene planes atdistributions the absorbance peak frequency of DLDGRAs 6.81 THz; (b) and |E| for the incidence, where (a) and (c) are respectively the |E| for the TM polarization along the upper and TE polarization along therespectively upper and lower graphene planes the absorbance peak the frequency 5.62 incidence, where (a,c) are the |E| for the TMatpolarization along upperofand lower lowerrespectively. graphene planes at the absorbance peak frequency of 6.81 THz; and (d)for arethe theTE |E|polarization for the THz, graphene planes at the absorbance peak frequency of 6.81 THz; (b,d) are(b)the |E| upper and loweratgraphene planes atpeak the absorbance frequency of 5.62 alongTE thepolarization upper andalong lowerthe graphene planes the absorbance frequencypeak of 5.62 THz, respectively.

60 70 50 60 40 50 30 40 20 30 10 20 0 102 0 2 70

1.0

(a)

TM 0.8 1.0

(a)

TM 0.6 0.8 0.4 0.6 0.2 0.4

μc = 0.2 eV

4 6 8 10 12 14

0.0 0.2

μc = 0.2 eV

Frequency (THz) 4 6 8 10 12 14

Frequency (THz)

(c)

Incidence  (deg) Incidence  (deg) angleangle

70

0.0 1.0

Incidence  (deg) Incidence  (deg) angleangle

Incidence  (deg) Incidence  (deg) angleangle

Incidence  (deg) Incidence  (deg) angleangle

THz, respectively.

70 60 70 50 60 40 50 30 40 20 30 10 20 0 102 0 2 70

1.0

(b)

TE 0.8 1.0

(b)

TE 0.6 0.8 0.4 0.6 0.2 0.4

μc = 0.3 eV

4 6 8 10 12 14

0.0 0.2

μc = 0.3 eV

Frequency (THz)

4 6 8 10 12 14

Frequency (THz)

0.0 1.0

(d)

TE TM 60 60 0.8 0.8 70 70 1.0 1.0 50 50 (d) (c) TE TM 60 60 0.6 0.6 0.8 0.8 40 40 50 50 30 30 0.4 0.4 0.6 0.6 40 40 20 20 30 30 0.2 0.2 0.4 0.4 10 10 20 μc = 1.0 eV 20 μc = 0.8 eV 0.0 0.0 0 0 0.2 0.2 102 4 6 8 10 12 14 102 4 6 8 10 12 14 μc = 0.8 eV μc = 1.0 eV 0.0 0.0 0 Frequency (THz) 0 Frequency (THz) 2 4 6 8 10 12 14 2 4 6 8 10 12 14 Figure 7. Simulated absorption spectra of the proposed absorber withdifferent different incidentangles anglesθθunder Figure 7. Simulated absorption spectra of the proposed absorber with incident Frequency (THz) Frequency (THz) under (a) TM polarization μc and = 0.2(b) eVTE and (b) TE polarization c = (c) 0.3TM eV. polarization (c) TM the (a) TM the polarization with µc = with 0.2 eV polarization with µc with = 0.3 μeV. 7.eV Simulated spectra of the proposed absorber with μ c = absorption 0.8 eV and (d) TE polarization with μ c = 1.0 eV.with different incident angles θ with polarization µFigure = 0.8 and (d) TE polarization with µ = 1.0 eV. c c under the (a) TM polarization with μc = 0.2 eV and (b) TE polarization with μc = 0.3 eV. (c) TM polarization with μc = 0.8 eV and (d) TE polarization with μc = 1.0 eV.

Nanomaterials 2018, x, x Nanomaterials 2018, 8, 834

9 of 11 9 of 11

3.3. Analytical Prediction of the Reconfigurable Absorbance Peak Frequencies

3.3. Analytical of the Reconfigurable Absorbance Frequencies To predictPrediction the reconfigurable frequencies of the Peak proposed absorbers, we further studied the relationship between the absorbance peak frequency f p and μ c . According to the analysis To predict the reconfigurable frequencies of the proposed absorbers, we quasi-static further studied the

