604 Vol. 5, No.

6 / December 2017 / Photonics Research Research Article

Actively controllable terahertz switches with

graphene-based nongroove gratings
LINBAO LUO,1 KUIYUAN WANG,1 CAIWANG GE,1 KAI GUO,2 FEI SHEN,2 ZHIPING YIN,1,2
2,
AND ZHONGYI GUO *
1
School of Electronic Science and Applied Physics, Hefei University of Technology, Hefei 230009, China
2
School of Computer and Information, Hefei University of Technology, Hefei 230009, China
*Corresponding author: guozhongyi@hfut.edu.cn

Received 3 July 2017; revised 26 August 2017; accepted 3 September 2017; posted 18 September 2017 (Doc. ID 301553);
published 26 October 2017

We systematically investigated the tunable dynamic characteristics of a broadband surface plasmon polariton
(SPP) wave on a silicon-graded grating structure in the range of 10–40 THz with the aid of single-layer graphene.
The theoretical and numerical simulated results demonstrate that the SPPs at different frequencies within a
broadband range can be trapped at different positions on the graphene surface, which can be used as a broadband
spectrometer and optical switch. Meanwhile, the group velocity of the SPPs can be modulated to be several hun-
dred times smaller than light velocity in vacuum. Based on the theoretical analyses, we have predicted the trapping
positions and corresponding group velocities of the SPP waves with different frequencies. By appropriately tuning
the gate voltages, the trapped SPP waves can be released to propagate along the surface of graphene or out of the
graded grating zone. Thus, we have also investigated the switching characteristics of the slow light system, where
the optical switching can be controlled as an “off” or “on” mode by actively adjusting the gate voltage. The slow
light system offers advantages, including broadband operation, ultracompact footprint, and tunable ability
simultaneously, which holds great promise for applications in optical switches. © 2017 Chinese Laser Press
OCIS codes: (050.2770) Gratings; (200.6715) Switching; (230.7370) Waveguides; (240.6680) Surface plasmons.

https://doi.org/10.1364/PRJ.5.000604

1. INTRODUCTION Graphene, a 2D material of carbon atoms arranged in a

Surface plasmon polaritons (SPPs) are electromagnetic (EM) honeycomb lattice, whose optical response is characterized
waves coherently coupled to electron oscillations that present by surface conductivity, behaves like the thin metal films with
the confined EM field at the corresponding metal interface, negative permittivity via external tunability, such as the electric
which can efficiently slow down the light and realize light field, chemical doping, and gate voltage at the THz range
manipulation in the nanoscale [1]. Noble metals, like silver [5–7]. These unique optical features have made graphene a
and gold, are typically regarded as the dominant materials for promising candidate for novel nanophotonic devices, such as
supporting SPPs at the visible and near-infrared range. Even in superlens, optical hyperlens, and SPP waveguides [6,8,9]. The
the terahertz (THz) range, SPP-based slow light systems can propagation of SPP waves along the graphene sheet have large
also be realized by using different noble metal nanostructures, wave vectors as well as extremely high field confinement, which
such as a flat metal stripe or metal-graded period grating [2,3]. enables us to build potential optical devices with dimensions
Such SPP-based systems have the advantages of overcoming the significantly below the diffraction limit. In addition, the large
diffraction limit of light and providing the possibility of the manipulating characteristics of graphene’s permittivity may en-
miniaturization of slow light devices [4]. However, in the THz able freedom to control the devices’ performances during op-
range, SPPs have weak confinement and high loss on the metal eration. It is therefore inferred that graphene plasmonics (GPs)
surface, so the noble metals are unsuitable in this waveband. In are promising in THz to the mid-infrared region (MIR), where
addition, the large electronic density of states in metals also there are various significant applications of slow light systems.
restricts the possibility of dynamically tuning their permittivity In fact, the application of GP-based THz slow light systems has
in active plasmonic devices. Current THz active plasmonic been extensively investigated. For example, Chen et al. first re-
devices can be usually realized with the assistance of another ported the GPs “rainbow trapping” by linearly increasing the
active material, including transparent conducting oxides, super- grooves’ width of silicon grating [10]. Then Lu et al. proposed
conductors, and graphene. another GPs “rainbow trapping” structure based on a graded

