Abstract

A novel graphene-based grating-coupled metamaterial structure is proposed, and the optical response of this structure can be obviously controlled by the Fermi level, which is theoretically regulated by the electric field of an applied voltage. The upper graphene monolayer can be intensely excited with the aid of periodic grating and thus it can be considered a bright mode. Meanwhile, the lower graphene monolayer cannot be directly excited, but it could be indirectly activated by the help of bright mode. The plasmonic polaritons resulting from the light-graphene interaction resonance can lead to a destructive interference effect, leading to a plasmonic induced transparency. This structure has a simple construction and retains the integrity of graphene. In the meantime, it can achieve a good tuning effect by adjusting the voltage regulation of microstructure array and it can obtain an outstanding reflection efficiency. Thus, this graphene-based metamaterial structure with these properties is very suitable for the plasmonic optical reflector. In contacting with the characteristics of material, the group delay of this device can reach to 0.3ps, which can well match the slow light performance. Therefore, the device is expected to make some contribution in optical reflection and slow light devices.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Graphene, previously considered to be an unstable structure, has attracted the attention of researchers all over the world with its debut [15]. In the train of this discovery, various devices are coming in a throng, which can be used in materials [6,7], biomedicine [8,9], energy [4,10] and many aspects [11,12]. Nowadays, the graphene monolayers with high mobility and large area have been prepared, and the Fermi level of graphene can be controlled artificially by electronic doping or chemical doping. Moreover, graphene has outstanding electronic, mechanical and optical properties, so it can be well used in various devices, such as photodetectors [13,14], optical modulators [15,16], optical absorbers [17,18] and so on. With the theoretical research and a further investigation to the monolayer graphene, the researchers are surprised to find that graphene has very similar properties to noble metal in terahertz band [1922]. Graphene can also excite the surface plasmon wave, but it has some different properties which are incomparable to noble metal. For example, graphene can completely agree with external direct regulation by voltage without changing the structural size, and this plays a decisive role in some optical adjustable devices. In addition, the surface plasmon wave excited by graphene has a longer propagation distance and life time [23,24], and these have a very important impact on the designed function of device. Moreover, the huge ohmic loss of traditional noble metal in micro-nano structure also greatly limits the development of noble metal-based devices [2528]. But unlike this, graphene can be talent showing itself with an excellent electrical and optical properties.

Researchers can design different metamaterial elements and artificially construct structural parameters of the designed elements. In this way, it is equivalent to making the designed structural unit act as an atomic three-level system [29,30]. Therefore, the mode excited by the designed elements can produce destructive interference effect, and then it can result in electromagnetically induced transparency (EIT) and plasmonically induced transparency (PIT) [3137]. Moreover, the optical plasmonically induced transparency phenomenon can slow down the speed of optical pulse in the micro-nano structure array, and thus it can realize a slow light device, also it has excellent application prospect in the optical storage. In the terahertz (THz) graphene-based system, the periodic incident source can successfully excite graphene surface plasmon under the action of auxiliary grating or graphene pattern [9,21,38,39]. Through the application of external voltage, an externally regulated electron doping can be constructed, and people could theoretically adjust the Fermi level of the graphene monolayer by this way.

In this work, we have built a novel periodic graphene-based grating-coupled structure. The structure is composed of two graphene monolayers and a dielectric grating. With the aid of grating, the upper graphene monolayer can strongly resonate with electromagnetic field of incident source, generating a transmission valley in the spectrum, thus this upper monolayer can be acted as a bright mode. In addition, the lower graphene monolayer has no effective excitation about the incident source, but a local strong resonance effect between the dark and bright mode has occurred, thus this layer is acted as a dark mode. Then, there is an interference between bright and dark modes, resulting in an obvious plasmonically induced transparency phenomenon. By changing the Fermi level of graphene, we can adjust the optical effect of this device very well. Because the graphene involved in this device is a complete plane, we can externally modulate it to tune the optical effect without changing any structural parameters. With the help of coupled mode theory between the bright and dark mode, we can comprehensive analysis the transmission spectra and reflection spectra. Combined with the data of numerical simulation, we have well analyzed the optical performance of this device. Through analyzing the dispersion relation of this device, we can find that the device has a good effective refractive index and it is expected to realize a slow light device. By the coupled mode theory theoretical calculation, the group delay of the device can reach 0.3 ps by calculation, which can meet the requirements of slow light devices. This research can provide some theoretical guidance and help in the optical reflector and slow light device.

2. Structure and theoretical model

As shown in Fig. 1, in a unit of the periodic structure, it is composed of two graphene monolayers sandwiched periodically in a silicon-air grating with relative permittivity of silicon εSi= 11.9 [40]. More narrowly, the upper graphene monolayer crosses the two air slits of the grating, and the lower graphene monolayer is located at the bottom of the dielectric silicon. All the numerical simulation data are obtained by the finite-difference time-domain (FDTD) method. In these simulations, the device is a periodic structure, thus a periodic boundary conditions are chosen in the x direction, and the perfectly matched layers is set at the z direction. Moreover, compared with the x direction of this device, the y direction of this device is a single form and can be considered as infinite, so we can use the two-dimensional model to analyze the phenomenon of this device in order to reduce the calculation time. Moreover, the structural parameters of this device are: L=1000 nm, H=150 nm, l=200 nm, h=50 nm, lg1= 920 nm, hg1=25 nm, lg2= 300 nm, hg2=25 nm. These parameters are fixed in this paper. Because this device operates at terahertz region and normal temperature, the optical conductivity of graphene can be approximated as a Drude-like model [41,42]:

$$\sigma = \frac{{i{e^2}{E_F}}}{{\pi {\hbar ^2}(\omega + i{\tau ^{ - 1}})}}, $$
here, the following condition also be required for this simplification: EF ≫ (ћω, kBT). Additionally, i, e, EF, kB, ћ, ω, τ, respectively, are the imaginary unit, elementary charge, Fermi level, Boltzmann constant, reduced Planck constant, angular frequency, carrier relaxation time. In this investigation, the temperature T is normal temperature (300 K). Moreover, the Fermi level of monolayer graphene could be experimentally modified from 0.2 eV to 1.2 eV after applying an appropriate bias voltage [1,24,43,44]. Thus, we can reasonably assume that the Fermi level of monolayer graphene in this design is located at 0.6 eV to 0.9 eV. It should be noted that the carrier relaxation time also satisfies the following equation: τ = μEF / (evF2), the carrier mobility [24,45] and Fermi velocity are 1.00 m2/ (V·s) and 106 m/s, respectively.

 figure: Fig. 1.

Fig. 1. (a) The tunable plasmonic graphene-based device. The inset is the right view of this device, and it is the theoretical regulated schematic diagram between the voltage and Fermi level of graphene. (b) The front view of one unit of the periodic device.