 to the quasi-static analysis ke relationship between the absorbance peak frequency f p and µc . According q c , where k = 0.1 denotes in References [39,40], a fitting mode for fp and μc is given by f p  ke W µc in References [39,40], a fitting mode for f p and µc is given by f p = } Wεe e εoo , where k = 0.1 denotes a dimensionless ribbon, εe εise is thethe effective permittivity of dimensionless fitting fittingconstant, constant,W Wisisthe thewidth widthofofgraphene graphene ribbon, effective permittivity the background materials surrounding thethe graphene of the background materials surrounding grapheneribbon ribbonarray, array,and andεεoo isis the the permittivity permittivity of vacuum, first compared thethe fp of withwith a SLDGRA obtained from vacuum, respectively. respectively. Here, Here,we we first compared f pthe of absorber the absorber a SLDGRA obtained this fitting fitting mode and theand simulated results, as shownasinshown Figurein 8a.Figure In this8a. case, was fromanalytical this analytical mode the simulated results, Inthe thisεe case, expressed as ε e = (ε Zro2 +1)/2. It was found that with μ c varying from 0.2 to 0.9 eV, f p increased from the εe was expressed as εe = (εZro2 + 1)/2. It was found that with µc varying from 0.2 to 0.9 eV, f p 5.58 to 11.97 THz. The results matched with the simulation results. Then, we increased from 5.58 to analytical 11.97 THz.fitting The analytical fitting well results matched well with the simulation verified this we analytical mode fitting for themode absorber the with DLDGRA case. Because it is results. Then, verified fitting this analytical for thewith absorber the DLDGRA case. Because polarization-dependent, we compared the fitting and and simulation results separately for TM andand TE it is polarization-dependent, we compared the fitting simulation results separately for TM polarizations, as shown in Figures 8b,c. ForFor TMTM polarization, thethe terahertz LSPPs predominated on TE polarizations, as shown in Figure 8b,c. polarization, terahertz LSPPs predominated the upper-layer graphene ribbon, as as shown ininFigure approximately on the upper-layer graphene ribbon, shown Figure6a. 6a.Therefore, Therefore,εεee was was also also approximately expressed as εεee = (ε (εZro2 Zro2 +1)/2. With + 1)/2. Withthe thesame samevalues valuesofofεεe efor forthe theabsorber absorberwith withDLDGRAs DLDGRAs under under TM polarization and the absorber with SLDGRA, the same analytical predictions predictions of of ffpp are are shown in both Figures 8a,b.On Oncontrary, contrary,the theLSPPs LSPPsmainly mainly concentrated concentrated on on the the lower-layer graphene ribbon for the Figure 8a,b. TE polarization, and εεee should should be be calculated calculated by byεεe e==εεZro2 Zro2 instead. instead. Both Both analytical analytical prediction prediction and and the simulation simulation results clearly showed that fppincreased increasedfrom from5.50 5.50(4.60) (4.60)to to 11.97 11.97 (10.09) (10.09) THz THz for for TM TM (TE) (TE) polarization with μ µcc varying varying from from 0.2 0.2 to to 0.9 0.9 eV eV with with good good agreement. agreement. Therefore, Therefore, this this analytical analytical fitting mode can be be used usedfor forthe theefficient efficientprediction prediction reconfigurable absorbance peak frequencies of of of thethe reconfigurable absorbance peak frequencies of this this variety of absorbers. variety of absorbers.

Analysis Simulation

10 8 6

12

TM & TE

Absorber with SLDGRA 4 0.2 0.4 0.6 0.8 1.0

c (eV)

14

(b) Analysis Simulation

12

fp (THz)

fp (THz)

12

14

(a)

fp (THz)

14

10 8 TM

6

Absorber with DLDGRA 4 0.2 0.4 0.6 0.8 1.0

c (eV)

(c) Analysis Simulation

10 8 TE

6

Absorber with DLDGRA 4 0.2 0.4 0.6 0.8 1.0

c (eV)

Figure 8. peak frequency with different µc (a) Figure 8. The variation variation of ofanalytical analyticaland andsimulation simulationabsorbance absorbance peak frequency with different μc for (a) the absorber with a SLDGRA under both TM and TE polarizations; (b) for the absorber with DLDGRAs for the absorber with a SLDGRA under both TM and TE polarizations; (b) for the absorber with under TM polarization, and (c) for the with DLDGRAs TE polarization. DLDGRAs under TM polarization, andabsorber (c) for the absorber with under DLDGRAs under TE polarization.