2327-9125/17/060604-08 Journal © 2017 Chinese Laser Press

 Research Article Vol. 5, No. 6 / December 2017 / Photonics Research 605

depth of silicon-grating to trap the generated SPPs of different

frequencies at different positions [11]. Nasari and Abrishamian
took advantage of the strong EM field of GPs to design a tun-
able THz Bragg reflector by using the Kerr nonlinear medium
[12]. Recently, Shi et al. designed a tunable band-stop filter
based on GPs with periodically modulated chemical potentials
[13]. However, there is little work focusing on the THz plas-
monic switch. The THz plasmonic switch is actually an impor-
tant component in modern telecommunication systems. The
GPs offers the potential building blocks for developing ultra- Fig. 1. Schematic of a uniform graphene-based grating structure: a
compact, high-performance, and actively tunable THz switch graphene monolayer on a uniform silicon grating structure with
devices. Recently, a deep-wavelength THz plasmonic wave- PMMA as the interlayer. p is the grating period, w1 and w2 denote
guide has been proposed by means of a graphene-metal struc- the widths of nongroove parts and groove parts of the grating, w2
ture, performing as a THz switch or an AND/OR logic gate is fixed at 30 nm in our work, and d 1 and d 2 are the depths of
graphene sheet to nongroove and groove parts, respectively.
[14], which is still difficult for practical implementation be-
cause of the complicated structures and suffering from high loss
in the metal.
In this paper, we propose a novel THz switch based on a And the second term corresponding to the interband tran-
graphene monolayer covered nongroove silicon graded-width sition contribution, for ℏω ≫ K B T and jμc j ≫ K B T , can be
grating, in which the graphene and silicon are separated by poly- described as
methylmethacrylate (PMMA) as an interlayer, and the optical  
e2 2jμc j − ℏω  iτ−1 
properties of graphene can be tuned via an external gate voltage. σ inter
i ln ; (2)
4πℏ2 2jμc j  ℏω  iτ−1 
We theoretically and numerically demonstrate that the SPPs at
different frequencies within a broadband region can be trapped where e is the electron charge, K B is the Boltzmann’s constant,
at different positions on the graphene surface. The group velocity T is the temperature, μc is the chemical potential, ω is the
of the generated SPPs can also be reduced several hundred times angular frequency, ℏ is the reduced Planck’s constant, and τ
than light velocity in vacuum. The trapping positions of the gen- stands for the momentum relaxation time due to charge carrier
erated SPPs with given frequencies can be accurately predicted; scattering. In the MIR, the surface conductivity of graphene
therefore, our proposed system can function as a broadband can be simplified into the Drude-like form [6]. In graphene,
spectrometer. Furthermore, the release of the trapped waves τ depends on the carrier mobility μ and can be expressed as
can be realized by actively tuning the gate voltage. Once a certain τ
μμc ∕ev 2f , and the chemical potential can be expressed
threshold voltage for a given trapped wave is reached, the wave as μc
ℏvf πns 1∕2 . Here, the Fermi velocity v f is set as
will finally be out of the graded grating zone, which can function 106 m∕s, the carrier mobility of graphene μ is assumed as
as an optical switch in broadband by actively adjusting the gate 40; 000 cm2 · V −1 · s−1 at T
300 K [17]. In particular,
voltage. The proposed structure would also find broad applica- the doping level of graphene ns shows a linear dependence
tions in other fields, such as optical storage, signal processing, on the external gate voltage described as ns
εp ε0 V b ∕eh
nonlinear optical enhancement, and so on. [18]. The εp and V b are the relativity permittivity of the dielec-
tric layer of PMMA and external voltage, respectively.
In the simulations, the proposed graphene-based structures
2. RESULTS AND DISCUSSION are simulated by using a home-made program based on the fi-
A. Basic Model and Analytical Theory nite-element method (FEM). Five-layer meshes are employed
We first consider a uniform silicon-grating structure, which con- to denote the graphene layer, while nonuniform meshes with a
sists of a graphene monolayer on a silicon-grating substrate with a maximum element size of 500 nm are adopted to represent the
dielectric layer of PMMA, as schematically shown in Fig. 1. other regions besides graphene. The surface plasmonic wave is
A gate voltage is applied between the graphene sheet and sub- excited by a surface current from the left side. Both scattering
strate to turn the Fermi energy of graphene by the electric-field boundary condition and perfectly matched layers have been
effect [15]. The distribution of the electric field is periodical due used to absorb any reflected and transmitted fields. The gra-
to the periodical distribution of the depths of d 1 and d 2 , which phene monolayer is treated as an ultrathin film layer with a
result in the periodical distributions of the chemical potential thickness of Δ
1 nm [19]. The relative permittivity of gra-
and the conductivity in the graphene layer. The monolayer gra- phene can be equivalent as [6]
phene can be characterized by a complex-valued surface conduc- iσ g
tivity σ g, which can be modeled following the Kubo formula εg
1  : (3)
ωε0 Δ
[16]. The frequency-dependent surface conductivity can be ex-
pressed as a sum of two terms:σ g
σ intra  σ inter . The first term Because SPPs are highly confined on the graphene surface,
corresponding to the intraband electron-photon scattering can the influence of Si substrate on the SPP dispersion can be ne-
be described as glected in our GPs structures [11]. By matching the boundary