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The light source is incident from the negative z-axis direction, as shown by the red arrow in Fig. 1(a). With the interaction with the light source, the upper graphene monolayer is a superradiant mode, considered as a bright mode whose optical transmission spectrum exhibits a very wide valley, as shown by the black line in Fig. 2(a). On the other hand, the lower graphene monolayer cannot be excited directly and it can act as a subradiant mode, seen as a dark mode whose spectrum is very narrow, as shown by the red line of Fig. 2(a). Thus, the superradiant and subradiant modes have arisen a destructive interference, resulting in an obvious induced transparent peak, as shown by the blue line of Fig. 2(a). Through the electric field corresponding to the resonant frequency, we can see that when there is only a single layer of the upper graphene, the energy is only distributed in the edge plane of the graphene layer. When there is only lower graphene monolayer, the energy distribution of the whole cycle is very small. When two layers of graphene exist at the same time, due to the interference effect between bright and dark modes, we can see that there is a very large energy distribution at the both two monolayer graphene (The upper and lower monolayers). The strong energy distribution in the two monolayer graphene also indicates the appearance of plasmonically induced transparency.

 figure: Fig. 2.

Fig. 2. (a) The optical transmission spectrum of the plasmonic graphene-based structure. (b) The equivalent coupled mode model of this device. (c-e) The electric field distribution of bright mode (c), dark mode (d) and plasmonically induced transparency at 5 THz (e). (f-g) The electric field distribution of plasmonically induced transparency at dip1 (f, 4.31 THz), dip2 (g, 6.57 THz), respectively. At this time, the Fermi level is equal to 0.8 eV.

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Under light source and assistance of periodic structure, the two graphene monolayers show different states in the optical effect. As shown in the transmission spectrum, the upper graphene monolayer can emerge strong coupling effect with the incident light. Thus, we call it as superradiant layer (A1), which corresponds to the bright mode. The graphene in the lower layer has little correlation with the incident light, and we can call is as subradiant layer (A2) which is corresponding to the dark mode. Moreover, the dark mode of subradiant layer can be indirectly excited by the bright mode of superradiant layer. Thus, interactions between the bright and dark mode can lead to resonance effect, resulting in a plasmonically induced transparency phenomenon. The coupling theoretical relationship between the two modes is shown in Fig. 2(b). The meanings of each parameter are as follows: A represents the incident or outgoing wave carried by each mode (where, the superscript in represents the incident wave, out represents the outgoing wave, the subscript + represents the wave propagating in the positive direction, and - represents the wave propagating in the negative direction, respectively). γin (n = 1, 2, representing the superradiant and subradiant modes) is the internal loss coefficient of nth mode. γon (n = 1, 2) is the external loss coefficient of nth mode. μnm is the coupling coefficient between nth and mth modes (n=1, 2; m=1,2; mn). If we respectively express a1 and a2 as the complex amplitudes of the bright (A1) and dark (A2) modes, the two oscillation radiation between resonant modes of this system can be expressed as [46]

$$\left( \begin{array}{cc}{{\gamma_1}}&{ - i{\mu_{12}}}\\ { - i{\mu_{21}}}&{{\gamma_2}} \end{array} \right) \cdot \left( \begin{array}{c} {{a_1}}\\ {{a_2}} \end{array} \right) = \left( \begin{array}{cc} { - {\gamma_{o1}}^{1/2}}&0\\ 0&{ - {\gamma_{o2}}^{1/2}} \end{array} \right) \cdot \left( \begin{array}{cc} {A_{1 + }^{in} + A_{1 - }^{in}}\\ {A_{2 + }^{in} + A_{2 - }^{in}} \end{array} \right), $$
here, ${\gamma _n} = i\omega - i{\omega _n} - \gamma _{in}^{} - \gamma _{on}^{}$(n=1, 2, ω is the angular frequency of incident source, ωn is the resonant angle frequency of the nth mode).

According to the conservation of energy in the coupled resonator, the incident and outgoing waves in the resonator also meet the following relationship:

$$A_{2 + }^{in} = A_{1 + }^{out}{e^{i\varphi }},A_{1 - }^{in} = A_{2 - }^{out}{e^{i\varphi }}$$
$$A_{n + }^{out} = A_{n + }^{in} - \gamma _{on}^{1/2}{a_n},A_{n - }^{out} = A_{n - }^{in} - \gamma _{on}^{1/2}{a_n}(n = 1,2)$$
Where, φ is phase difference between the superradiant and subradiant modes. Combining the Eq. (2)–(4) and assuming that the excitation source only incident from the positive direction (i.e. $A_{2 - }^{in} = 0$), we can receive the transmission / reflection coefficient about this system:
$$\begin{aligned} t = \frac{{A_{2 + }^{out}}}{{A_{1 + }^{in}}} = &{e^{i\varphi }} + ({\gamma _{o1}}{\gamma _2}{e^{i\varphi }} + {\gamma _1}{\gamma _{o2}}{e^{i\varphi }} + {({\gamma _{o1}}{\gamma _{o2}})^{1/2}}{e^{2i\varphi }}{\chi _1}\\ &+ {({\gamma _{o1}}{\gamma _{o2}})^{1/2}}{\chi _2}){({\gamma _1}{\gamma _2} - {\chi _1}{\chi _2})^{ - 1}} \end{aligned},$$
$$\begin{aligned} r = \frac{{A_{1 - }^{out}}}{{A_{1 + }^{in}}} = &({\gamma _{o1}}{\gamma _2} + {\gamma _{o2}}{\gamma _1}{e^{2i\varphi }} + {({\gamma _{o1}}{\gamma _{o2}})^{1/2}}{\chi _1}{e^{i\varphi }}\\ &+ {({\gamma _{o1}}{\gamma _{o2}})^{1/2}}{\chi _2}{e^{i\varphi }}){({\gamma _1}{\gamma _2} - {\chi _1}{\chi _2})^{ - 1}} \end{aligned}. $$
Here, ${\chi _1} = i{\mu _{12}} + {(\gamma _{o1}^{^{}}\gamma _{o2}^{^{}})^{1/2}}{e^{i\varphi }},{\chi _2} = i{\mu _{21}} + {(\gamma _{o1}^{^{}}\gamma _{o2}^{^{}})^{1/2}}{e^{i\varphi }}$. Therefore, according to this transmission and reflection coefficient, we can easily get the transmission (T) and reflection (R) of the system as follows: T = t^2, R = r^2.