4. Conclusions 4. Conclusions We systematically demonstrated a new variety of frequency-reconfigurable absorbers using We systematically demonstrated a new variety of frequency-reconfigurable absorbers using S/DLDGRAs. The absorbers had excellent properties of narrowband near-unity terahertz absorbance, S/DLDGRAs. The absorbers had excellent properties of narrowband near-unity terahertz absorbance, ultra-wide frequency reconfiguration, and angular stability. For the absorber with a SLDGRA, the over ultra-wide frequency reconfiguration, and angular stability. For the absorber with a SLDGRA, the 90% absorbance peak frequency could be flexibly adjusted from 6.85 to 9.85 THz for both polarizations over 90% absorbance peak frequency could be flexibly adjusted from 6.85 to 9.85 THz for both under normal incidence by tuning µ from 0.3 to 0.6 eV. For the absorber with DLDGRAs, the polarizations under normal incidencec by tuning μc from 0.3 to 0.6 eV. For the absorber with absorbance peak frequencies of each reconfigurable bands could be significantly extended from 5.50 to DLDGRAs, the absorbance peak frequencies of each reconfigurable bands could be significantly 11.31 THz and 5.60 to 10.61 THz under TM and TE polarizations, respectively, approaching two octaves. extended from 5.50 to 11.31 THz and 5.60 to 10.61 THz under TM and TE polarizations, respectively, Good angular stability of these absorbers was achieved, with the absorbance peaks of the reconfigurable approaching two octaves. Good angular stability of these absorbers was achieved, with the absorbance bands maintained over 70% in a wide angle of incidence ranging from 0◦ to 70◦ for absorbance peaks of the reconfigurable absorbance bands maintained over 70% in a wide angle of

Nanomaterials 2018, 8, 834

10 of 11

both polarizations. We proposed an analytical fitting model to predict the absorbers’ reconfigurable absorbance peak frequencies. Our results demonstrated that the proposed frequency-reconfigurable absorbers offer significant potential to realize novel reconfigurable optoelectronic devices, which may have great applications in the emerging terahertz regime. Author Contributions: L.Y. and F.Z. conceived the research, undertook the simulations and analysis, and wrote the manuscript. Y.Z., X.X., X.Y. and Q.H.L. contributed to the analysis and the manuscript review. Funding: This research was funded by the National Natural Science Foundation of China (61601393 and 61601472); the Shenzhen Science and Technology Innovation Committee (Project No. 201887656); the Natural Science Foundation of Fujian Province of China (2016J01321). Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2. 3.

4. 5. 6. 7. 8. 9.

10. 11. 12. 13. 14. 15. 16. 17.

18.