    conditions for the air-graphene-PMMA spacer system, the
e2K B T μc μc
σ intra
i 2 2ln exp − 1 : (1) dispersion relation of SPP modes in graphene can be derived
π ωiτ−1  K B T K BT from Maxwell’s equations [20]:
 606 Vol. 5, No. 6 / December 2017 / Photonics Research Research Article

cosK p
neff ;1  neff ;2  n − n 

cosφ1  φ2  − eff ;1 eff ;2 cosφ1 − φ2 ;
4neff ;1 neff ;2 4neff ;1 neff ;2
(5)

where K is the Bloch wave number of the SPPs in the direction

along the propagating direction, p
w1  w2 is the period of
the grating, φ1
k0 neff ;1 w1 and φ2
k 0 neff ;2 w2 represent
the phases of the graphene zones with PMMA depth of d 1
(nongroove parts) and d 2 (groove parts), respectively.
As shown in Fig. 3(a), the dispersion curves of SPP modes in
the uniform grating with w2
30 nm (groove parts) and
V b
60 V but different w1 (nongroove parts) are calculated
by solving Eq. (5). It can be seen that the cutoff frequency dem-
onstrates a visible redshift characteristics with increasing the
nongroove parts’ width w1 . At approaching cutoff frequency,
the SPP mode dispersion is flat compared with that of the
light (straight line), which implies that the group velocity
(v g
d ω ∕d k ) of the SPP mode significantly slows down [21].
Therefore, based on this theory, a slow-light waveguide can be
realized. The slow-down factor (S), which can describe how
many times light has been slowed, is defined as S
c∕v g ,
where the group velocity v g is obtained from the slope of

Fig. 2. Real parts of the effective refractive index (neff ) of SPP

modes supported by the graphene monolayer, (a) as the function of
frequency and the PMMA spacer depth d
d 1
d 2 with a constant
gate voltage of V b
60 V, and (b) as the function of frequency and
the influence of the gate voltage V b with constant PMMA spacer
(d
d 1
d 2
50 nm).

εc εp iσ g
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 
0; (4)
2 2
k 0 neff − εc k0 neff − εp ωε 0

where k 0
2π∕λ is the free-space wave vector of light, λ is the

incident wavelength in vacuum, neff is the effective refractive
index of SPP mode, εp is the relative permittivity of
PMMA, εc denotes the relative permittivity of air, and ε0 is
the permittivity of air. Here, we set εc
1, εp
2.25, respec-
tively [21]. According to Eq. (4), the surface conductivity of
graphene determines the neff of the SPP mode, which is sensi-
tive to the depth (d ) and gate voltage V b . As show in Figs. 2(a)
and 2(b), for a nongrating structure (d
d 1
d 2
50 nm),
the real part of effective refractive index Reneff  as a function of
d and V b can be obtained by solving Eqs. (1)–(4). The real
parts of neff increase significantly with increasing spacer depth
of d and show a pronounced decrease with increasing gate volt-
age of V b . Therefore, for a uniform graphene-based silicon-
grating structure, the different depths and gate voltages can
result in different effective refractive index.
Fig. 3. (a) Dispersion curves for different nongroove parts’ widths
B. Uniform Grating Structure in the graphene-based uniform grating structure. (b) Dependence of
For a uniform graphene-based silicon-grating structure (Fig. 1), slow-down factor S on the excitation frequencies for different non-
the dispersion relation can be calculated by the characteristic groove widths. In the calculations, d 1
50 nm, d 2
250 nm,
equation [22]: w2
30 nm, V b
60 V.
 Research Article Vol. 5, No. 6 / December 2017 / Photonics Research 607