3. Simulation and discussion

The excited surface plasma wave propagates along the surface between graphene and dielectric. We can approximate the dispersion relationship of this device according to the design of the whole structure and the boundary conditions of electromagnetic field, and then we can understand the propagation properties of graphene surface plasmon. Due to the transverse magnetic (TM) wave properties of graphene-based plasmonic wave in terahertz region, we can name the electromagnetic components as: Hy component for the magnetic field, Ex and Ez components for the electric field. For Helmholtz equation and harmonic time dependence $\frac{\partial }{{\partial t}} ={-} i\omega$, we can arrive at the following set of coupled equations for TM mode:

$$\left\{ \begin{array}{l} {{E_x} ={-} i\frac{1}{{\omega {\varepsilon_0}{\varepsilon}}}\frac{{\partial {H_y}}}{{{\partial {z}}}},{E_z} ={-} \frac{\beta }{{\omega {\varepsilon_0}{\varepsilon}}}{H_y}}\\ {\frac{{{\partial^2}{H_y}}}{{\partial {z^2}}} + ({k_0}^2\varepsilon - {\beta^2}){H_y} = 0} \end{array} \right., $$
for z > d, the respective expressions of field components are
$$\left\{ \begin{array}{l} {{H_{y1}} = A{e^{i\beta x}}{e^{ - {k_1}z}}}\\ {{E_{x1}} = iA\frac{1}{{\omega {\varepsilon_0}{\varepsilon_1}}}{k_1}{e^{i\beta x}}{e^{ - {k_1}z}}}\\ {{E_{z1}} ={-} A\frac{\beta }{{\omega {\varepsilon_0}{\varepsilon_1}}}{e^{i\beta x}}{e^{ - {k_1}z}}} \end{array} \right., $$
where, for 0 > z, we get
$$\left\{ \begin{array}{l} {{H_{y3}} = D{e^{i\beta x}}{e^{{k_3}z}}}\\ {{E_{x3}} ={-} iD\frac{1}{{\omega {\varepsilon_0}{\varepsilon_3}}}{k_3}{e^{i\beta x}}{e^{{k_3}z}}}\\ {{E_{z3}} ={-} D\frac{\beta }{{\omega {\varepsilon_0}{\varepsilon_3}}}{e^{i\beta x}}{e^{{k_3}z}}} \end{array} \right.. $$
In the core region d > z > 0, the modes localized at the bottom and top interface couple, yielding
$$\left\{ \begin{array}{l} {{H_{y2}} = B{e^{i\beta x}}{e^{{k_2}z}} + C{e^{i\beta x}}{e^{ - {k_2}z}}}\\ {{E_{x2}} ={-} iB\frac{1}{{\omega {\varepsilon_0}{\varepsilon_2}}}{k_2}{e^{i\beta x}}{e^{{k_2}z}} + iC\frac{1}{{\omega {\varepsilon_0}{\varepsilon_2}}}{k_2}{e^{i\beta x}}{e^{ - {k_2}z}}} \\ {{E_{z2}} ={-} B\frac{\beta }{{\omega {\varepsilon_0}{\varepsilon_2}}}{e^{i\beta x}}{e^{{k_2}z}} - C\frac{\beta }{{\omega {\varepsilon_0}{\varepsilon_2}}}{e^{i\beta x}}{e^{ - {k_2}z}}} \end{array} \right.. $$
Here, ${k_1}^2 = {\beta ^2} - {\varepsilon _1}{k_0}^2,{k_2}^2 = {\beta ^2} - {\varepsilon _2}{k_0}^2,{k_3}^2 = {\beta ^2} - {\varepsilon _3}{k_0}^2.$ β is propagation constant and k0 is the wave vector of the propagating wave in free space, respectively.

The boundary conditions of electromagnetic field (${H_{1t}} - {H_{2t}} = \sigma E,{E_{1t}} = {E_{2t}}$) and the requirement of continuity of Hy and Ex leads to

$$\left\{ \begin{array}{l} {z = d:\frac{{\frac{{{k_1}}}{{{\varepsilon_1}}}}}{{1 + \frac{{i\sigma }}{{\omega {\varepsilon_0}}}\frac{{{k_1}}}{{{\varepsilon_1}}}}} = \frac{{ - B\frac{{{k_2}}}{{{\varepsilon_2}}}{e^{{k_2}d}} + C\frac{{{k_2}}}{{{\varepsilon_2}}}{e^{ - {k_2}d}}}}{{B{e^{{k_2}d}} + C{e^{ - {k_2}d}}}}}\\ {z = 0:\frac{{ - \frac{{{k_3}}}{{{\varepsilon_3}}}}}{{1 + \frac{{i\sigma }}{{\omega {\varepsilon_0}}}\frac{{{k_3}}}{{{\varepsilon_3}}}}} = \frac{{ - B\frac{{{k_2}}}{{{\varepsilon_2}}} + C\frac{{{k_2}}}{{{\varepsilon_2}}}}}{{B + C}}} \end{array} \right.. $$

Solving this system of linear equations results in an implicit expression for the dispersion relation linking β and ω via

$${e^{2{k_2}d}} = \frac{{\frac{{{k_1}}}{{{\varepsilon _1}}} - \frac{{{k_2}}}{{{\varepsilon _2}}}(1 + \frac{{i\sigma }}{{\omega {\varepsilon _0}}}\frac{{{k_1}}}{{{\varepsilon _1}}})}}{{\frac{{{k_1}}}{{{\varepsilon _1}}} + \frac{{{k_2}}}{{{\varepsilon _2}}}(1 + \frac{{i\sigma }}{{\omega {\varepsilon _0}}}\frac{{{k_1}}}{{{\varepsilon _1}}})}} \cdot \frac{{\frac{{{k_3}}}{{{\varepsilon _3}}} - \frac{{{k_2}}}{{{\varepsilon _2}}}(1 + \frac{{i\sigma }}{{\omega {\varepsilon _0}}}\frac{{{k_3}}}{{{\varepsilon _3}}})}}{{\frac{{{k_3}}}{{{\varepsilon _3}}} + \frac{{{k_2}}}{{{\varepsilon _2}}}(1 + \frac{{i\sigma }}{{\omega {\varepsilon _0}}}\frac{{{k_3}}}{{{\varepsilon _3}}})}}. $$

The composite equivalent permittivity of grating can be requested approximately through the following formula: ${\varepsilon _{grating}} = n{\varepsilon _{\textrm{dielectric}}} + (1 - n){\varepsilon _{air}},n = \frac{{{l_{\textrm{dielectric}}}}}{{{L_{grating}}}}$ is the occupation ratio of the dielectric [47,48]. Thus, we can approximate the propagation constant of the graphene surface plasma from the above dispersion relation. According to the definition and the above formula, we can get the effective refractive index (neff =β/k0) of the device. The numerical value of neff is obtained by calculation, and then we have plotted the real part and the imaginary part of the propagation constant and the effective index in the Fig. 3. Obviously, it can be seen from Fig. 3(b) that Re(neff) decreases with the increase of Fermi level at a fixed frequency, meaning that the graphene surface plasmons polaritons can be better limited at a lower Fermi level. Moreover, the numerical value of Re(neff) changes greatly with a slight change of Fermi level, which can be used in the design of dynamic tunable modulator.

 figure: Fig. 3.

Fig. 3. (a) The real part of the propagation constant. (b) The imaginary part of the propagation constant. (c) The real part of the effective index. (d) The imaginary part of the effective index. Fermi level EF = 0.6 eV, 0.7 eV, 0.8 eV, 0.9 eV.

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One of the advantages of graphene is that the applied voltage can be used to adjust the electron concentration, and the Fermi level of graphene can be regulated by the applied voltage. Thus, the device based on graphene can achieve a good tuning effect. The relationship between voltage and Fermi level are as following [45,49,50]:

$${E_F} = \hbar {v_F}{(\frac{{\pi {\varepsilon _0}{\varepsilon _{grating}}{V_g}}}{{{d_{sub}}e}})^{1/2}}$$
here, vF is Fermi velocity 106 m/s, Vg is the applied voltage, and dsub is the distance between the monolayer graphene and the applied electrode.