Tonouchi, M. Cutting-edge THz technology. Nat. Photonics 2007, 1, 97–105. [CrossRef] Ye, L.; Xu, R.; Wang, Z.; Lin, W. A novel broadband coaxial probe to parallel plate dielectric waveguide transition at THz frequency. Opt. Express 2010, 18, 21725–21731. [CrossRef] [PubMed] Vicarelli, L.; Vitiello, M.S.; Coquillat, D.; Lombardo, A.; Ferrari, A.C.; Knap, W.; Polini, M.; Pellegrini, V.; Tredicucci, A. Graphene field-effect transistors as room-temperature terahertz detectors. Nat. Mater. 2012, 11, 865–871. [CrossRef] [PubMed] Liu, L.; Rahman, S.M.; Jiang, Z.; Li, W.; Fay, P. Advanced Terahertz Sensing and Imaging Systems Based on Integrated III-V Interband Tunneling Devices. Proc. IEEE 2017, 105, 1020–1034. [CrossRef] Landy, N.I.; Sajuyigbe, S.; Mock, J.J.; Smith, D.R.; Padilla, W.J. A perfect metamaterial absorber. Phys. Rev. Lett. 2008, 100, 207402. [CrossRef] [PubMed] Chen, H.T.; O’Hara, J.F.; Azad, A.K.; Taylor, A.J.; Averitt, R.D.; Shrekenhamer, D.B.; Padilla, W.J. Experimental demonstration of frequency-agile terahertz metamaterials. Nat. Photonics 2008, 2, 295–298. [CrossRef] Zhao, J.; Cheng, Q.; Chen, J.; Qi, M.; Jiang, W.; Cui, T. A tunable metamaterial absorber using varactor diodes. New J. Phys. 2013, 15, 043049. [CrossRef] Zhao, X.; Zhang, J.; Fan, K.; Duan, G.; Metcalfe, G.D.; Wraback, M.; Zhang, X.; Averitt, R.D. Nonlinear terahertz metamaterial perfect absorbers using GaAs. Photonics Res. 2016, 4, A16–A21. [CrossRef] Liu, M.K.; Susli, M.; Silva, D.; Putrino, G.; Kala, H.; Fan, S.T.; Faraone, L.; Wallace, V.P.; Padilla, W.J.; Powell, D.A.; et al. Ultrathin tunable terahertz absorber based on MEMS-driven metamaterial. Microsyst. Nanoeng. 2017, 3, 17033–17045. [CrossRef] Zhu, B.; Feng, Y.; Zhao, J.; Huang, C.; Wang, Z.; Jiang, T. Polarization modulation by tunable electromagnetic metamaterial reflector/absorber. Opt. Express 2010, 18, 23196–23203. [CrossRef] [PubMed] Wang, L.; Ge, S.; Hu, W.; Nakajima, M.; Lu, Y. Graphene-assisted high-efficiency liquid crystal tunable terahertz metamaterial absorber. Opt. Express 2017, 25, 23873–23879. [CrossRef] [PubMed] Novoselov, K.S.; Fal’ko, V.I.; Colombo, L.; Gellert, P.R.; Schwab, M.G.; Kim, K. A roadmap for graphene. Nature 2012, 490, 192–200. [CrossRef] [PubMed] Grigorenko, A.N.; Polini, M.; Novoselov, K.S. Graphene plasmonics. Nat. Photonics 2012, 6, 749–758. [CrossRef] Koppens, F.H.; Chang, D.E.; García de Abajo, F.J. Graphene plasmonics: A platform for strong light-matter interactions. Nano Lett. 2011, 11, 3370–3377. [CrossRef] [PubMed] Low, T.; Avouris, P. Graphene plasmonics for terahertz to mid-infrared applications. ACS Nano 2014, 8, 1086–1101. [CrossRef] [PubMed] Meng, F.; Wang, H.; Huang, F.; Guo, Y.; Wang, Z.; Hui, D.; Zhou, Z. Graphene-based microwave absorbing composites: A review and prospective. Compos. Part B 2018, 137, 260–277. [CrossRef] Ye, L.; Chen, Y.; Cai, G.; Liu, N.; Zhu, J.; Song, Z.; Liu, Q.H. Broadband absorber with periodically sinusoidally-patterned graphene layer in terahertz range. Opt. Express 2017, 25, 11223–11232. [CrossRef] [PubMed] Thongrattanasiri, S.; Koppens, F.H.; Garcia, F.J. Complete optical absorption in periodically patterned graphene. Phys. Rev. Lett. 2012, 108, 047401. [CrossRef] [PubMed]

Nanomaterials 2018, 8, 834

19. 20. 21. 22. 23. 24.

25. 26. 27. 28. 29. 30.

31. 32.

33. 34. 35.

36. 37. 38. 39.

40.