the tangent of a dispersion curve at a given point [23]. Figure 3(b) the MIR and a TM polarized SPP mode will propagate along the
shows the slow-down factor S as a function of light frequency for graphene monolayer. For example, the waves with the wave-
different w1 , which reveals that the S at the asymptotic cutoff lengths of 9, 9.5, and 10 μm are trapped at x
280, 975,
frequency can reach to its maximum value and can significantly and 1855 nm, corresponding to the nongroove width of
be decreased with increasing the w1 . It can be seen that the v g w1
34, 44, and 55 nm. Figure 5(b) illustrates the correspond-
of SPP mode can be reduced to several hundred times than ing electric field intensity (jE y j2 ) distribution in the x–y plane of
light velocity in vacuum, which could be used for implementing the structure for incident wavelengths of 9, 9.5, 10 μm, and the
practical slow-light applications. However, the uniform grating incident waves are trapped at different positions along the gra-
structure (with a fixed groove and nongroove widths) can only phene waveguide, respectively, which result in the so-called
slow down the group velocity of SPP mode within a rather narrow “trapped rainbow” and can be used for the storage of light.
bandwidth near the cutoff frequency, which hinders further We can clearly observe that the electric field intensity reaches
improvement of slow-light capacity. its maximum value near the corresponding cutoff position, asso-
ciated with the nongroove width of w1 , but shows a gradual re-
C. Graded Grating Structure duction as the increase of the excitation wavelength [Fig. 5(c)]. As
In Fig. 3(b), we can find that the most efficient reduction of the shown in Figs. 5(a) and 5(b), we can know that the propagation
group velocity in the graphene-based grating structure occurs distance increases with increasing the excitation wavelength, so
when the SPP frequency approaches to the cutoff value of a the absorption loss in graphene also increases as the propagation
given nongroove width w1 . The w1 for the most pronounced of the SPP mode along the graphene surface. In addition, the
slowdown factor increases with increasing the operating wave- group velocity of SPP mode can also be effectively reduced in
length. Therefore, to broaden the spectral region where light the graphene-based graded grating structure. Figure 5(d) reveals
signal can be slowed down, a graphene-based graded grating the slow-down factor as a function of the trapping position of the
structure is proposed, as illustrated in Fig. 4. The graded gra- SPP mode for the incident wavelengths of 9, 9.5, and 10 μm,
ting is achieved by linearly increasing the width of nongroove accordingly. We can find that the slow-down factor strongly de-
parts, w1 , along the x direction, while keeping the width of pends on the nongroove width at a given excitation wavelength.
groove parts, w2 , as a constant. Here, the nongroove width The most efficient reduction of the group velocity in the structure
w1 is chosen to gradually increase from 30 to 65 nm by a fixed presented here occurs when the nongroove width w1 approaches
step of Δ
1 nm. The total length of the graded grating struc- the cutoff value of a given frequency. For example, the slow-down
ture is only 2760 nm and the grade (Δ
1 nm) is small factor up to 375 at x
1855 nm corresponding to the non-
enough, which meet the adiabatic condition (δ
∂k−1 ∕∂x ≈ groove width w1
55 nm when the excitation wavelength is
1∕k 1 −1∕k 2
p ≪ 1, where k1 and k2 are the wavenumbers in the 10 μm. In a word, we can clearly predict that the incident wave
adjacent grating units, and p is the period of the grating) and with different frequencies will stop at different positions along the
ensure that the stop-band edge of the graded grating changes graphene-based graded grating system, from which they will be
slowly with the position along the structure as the nongroove separated to different positions. Therefore, such a graphene-based
widths increase [24]. slow-down system can be used to disperse different frequency
As shown in Fig. 5(a), the theoretical results show that the components of the incoming THz signals and function as a
SPP modes with different incident wavelengths can be trapped broadband spectrometer.
at different positions along the graphene monolayer, associated D. Active Optical Switching Performance
with the corresponding nongroove width w1 . A broadband of The next question is how to release the trapped waves at
5.6 THz wave within a range of 28.6–34.2 THz can be dramati- different positions along the graded grating. It has been
cally slowed down in the designed grating system. The theoreti- demonstrated that trapped waves in the previous metal-based
cal prediction above can be validated by 2D FEM simulations, as plasmonic rainbow trapping systems can be released by capping
shown in the dash–dot lines in Fig. 5(a). The light excitation in the metal grating with a dielectric material and temperature-
tune the refractive index of the material filling the grooves
via the thermo-optic effect [25]. However, a complete release
within a wide bandwidth is still challenging due to the com-
paratively small refractive variation induced by the thermo-
optic materials. In addition, the temperature change may also
affect the optical performance of the device. As discussed in the
previous section [Figs. 1(a) and 1(b)], we can know that the
spacer depth and gate voltage can modulate the dispersion re-
lation of SPP modes. Therefore, to our graphene-based graded
grating structure above, one approach might be the use of a
piezoelectric material to replace the PMMA as the dielectric
Fig. 4. Schematic illustration of the graphene-based graded grating interlayer, whose thickness properties could be temporally
structure. Here, d 1
50 nm, d 2
250 nm, w2
30 nm, and modulated by an external electric field [26]. Alternatively,
V b
60 V. The nongroove width increases linearly from 30 to we could also employ the other more feasible way to control
65 nm with a step of Δ
1 nm; in our simulations, the width of the graphene’s surface conductivity to tune the dispersion re-
the whole structure along the x axis is 2760 nm. lation of SPP modes by adjusting the external gate voltage.
 608 Vol. 5, No. 6 / December 2017 / Photonics Research Research Article