As mentioned earlier, γin is the internal loss coefficient and it can meet γinn/(2Qin), here, Qin is the internal loss quality factor. γon is the external loss coefficient and it can meet γonn/(2Qon), here, Qon is the external loss quality factor. Moreover, the loss quality factor can match the following formula: 1/Qtn=1/Qon+1/Qin. Qtn is the total quality factor and Qtn=f/Δf, here, f is the resonant frequency of nth mode and Δf is full width of half maximum of nth mode. Besides that, according to the effective refractive index, we can get the value of Qi by the definition: the value of Qi can be obtained by dividing the real part and the imaginary part of the effective refractive index, namely, Qi=Re(neff)/Im(neff). In this way, we can get the theoretical parameters used in the coupled mode theory. Then the value of each Qin can be obtained according to the resonant frequency, and the quality factor values are clearly classified as follows: Qt1=(4.99, 4.81, 4.61, 4.40), Qt2=(3.99, 3.76, 3.54, 3.35), Qi1=(26.81, 33.69, 41.27, 49.37), Qi2=(31.73, 39.73, 48.51, 57.88) as EF= (0.6 eV, 0.7 eV, 0.8 eV, 0.9 eV) in this graphene-based grating-coupled metamaterial structure, respectively. The values of these parameter are shown in Fig. 4.

 figure: Fig. 4.

Fig. 4. (a) The evolutionary relationship between the internal loss quality factor and frequency, where Fermi level of the graphene monolayer is 0.6 eV, 0.7 eV, 0.8 eV, 0.9 eV. (b) The evolution of the resonant frequency with the Fermi level at the resonant dip and peak. dip1, peak1 and dip2 are the low frequency trough, PIT peak and high frequency trough, respectively. (c-d) The value of total quality factor and internal loss quality factor, respectively.

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Therefore, at this time, we can successfully calculate the theoretical transmission spectra of this device according to the Eqs. (5)–(6) obtained by the coupling mode theory, as shown in the red dot line in Fig. 5. It can be seen clearly that the optical transmission and reflection of this designed device fitted by the coupled mode theory are very consistent with the numerical calculation, verifying the correctness of coupled mode theory.

 figure: Fig. 5.

Fig. 5. (a-b) The numerical calculation and theoretical fitting curve of the optical transmission and reflection. The blue solid line is the FDTD numerical result, and the red dotted line is the coupled mode theory data. Fermi level of the graphene monolayer is 0.6 eV, 0.7 eV, 0.8 eV, 0.9 eV.

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From the changing curve in these figures, we can see that the plasmonically induced transparency obtained by this device has a blue shift with the increase of Fermi level. This can be attributed to the increasing resonant energy. As increasing Fermi level of monolayer graphene, the produced resonance between the electron and the incident electromagnetic wave requires a higher energy. Therefore, the resonant frequencies move towards an increasing direction. In other words, there is a blue shift.

We can see that the device has a very high reflection in the spectrum. The value of the reflection can reach over 90 percent. Moreover, the total quality factor of this device at each Fermi level is about equal to Qt1= (4.99, 4.81, 4.61, 4.40) and Qt2= (3.99, 3.76, 3.54, 3.35) for dip1 and dip2, respectively. For the high resonance frequency, the values of total quality factor are relatively low, and it shows that the device has a wide reflection band. With the increase of Fermi level of graphene monolayer, the reflectance also gradually increases. The device has a good reflectance at the resonant frequency and this good reflectance makes this designed system can be used as an optical plasmonic reflector. And it can provide a certain basis for some applications.

In addition, when the surface plasmonically induced transparent phenomenon occurs, the system will have a very instantaneous phase change near the resonant peak, making the designed system have slow light effect. According to this idea, we can calculate the change of group delay data against frequency to express the slow light effect [51,52]: ${\tau _g} = \textrm{d}\theta /\textrm{d}\omega$, here, θ=arg(t) (t is the transmission coefficient).

As shown in Fig. 6, we can see the group delay against frequency at different Fermi levels. Due to the resonance phenomenon caused by the interaction between the graphene monolayers and the incident light, the phase will change greatly, and then it also can lead to a high group delay near the peak of plasmonically induced transparency window. That is to say, the slow light effect is obvious. Through theoretical and numerical calculation, we can know the following information: the group delay of our designed structure can achieve a maximum point of 0.3 picosecond (ps). For the same type of slow light devices, our proposed structure has a good slow light performance [53,54]. This excellent performance can enable our research of this system to supply some constructive guidance for the realization about the slow light applications.

 figure: Fig. 6.

Fig. 6. (a-d) The trend of phase and group delay (ps) against frequency, respectively. Fermi level is equal to 0.6 eV, 0.7 eV, 0.8 eV, 0.9 eV.

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4. Conclusion

In this study, we have constructed a novel periodic grating-coupled graphene-based hybrid system. The system is composed of two graphene monolayers and an auxiliary grating. The graphene can strongly interfere with the incident electromagnetic wave under the excitation of periodic grating. It is found that the upper graphene monolayer considered as bright mode is a superradiant layer due to its good coupling with the incident energy. The lower graphene monolayer considered as dark mode cannot be directly excited by the incident energy, but it can be indirectly excited by the superradiant layer, as a subradiant layer. The destructive interference between the two radiant modes leads to a superior plasmonically induced transparency phenomenon. Through the external voltage modulation of graphene, we have found that the designed device has a good tuning performance with the increase of Fermi level of the graphene monolayer. Moreover, the graphene monolayer in this structure is a complete plane, which has a huge structural advantage compared with those discrete devices. This structure has a very good reflection efficiency and can be used as an optical reflector. Through the analysis of slow light effect, it is also found that this structure has a good group delay coefficient, which can reach 0.3ps, and this coefficient can well meet the requirements of slow light devices. Thus, the designed structure and these obtained data are promising for building high-performance active plasmonic devices.

Funding

National Natural Science Foundation of China (11847026, 61275174).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

References

1. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007). [CrossRef]  

2. P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, and R. A. Wolkow, “Field regulation of single-molecule conductivity by a charged surface atom,” Nature 435(7042), 658–661 (2005). [CrossRef]  

3. Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019). [CrossRef]  

4. I.-H. Lee, D. Yoo, P. Avouris, T. Low, and S.-H. Oh, “Graphene acoustic plasmon resonator for ultrasensitive infrared spectroscopy,” Nat. Nanotechnol. 14(4), 313–319 (2019). [CrossRef]  

5. Q. Ren, J. W. You, and N. C. Panoiu, “Large enhancement of the effective second-order nonlinearity in graphene metasurfaces,” Phys. Rev. B 99(20), 205404 (2019). [CrossRef]  

6. B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018). [CrossRef]  

7. J. Horng, H. B. Balch, A. F. McGuire, H.-Z. Tsai, P. R. Forrester, M. F. Crommie, B. Cui, and F. Wang, “Imaging electric field dynamics with graphene optoelectronics,” Nat. Commun. 7(1), 13704 (2016). [CrossRef]  