11 of 11

Ye, L.; Chen, X.; Cai, G.; Zhu, J.; Liu, N.; Liu, Q.H. Electrically Tunable Broadband Terahertz Absorption with Hybrid-Patterned Graphene Metasurfaces. Nanomaterials 2018, 8, 562. [CrossRef] [PubMed] Zhu, J.; Yan, S.; Feng, N.; Ye, L.; Ou, J.Y.; Liu, Q.H. Near unity ultraviolet absorption in graphene without patterning. Appl. Phys. Lett. 2018, 112, 153106. [CrossRef] Ning, Y.; Dong, Z.; Si, J.; Deng, X. Tunable polarization-independent coherent perfect absorber based on a metal-graphene nanostructure. Opt. Express 2017, 25, 32467–32474. [CrossRef] Li, H.; Wang, L.; Zhai, X. Tunable graphene-based mid-infrared plasmonic wide-angle narrowband perfect absorber. Sci. Rep. 2016, 6, 36651. [CrossRef] [PubMed] Wu, J. Tunable ultranarrow spectrum selective absorption in a graphene monolayer at terahertz frequency. J. Phys. D. Appl. Phys. 2016, 49, 215108. [CrossRef] He, X.; Yao, Y.; Zhu, Z.; Chen, M.; Zhu, L.; Yang, W.; Yang, Y.; Wu, F.; Jiang, J. Active graphene metamaterial absorber for terahertz absorption bandwidth, intensity and frequency control. Opt. Mater. Express 2018, 8, 1031–1042. [CrossRef] Zhang, Y.; Feng, Y.; Zhu, B.; Zhao, J.; Jiang, T. Graphene based tunable metamaterial absorber and polarization modulation in terahertz frequency. Opt. Express 2014, 22, 22743–22752. [CrossRef] [PubMed] Yao, G.; Ling, F.; Yue, J.; Luo, C.; Ji, J.; Yao, J. Dual-band tunable perfect metamaterial absorber in the THz range. Opt. Express 2016, 24, 1518–1527. [CrossRef] [PubMed] Vasic, B.; Gajic, R. Graphene induced spectral tuning of metamaterial absorbers at mid-infrared frequencies. Appl. Phys. Lett. 2013, 103, 207403. [CrossRef] Hanson, G.W. Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene. J. Appl. Phys. 2008, 103, 064302. [CrossRef] Hanson, G.W. Dyadic Green’s functions for an anisotropic, non-local model of biased graphene. IEEE Trans. Antennas Propag. 2008, 56, 747–757. [CrossRef] Du, D.; Liu, J.; Zhang, X.; Cui, X.; Lin, Y. One-step electrochemical deposition of a graphene-ZrO2 nanocomposite: Preparation, characterization and application for detection of organophosphorus agents. J. Mater. Chem. 2011, 21, 8032–8037. [CrossRef] Cho, B.H.; Ko, W.B. Preparation of graphene-ZrO2 nanocomposites by heat treatment and photocatalytic degradation of organic dyes. J. Mater. Chem. 2013, 13, 7625–7630. Ordal, M.A.; Long, L.L.; Bell, R.J.; Bell, S.E.; Bell, R.R.; Alexander, R.W., Jr.; Ward, C.A. Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared. Appl. Opt. 1983, 22, 1099. [CrossRef] [PubMed] Guo, J.; Jiang, L.; Dai, Y.; Xiang, Y.; Fan, D. Low threshold optical bistability in one-dimensional gratings based on graphene plasmonics. Opt. Express 2017, 25, 5972–5981. [CrossRef] [PubMed] Gómez-Díaz, J.S.; Esquius-Morote, M.; Perruisseau-Carrier, J. Plane wave excitation-detection of nonresonant plasmons along finite-width graphene strips. Opt. Express 2013, 21, 24856–24872. [CrossRef] [PubMed] Ye, L.; Sui, K.; Liu, Y.; Zhang, M.; Liu, Q.H. Graphene-based hybrid plasmonic waveguide for highly efficient broadband mid-infrared propagation and modulation. Opt. Express 2018, 26, 15935–15947. [CrossRef] [PubMed] Bokdam, M.; Khomyakov, P.A.; Brocks, G.; Zhong, Z.; Kelly, P.J. Electrostatic doping of graphene through ultrathin hexagonal boron nitride films. Nano Lett. 2011, 11, 4631. [CrossRef] [PubMed] Balci, S.; Balci, O.; Kakenov, N.; Atar, F.B.; Kocabas, C. Dynamic tuning of plasmon resonance in the visible using graphene. Opt. Lett. 2016, 41, 1241. [CrossRef] [PubMed] Smith, D.R.; Vier, D.C.; Koschny, T.; Soukoulis, C.M. Electromagnetic parameter retrieval from inhomogeneous metamaterials. Phys. Rev. E 2005, 71, 036617. [CrossRef] [PubMed] Ju, L.; Geng, B.; Horng, J.; Girit, C.; Martin, M.; Hao, Z.; Bechtel, H.A.; Liang, X.; Zettl, A.; Shen, Y.R.; et al. Graphene plasmonics for tunable terahertz metamaterials. Nat. Nanotechnol. 2011, 6, 630. [CrossRef] [PubMed] Nikitin, A.Y.; Guinea, F.; Garca-Vidal, F.J.; Martin Moreno, L. Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons. Phys. Rev. B 2012, 85, 081405. [CrossRef] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).