Fig. 5. (a) Trapping position as a function of cutoff frequency. (b) Electric field distributions of jE y j2 in the x–y plane of the graphene graded
grating structure in Fig. 4 for incident wavelengths of 9, 9.5, and 10 μm, respectively. (c) Corresponding normalized field intensities distribution
2 nm above the graphene surface. (d) The slow-down factor S as a function of trapping position for different operating wavelength.

As shown in Fig. 6(a), the value of the cutoff frequency for the will shift to 27.2–34 THz by increasing the gate voltage to 80 V.
SPP mode undergoes a blueshift as V b increases for a given w1 . In other words, this trapped frequency span can be actively tuned
For example, the cutoff frequency for w1
30 nm with V b
by changing the gate voltage between the silicon substrate and the
60 V is 34.4 THz, which shifts to 36.9 THz with V b
80 V. graphene sheet. Thus, the trapping band can be flexibly broad-
Namely, the trapped SPPs located at the corresponding position ened for a given graphene-based graded grating structure. Once a
will move to the other position with adjusting the external gate certain threshold voltage for a given trapped wave is reached, the
voltage. If the V b is big enough, the trapped waves will be re- wave will finally be able to propagate along the graphene wave-
leased and outputted from the edge of the graphene-based wave- guide and out of the graded grating zone, which can function as a
guide [see Fig. 6(b)]. As illustrated in Fig. 6(b), the dotted line tunable broadband optical switching. The optical switching can
shows the trapping positions of 30 THz shifts from 306 to actively control “off” or “on” by properly adjusting the gate volt-
1855 nm along the x axis when the gate voltage increased age. If we want to realize the optical switching characteristics for
from 40 to 60 V. When the V b further increased to 80 V, the our designed system, there will be a critical voltage for different
trapped wave will be released from the graphene waveguide. wavelengths of incident waves, which has been calculated and
Thus, the trapped waves are released as the gate voltage increases. plotted as a function of frequency, as shown in Fig. 7. The critical
Figure 6(c) illustrates the corresponding electric field inten- voltage increases with the frequency of the optical signal propa-
sity (jE y j2 ) distributions for incident frequency of 30 THz gated in the graphene-based optical waveguide. In a word, the
(λ
10 μm) at V b
40, 60, and 80 V, which agree well with structure provides a flexibly broadband slow SPP waveguide to
the corresponding results of the above theoretical prediction. trap and control the light signals in the nanoscale domain, offer-
In addition, it should be noted that the trapped frequency ing potential applications in on-chip light localization, broadband
span is from 24.8 to 30.8 THz at V b
40 V, while the span spectrometer, and optical switching.
 Research Article Vol. 5, No. 6 / December 2017 / Photonics Research 609

Fig. 6. (a) Dispersion curves for w1
30 nm and w1
65 nm with different gate voltages (V b
60 V and V b
80 V). (b) Trapping position
as a function of frequency for different gate voltages. (c) Electric field distributions of jE y j2 in the x–y plane of the structure in Fig. 4 for 10 μm of
V b
40, 60, and 80 V, respective.