8. L. Yang, J.-H. Lee, C. Rathnam, Y. Hou, J.-W. Choi, and K.-B. Lee, “Dual-Enhanced Raman Scattering-Based Characterization of Stem Cell Differentiation Using Graphene-Plasmonic Hybrid Nanoarray,” Nano Lett. 19(11), 8138–8148 (2019). [CrossRef]  

9. D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. De Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015). [CrossRef]  

10. H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019). [CrossRef]  

11. W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013). [CrossRef]  

12. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018). [CrossRef]  

13. T. J. Echtermeyer, S. Milana, U. Sassi, A. Eiden, M. Wu, E. Lidorikis, and A. C. Ferrari, “Surface Plasmon Polariton Graphene Photodetectors,” Nano Lett. 16(1), 8–20 (2016). [CrossRef]  

14. Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012). [CrossRef]  

15. Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016). [CrossRef]  

16. D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015). [CrossRef]  

17. X.-T. Kong, L. Khosravi Khorashad, Z. Wang, and A. O. Govorov, “Photothermal Circular Dichroism Induced by Plasmon Resonances in Chiral Metamaterial Absorbers and Bolometers,” Nano Lett. 18(3), 2001–2008 (2018). [CrossRef]  

18. S. Kim, M. S. Jang, V. W. Brar, K. W. Mauser, L. Kim, and H. A. Atwater, “Electronically Tunable Perfect Absorption in Graphene,” Nano Lett. 18(2), 971–979 (2018). [CrossRef]  

19. L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008). [CrossRef]  

20. L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007). [CrossRef]  

21. W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of Plasmonic Waves in Graphene by Guided-Mode Resonances,” ACS Nano 6(9), 7806–7813 (2012). [CrossRef]  

22. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011). [CrossRef]  

23. F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018). [CrossRef]  

24. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]  

25. Z. He, J. Zhao, and H. Lu, “Tunable nonreciprocal reflection and its stability in a non-PT-symmetric plasmonic resonators coupled waveguide systems,” Appl. Phys. Express 13(1), 012009 (2020). [CrossRef]  

26. Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019). [CrossRef]  

27. M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017). [CrossRef]  

28. C. Xiong, H. Li, H. Xu, M. Zhao, B. Zhang, C. Liu, and K. Wu, “Coupling effects in single-mode and multimode resonator-coupled system,” Opt. Express 27(13), 17718–17728 (2019). [CrossRef]  

29. H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable Phonon-Induced Transparency in Bilayer Graphene Nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014). [CrossRef]  

30. N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009). [CrossRef]  

31. T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018). [CrossRef]  

32. Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020). [CrossRef]  

33. S. Xia, X. Zhai, L. Wang, and S. Wen, “Plasmonically induced transparency in double-layered graphene nanoribbons,” Photonics Res. 6(7), 692–702 (2018). [CrossRef]  

34. H. Xu, M. Zhao, M. Zheng, C. Xiong, B. Zhang, Y. Peng, and H. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D: Appl. Phys. 52(2), 025104 (2019). [CrossRef]  

35. S. Xia, X. Zhai, L. Wang, and S. Wen, “Plasmonically induced transparency in in-plane isotropic and anisotropic 2D materials,” Opt. Express 28(6), 7980–8002 (2020). [CrossRef]  

36. J. Guan, S. Xia, Z. Zhang, J. Wu, H. Meng, J. Yue, X. Zhai, L. Wang, and S. Wen, “Two Switchable Plasmonically Induced Transparency Effects in a System with Distinct Graphene Resonators,” Nanoscale Res. Lett. 15(1), 142 (2020). [CrossRef]  

37. C. Liu, H. Li, H. Xu, M. Zhao, C. Xiong, B. Zhang, and K. Wu, “Slow light effect based on tunable plasmon-induced transparency of monolayer black phosphorus,” J. Phys. D: Appl. Phys. 52(40), 405203 (2019). [CrossRef]  

38. M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013). [CrossRef]  

39. F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017). [CrossRef]  

40. E. D. Palik, Handbook of optical constants of solids (Academic Press, 1985).

41. C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B 85(12), 125431 (2012). [CrossRef]  

42. H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20(40), 25959–25966 (2018). [CrossRef]  

43. D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010). [CrossRef]  

44. S. Balci, O. Balci, N. Kakenov, F. B. Atar, and C. Kocabas, “Dynamic tuning of plasmon resonance in the visible using graphene,” Opt. Lett. 41(6), 1241–1244 (2016). [CrossRef]  

45. S. Xia, X. Zhai, L. Wang, B. Sun, J. Liu, and S. Wen, “Dynamically tunable plasmonically induced transparency in sinusoidally curved and planar graphene layers,” Opt. Express 24(16), 17886–17899 (2016). [CrossRef]  

46. H. A. Haus and W. Huang, “Coupled-Mode Theory “ Proc,” Proc. IEEE 79(10), 1505–1518 (1991). [CrossRef]  

47. X. Zhao, L. Zhu, C. Yuan, and J. Yao, “Tunable plasmon-induced transparency in a grating-coupled double-layer graphene hybrid system at far-infrared frequencies,” Opt. Lett. 41(23), 5470–5473 (2016). [CrossRef]  

48. S. Xia, X. Zhai, Y. Huang, J. Liu, L. Wang, and S. Wen, “Multi-band perfect plasmonic absorptions using rectangular graphene gratings,” Opt. Lett. 42(15), 3052–3055 (2017). [CrossRef]  

49. Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012). [CrossRef]  

50. S. Xia, X. Zhai, L. Wang, Q. Lin, and S. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons,” Opt. Express 24(1), 427–436 (2016). [CrossRef]  

51. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009). [CrossRef]  

52. L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2(8), 474–481 (2008). [CrossRef]  

53. B. Xiao, S. Tong, A. Fyffe, and Z. Shi, “Tunable electromagnetically induced transparency based on graphene metamaterials,” Opt. Express 28(3), 4048–4057 (2020). [CrossRef]  

54. X. Zhao, C. Yuan, L. Zhu, and J. Yao, “Graphene-based tunable terahertz plasmon-induced transparency metamaterial,” Nanoscale 8(33), 15273–15280 (2016). [CrossRef]  

References

  • View by:

  1. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
    [Crossref]
  2. P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, and R. A. Wolkow, “Field regulation of single-molecule conductivity by a charged surface atom,” Nature 435(7042), 658–661 (2005).
    [Crossref]
  3. Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019).
    [Crossref]
  4. I.-H. Lee, D. Yoo, P. Avouris, T. Low, and S.-H. Oh, “Graphene acoustic plasmon resonator for ultrasensitive infrared spectroscopy,” Nat. Nanotechnol. 14(4), 313–319 (2019).
    [Crossref]
  5. Q. Ren, J. W. You, and N. C. Panoiu, “Large enhancement of the effective second-order nonlinearity in graphene metasurfaces,” Phys. Rev. B 99(20), 205404 (2019).
    [Crossref]
  6. B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
    [Crossref]
  7. J. Horng, H. B. Balch, A. F. McGuire, H.-Z. Tsai, P. R. Forrester, M. F. Crommie, B. Cui, and F. Wang, “Imaging electric field dynamics with graphene optoelectronics,” Nat. Commun. 7(1), 13704 (2016).
    [Crossref]
  8. L. Yang, J.-H. Lee, C. Rathnam, Y. Hou, J.-W. Choi, and K.-B. Lee, “Dual-Enhanced Raman Scattering-Based Characterization of Stem Cell Differentiation Using Graphene-Plasmonic Hybrid Nanoarray,” Nano Lett. 19(11), 8138–8148 (2019).
    [Crossref]
  9. D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. De Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015).
    [Crossref]
  10. H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
    [Crossref]
  11. W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013).
    [Crossref]
  12. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
    [Crossref]
  13. T. J. Echtermeyer, S. Milana, U. Sassi, A. Eiden, M. Wu, E. Lidorikis, and A. C. Ferrari, “Surface Plasmon Polariton Graphene Photodetectors,” Nano Lett. 16(1), 8–20 (2016).
    [Crossref]
  14. Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
    [Crossref]
  15. Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
    [Crossref]
  16. D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
    [Crossref]
  17. X.-T. Kong, L. Khosravi Khorashad, Z. Wang, and A. O. Govorov, “Photothermal Circular Dichroism Induced by Plasmon Resonances in Chiral Metamaterial Absorbers and Bolometers,” Nano Lett. 18(3), 2001–2008 (2018).
    [Crossref]
  18. S. Kim, M. S. Jang, V. W. Brar, K. W. Mauser, L. Kim, and H. A. Atwater, “Electronically Tunable Perfect Absorption in Graphene,” Nano Lett. 18(2), 971–979 (2018).
    [Crossref]
  19. L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
    [Crossref]
  20. L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
    [Crossref]
  21. W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of Plasmonic Waves in Graphene by Guided-Mode Resonances,” ACS Nano 6(9), 7806–7813 (2012).
    [Crossref]
  22. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
    [Crossref]
  23. F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
    [Crossref]
  24. A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
    [Crossref]
  25. Z. He, J. Zhao, and H. Lu, “Tunable nonreciprocal reflection and its stability in a non-PT-symmetric plasmonic resonators coupled waveguide systems,” Appl. Phys. Express 13(1), 012009 (2020).
    [Crossref]
  26. Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
    [Crossref]
  27. M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017).
    [Crossref]
  28. C. Xiong, H. Li, H. Xu, M. Zhao, B. Zhang, C. Liu, and K. Wu, “Coupling effects in single-mode and multimode resonator-coupled system,” Opt. Express 27(13), 17718–17728 (2019).
    [Crossref]
  29. H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable Phonon-Induced Transparency in Bilayer Graphene Nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
    [Crossref]
  30. N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
    [Crossref]
  31. T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018).
    [Crossref]
  32. Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
    [Crossref]
  33. S. Xia, X. Zhai, L. Wang, and S. Wen, “Plasmonically induced transparency in double-layered graphene nanoribbons,” Photonics Res. 6(7), 692–702 (2018).
    [Crossref]
  34. H. Xu, M. Zhao, M. Zheng, C. Xiong, B. Zhang, Y. Peng, and H. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D: Appl. Phys. 52(2), 025104 (2019).
    [Crossref]
  35. S. Xia, X. Zhai, L. Wang, and S. Wen, “Plasmonically induced transparency in in-plane isotropic and anisotropic 2D materials,” Opt. Express 28(6), 7980–8002 (2020).
    [Crossref]
  36. J. Guan, S. Xia, Z. Zhang, J. Wu, H. Meng, J. Yue, X. Zhai, L. Wang, and S. Wen, “Two Switchable Plasmonically Induced Transparency Effects in a System with Distinct Graphene Resonators,” Nanoscale Res. Lett. 15(1), 142 (2020).
    [Crossref]
  37. C. Liu, H. Li, H. Xu, M. Zhao, C. Xiong, B. Zhang, and K. Wu, “Slow light effect based on tunable plasmon-induced transparency of monolayer black phosphorus,” J. Phys. D: Appl. Phys. 52(40), 405203 (2019).
    [Crossref]
  38. M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
    [Crossref]
  39. F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
    [Crossref]
  40. E. D. Palik, Handbook of optical constants of solids (Academic Press, 1985).
  41. C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B 85(12), 125431 (2012).
    [Crossref]
  42. H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20(40), 25959–25966 (2018).
    [Crossref]
  43. D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
    [Crossref]
  44. S. Balci, O. Balci, N. Kakenov, F. B. Atar, and C. Kocabas, “Dynamic tuning of plasmon resonance in the visible using graphene,” Opt. Lett. 41(6), 1241–1244 (2016).
    [Crossref]
  45. S. Xia, X. Zhai, L. Wang, B. Sun, J. Liu, and S. Wen, “Dynamically tunable plasmonically induced transparency in sinusoidally curved and planar graphene layers,” Opt. Express 24(16), 17886–17899 (2016).
    [Crossref]
  46. H. A. Haus and W. Huang, “Coupled-Mode Theory “ Proc,” Proc. IEEE 79(10), 1505–1518 (1991).
    [Crossref]
  47. X. Zhao, L. Zhu, C. Yuan, and J. Yao, “Tunable plasmon-induced transparency in a grating-coupled double-layer graphene hybrid system at far-infrared frequencies,” Opt. Lett. 41(23), 5470–5473 (2016).
    [Crossref]
  48. S. Xia, X. Zhai, Y. Huang, J. Liu, L. Wang, and S. Wen, “Multi-band perfect plasmonic absorptions using rectangular graphene gratings,” Opt. Lett. 42(15), 3052–3055 (2017).
    [Crossref]
  49. Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
    [Crossref]
  50. S. Xia, X. Zhai, L. Wang, Q. Lin, and S. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons,” Opt. Express 24(1), 427–436 (2016).
    [Crossref]
  51. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
    [Crossref]
  52. L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2(8), 474–481 (2008).
    [Crossref]
  53. B. Xiao, S. Tong, A. Fyffe, and Z. Shi, “Tunable electromagnetically induced transparency based on graphene metamaterials,” Opt. Express 28(3), 4048–4057 (2020).
    [Crossref]
  54. X. Zhao, C. Yuan, L. Zhu, and J. Yao, “Graphene-based tunable terahertz plasmon-induced transparency metamaterial,” Nanoscale 8(33), 15273–15280 (2016).
    [Crossref]

2020 (5)

Z. He, J. Zhao, and H. Lu, “Tunable nonreciprocal reflection and its stability in a non-PT-symmetric plasmonic resonators coupled waveguide systems,” Appl. Phys. Express 13(1), 012009 (2020).
[Crossref]

Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
[Crossref]

S. Xia, X. Zhai, L. Wang, and S. Wen, “Plasmonically induced transparency in in-plane isotropic and anisotropic 2D materials,” Opt. Express 28(6), 7980–8002 (2020).
[Crossref]

J. Guan, S. Xia, Z. Zhang, J. Wu, H. Meng, J. Yue, X. Zhai, L. Wang, and S. Wen, “Two Switchable Plasmonically Induced Transparency Effects in a System with Distinct Graphene Resonators,” Nanoscale Res. Lett. 15(1), 142 (2020).
[Crossref]