Fig. 8. Electric field distributions of jE y j2 in the x–y plane of the

modified structure for 10 μm at V b
40, 60, and 80 V, respectively.
Fig. 7. Theoretical critical gate voltages needed to turn on the op- White lines mark the material boundaries of the modified structure.
tical switching as a function of frequency at the position x
2760 nm The nongroove width increases linearly from 30 to 37 nm with a step
(output position). of Δ
1 nm, and the groove width is fixed at 30 nm.

It should be noted that the electric field intensity (jE y j2 ) of have designed a new switching structure consisting of a graded
the SPP mode in Fig. 6 is gradually weakening with increasing grating (input block) to actively control light and a monolayer
the propagation distance. This attenuation can be contributed graphene waveguide (output block) as an extension to the input
to the inherent materials absorption, scattering loss, and the block to conduct the propagation wave, respectively, as shown
coupling loss (due to the mode momentum mismatching) by the white lines in Fig. 8. The nongroove width of the input
during the longer propagation in the graded grating system. block increases linearly from 30 to 37 nm with a step of
In order to enhance the transmission efficiency of the switching Δ
1 nm (the groove width is fixed at 30 nm), and the cor-
while keeping the characteristic of dynamic adjustment, we responding critical voltage is 45 V. Figure 8(a) shows the field
 610 Vol. 5, No. 6 / December 2017 / Photonics Research Research Article

distribution when the graphene layer is biased by 20 V and surface. The applied gate voltages can be employed to effi-
incident frequency is 30 THz (λ
10 μm), and we can ob- ciently tune the trapping positions and group velocities of
serve that the SPP wave stopped on the front end of the input the trapped SPPs. Thus, inputting optical signals with different
block, and almost no light can reach to the out block due to the frequencies can be accordingly separated and trapped at differ-
bias voltage being much less than the corresponding critical ent positions in the graphene surface, which can be used as a
voltage. When the bias voltage is close to but less than the criti- broadband spectrometer. Also, the release mechanism is dis-
cal voltage (e.g., 40 V), only little energy can be derived from cussed in terms of real-time modification of the gate voltage.
the input block, which will stop at one certain position in the Once a certain threshold voltage for a given trapped wave is
input block, as shown in Fig. 8(b). And once the bias voltage reached, the wave will finally be out of the graded grating zone.
reaches to and becomes greater than the critical voltage (e.g., The trapped waves within a broad frequency band are predicted
60 V), the switching will be opened; meanwhile, the transmis- to propagate along the graphene or out of the graded grating
sion efficiency is high, which can be confirmed by the corre- zone by modulating the dispersion curve via bias voltage. In a
sponding field distribution shown in Fig. 8(c). Furthermore, as word, the unique optical features of the graphene-based graded
depicted in the Figs. 5 and 6, we can know that the switching grating structure can be applied in the novel designs of the
also has a wide optical bandwidth by applying an appropriate plasmonic devices targeted toward the applications in optical
gate voltage. Without changing any design parameters, as long buffers, spectrometer, optical switching, slow-light systems,
as ascertaining the corresponding critical voltage, one can and nonlinear optical devices.
obtain a wide range of operating wavelengths and a flexible con-
trol of transmission efficiency by appropriately tuning the bias Funding. Fundamental Research Funds for the Central
voltage, which holds great promise for application in future Universities (JD2017JGPY0005); National Natural Science
dynamic switching devices. Foundation of China (NSFC) (61775050).
E. Discussion
Acknowledgment. The authors gratefully acknowledge
In fact, with the development of the THz optoelectronic inte-
the financial support for this work from the National
grated circuits, THz devices have attracted significant attention.
Natural Science Foundation of China and the Fundamental
Among them, the THz switch is of particular interest because it
Research Funds for the Central Universities.
is a dispensable element for information processing at THz
communication and surveillance. In our designed graphene-
based-graded grating system, the applied gate voltages can be
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