B. Xiao, S. Tong, A. Fyffe, and Z. Shi, “Tunable electromagnetically induced transparency based on graphene metamaterials,” Opt. Express 28(3), 4048–4057 (2020).
[Crossref]

2019 (9)

H. Xu, M. Zhao, M. Zheng, C. Xiong, B. Zhang, Y. Peng, and H. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D: Appl. Phys. 52(2), 025104 (2019).
[Crossref]

C. Liu, H. Li, H. Xu, M. Zhao, C. Xiong, B. Zhang, and K. Wu, “Slow light effect based on tunable plasmon-induced transparency of monolayer black phosphorus,” J. Phys. D: Appl. Phys. 52(40), 405203 (2019).
[Crossref]

C. Xiong, H. Li, H. Xu, M. Zhao, B. Zhang, C. Liu, and K. Wu, “Coupling effects in single-mode and multimode resonator-coupled system,” Opt. Express 27(13), 17718–17728 (2019).
[Crossref]

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019).
[Crossref]

I.-H. Lee, D. Yoo, P. Avouris, T. Low, and S.-H. Oh, “Graphene acoustic plasmon resonator for ultrasensitive infrared spectroscopy,” Nat. Nanotechnol. 14(4), 313–319 (2019).
[Crossref]

Q. Ren, J. W. You, and N. C. Panoiu, “Large enhancement of the effective second-order nonlinearity in graphene metasurfaces,” Phys. Rev. B 99(20), 205404 (2019).
[Crossref]

L. Yang, J.-H. Lee, C. Rathnam, Y. Hou, J.-W. Choi, and K.-B. Lee, “Dual-Enhanced Raman Scattering-Based Characterization of Stem Cell Differentiation Using Graphene-Plasmonic Hybrid Nanoarray,” Nano Lett. 19(11), 8138–8148 (2019).
[Crossref]

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

2018 (8)

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref]

X.-T. Kong, L. Khosravi Khorashad, Z. Wang, and A. O. Govorov, “Photothermal Circular Dichroism Induced by Plasmon Resonances in Chiral Metamaterial Absorbers and Bolometers,” Nano Lett. 18(3), 2001–2008 (2018).
[Crossref]

S. Kim, M. S. Jang, V. W. Brar, K. W. Mauser, L. Kim, and H. A. Atwater, “Electronically Tunable Perfect Absorption in Graphene,” Nano Lett. 18(2), 971–979 (2018).
[Crossref]

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

S. Xia, X. Zhai, L. Wang, and S. Wen, “Plasmonically induced transparency in double-layered graphene nanoribbons,” Photonics Res. 6(7), 692–702 (2018).
[Crossref]

T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018).
[Crossref]

H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20(40), 25959–25966 (2018).
[Crossref]

2017 (3)

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

S. Xia, X. Zhai, Y. Huang, J. Liu, L. Wang, and S. Wen, “Multi-band perfect plasmonic absorptions using rectangular graphene gratings,” Opt. Lett. 42(15), 3052–3055 (2017).
[Crossref]

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017).
[Crossref]

2016 (8)

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

J. Horng, H. B. Balch, A. F. McGuire, H.-Z. Tsai, P. R. Forrester, M. F. Crommie, B. Cui, and F. Wang, “Imaging electric field dynamics with graphene optoelectronics,” Nat. Commun. 7(1), 13704 (2016).
[Crossref]

T. J. Echtermeyer, S. Milana, U. Sassi, A. Eiden, M. Wu, E. Lidorikis, and A. C. Ferrari, “Surface Plasmon Polariton Graphene Photodetectors,” Nano Lett. 16(1), 8–20 (2016).
[Crossref]

S. Xia, X. Zhai, L. Wang, Q. Lin, and S. Wen, “Excitation of crest and trough surface plasmon modes in in-plane bended graphene nanoribbons,” Opt. Express 24(1), 427–436 (2016).
[Crossref]

X. Zhao, C. Yuan, L. Zhu, and J. Yao, “Graphene-based tunable terahertz plasmon-induced transparency metamaterial,” Nanoscale 8(33), 15273–15280 (2016).
[Crossref]

X. Zhao, L. Zhu, C. Yuan, and J. Yao, “Tunable plasmon-induced transparency in a grating-coupled double-layer graphene hybrid system at far-infrared frequencies,” Opt. Lett. 41(23), 5470–5473 (2016).
[Crossref]

S. Balci, O. Balci, N. Kakenov, F. B. Atar, and C. Kocabas, “Dynamic tuning of plasmon resonance in the visible using graphene,” Opt. Lett. 41(6), 1241–1244 (2016).
[Crossref]

S. Xia, X. Zhai, L. Wang, B. Sun, J. Liu, and S. Wen, “Dynamically tunable plasmonically induced transparency in sinusoidally curved and planar graphene layers,” Opt. Express 24(16), 17886–17899 (2016).
[Crossref]

2015 (2)

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. De Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015).
[Crossref]

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref]

2014 (1)

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable Phonon-Induced Transparency in Bilayer Graphene Nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref]

2013 (2)

M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
[Crossref]

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013).
[Crossref]

2012 (5)

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of Plasmonic Waves in Graphene by Guided-Mode Resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B 85(12), 125431 (2012).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

2011 (1)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref]

2010 (1)

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
[Crossref]

2009 (2)

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
[Crossref]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref]

2008 (2)

L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
[Crossref]

L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2(8), 474–481 (2008).
[Crossref]

2007 (2)

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref]

2005 (1)

P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, and R. A. Wolkow, “Field regulation of single-molecule conductivity by a charged surface atom,” Nature 435(7042), 658–661 (2005).
[Crossref]

1991 (1)

H. A. Haus and W. Huang, “Coupled-Mode Theory “ Proc,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

Ajayan, P. M.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013).
[Crossref]

Altug, H.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. De Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015).
[Crossref]

Amani, J. A.

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Ansell, D.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref]

Atar, F. B.

Atwater, H. A.

S. Kim, M. S. Jang, V. W. Brar, K. W. Mauser, L. Kim, and H. A. Atwater, “Electronically Tunable Perfect Absorption in Graphene,” Nano Lett. 18(2), 971–979 (2018).
[Crossref]

Avouris, P.

I.-H. Lee, D. Yoo, P. Avouris, T. Low, and S.-H. Oh, “Graphene acoustic plasmon resonator for ultrasensitive infrared spectroscopy,” Nat. Nanotechnol. 14(4), 313–319 (2019).
[Crossref]

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable Phonon-Induced Transparency in Bilayer Graphene Nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref]

Bagci, H.

M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
[Crossref]

Balch, H. B.

J. Horng, H. B. Balch, A. F. McGuire, H.-Z. Tsai, P. R. Forrester, M. F. Crommie, B. Cui, and F. Wang, “Imaging electric field dynamics with graphene optoelectronics,” Nat. Commun. 7(1), 13704 (2016).
[Crossref]

Balci, O.

Balci, S.

Bangert, U.

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Bao, Q.

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref]

Bao, W.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Basov, D. N.

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Bozhevolnyi, S. I.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref]

Brar, V. W.

S. Kim, M. S. Jang, V. W. Brar, K. W. Mauser, L. Kim, and H. A. Atwater, “Electronically Tunable Perfect Absorption in Graphene,” Nano Lett. 18(2), 971–979 (2018).
[Crossref]

Cao, Y.

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref]

Castro Neto, A. H.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Chen, K.-P.

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Chen, Y.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Chen, Z.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Cheng, C.-W.

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Choi, C.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Choi, J.-W.

L. Yang, J.-H. Lee, C. Rathnam, Y. Hou, J.-W. Choi, and K.-B. Lee, “Dual-Enhanced Raman Scattering-Based Characterization of Stem Cell Differentiation Using Graphene-Plasmonic Hybrid Nanoarray,” Nano Lett. 19(11), 8138–8148 (2019).
[Crossref]

Chu, H. S.

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B 85(12), 125431 (2012).
[Crossref]

Chung, D. S.

T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018).
[Crossref]

Chung, Y.-C.

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Crommie, M. F.

J. Horng, H. B. Balch, A. F. McGuire, H.-Z. Tsai, P. R. Forrester, M. F. Crommie, B. Cui, and F. Wang, “Imaging electric field dynamics with graphene optoelectronics,” Nat. Commun. 7(1), 13704 (2016).
[Crossref]

Cui, B.

J. Horng, H. B. Balch, A. F. McGuire, H.-Z. Tsai, P. R. Forrester, M. F. Crommie, B. Cui, and F. Wang, “Imaging electric field dynamics with graphene optoelectronics,” Nat. Commun. 7(1), 13704 (2016).
[Crossref]

Cui, W.

Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
[Crossref]

Dai, S.

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

De Abajo, F. J. G.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. De Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015).
[Crossref]

DiLabio, G. A.

P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, and R. A. Wolkow, “Field regulation of single-molecule conductivity by a charged surface atom,” Nature 435(7042), 658–661 (2005).
[Crossref]

Dogel, S.

P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, and R. A. Wolkow, “Field regulation of single-molecule conductivity by a charged surface atom,” Nature 435(7042), 658–661 (2005).
[Crossref]

Dominguez, G.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Duan, H.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Duan, X.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Echtermeyer, T. J.

T. J. Echtermeyer, S. Milana, U. Sassi, A. Eiden, M. Wu, E. Lidorikis, and A. C. Ferrari, “Surface Plasmon Polariton Graphene Photodetectors,” Nano Lett. 16(1), 8–20 (2016).
[Crossref]

Efetov, D. K.

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
[Crossref]

Eiden, A.

T. J. Echtermeyer, S. Milana, U. Sassi, A. Eiden, M. Wu, E. Lidorikis, and A. C. Ferrari, “Surface Plasmon Polariton Graphene Photodetectors,” Nano Lett. 16(1), 8–20 (2016).
[Crossref]

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref]

Etezadi, D.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. De Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015).
[Crossref]

Falkovsky, L. A.

L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
[Crossref]

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Fan, Y.

Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019).
[Crossref]

Fang, S.

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref]

Farhat, M.

M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
[Crossref]

Fatemi, V.

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref]

Fei, Z.

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Feng, J.

Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
[Crossref]

Ferrari, A. C.

T. J. Echtermeyer, S. Milana, U. Sassi, A. Eiden, M. Wu, E. Lidorikis, and A. C. Ferrari, “Surface Plasmon Polariton Graphene Photodetectors,” Nano Lett. 16(1), 8–20 (2016).
[Crossref]

Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref]

Flor Flores, J.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Fogler, M. M.

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Forrester, P. R.

J. Horng, H. B. Balch, A. F. McGuire, H.-Z. Tsai, P. R. Forrester, M. F. Crommie, B. Cui, and F. Wang, “Imaging electric field dynamics with graphene optoelectronics,” Nat. Commun. 7(1), 13704 (2016).
[Crossref]

Fu, Q.

Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019).
[Crossref]

Fyffe, A.

Gan, C. H.

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B 85(12), 125431 (2012).
[Crossref]

Gao, W.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013).
[Crossref]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of Plasmonic Waves in Graphene by Guided-Mode Resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref]

Geim, A. K.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref]

Giessen, H.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref]

Gjerding, M. N.

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Goldflam, M. D.

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

Govorov, A. O.

X.-T. Kong, L. Khosravi Khorashad, Z. Wang, and A. O. Govorov, “Photothermal Circular Dichroism Induced by Plasmon Resonances in Chiral Metamaterial Absorbers and Bolometers,” Nano Lett. 18(3), 2001–2008 (2018).
[Crossref]

Grigorenko, A. N.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

Guan, J.

J. Guan, S. Xia, Z. Zhang, J. Wu, H. Meng, J. Yue, X. Zhai, L. Wang, and S. Wen, “Two Switchable Plasmonically Induced Transparency Effects in a System with Distinct Graphene Resonators,” Nanoscale Res. Lett. 15(1), 142 (2020).
[Crossref]

Guenneau, S.

M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
[Crossref]

Guinea, F.

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable Phonon-Induced Transparency in Bilayer Graphene Nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref]

Gwo, S.

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Ha, T.

T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018).
[Crossref]

Hage, F. S.

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Han, Z.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref]

Hardcastle, T. P.

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Haus, H. A.

H. A. Haus and W. Huang, “Coupled-Mode Theory “ Proc,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

He, Z.

Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
[Crossref]

Z. He, J. Zhao, and H. Lu, “Tunable nonreciprocal reflection and its stability in a non-PT-symmetric plasmonic resonators coupled waveguide systems,” Appl. Phys. Express 13(1), 012009 (2020).
[Crossref]

Hofer, W. A.

P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, and R. A. Wolkow, “Field regulation of single-molecule conductivity by a charged surface atom,” Nature 435(7042), 658–661 (2005).
[Crossref]

Hofsaess, H. C.

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Hong, K.-B.

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Horng, J.

J. Horng, H. B. Balch, A. F. McGuire, H.-Z. Tsai, P. R. Forrester, M. F. Crommie, B. Cui, and F. Wang, “Imaging electric field dynamics with graphene optoelectronics,” Nat. Commun. 7(1), 13704 (2016).
[Crossref]

Hou, Y.

L. Yang, J.-H. Lee, C. Rathnam, Y. Hou, J.-W. Choi, and K.-B. Lee, “Dual-Enhanced Raman Scattering-Based Characterization of Stem Cell Differentiation Using Graphene-Plasmonic Hybrid Nanoarray,” Nano Lett. 19(11), 8138–8148 (2019).
[Crossref]

Hsu, C.-Y.

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Hu, F.

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

Huang, S.-W.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Huang, W.

H. A. Haus and W. Huang, “Coupled-Mode Theory “ Proc,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

Huang, Y.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

S. Xia, X. Zhai, Y. Huang, J. Liu, L. Wang, and S. Wen, “Multi-band perfect plasmonic absorptions using rectangular graphene gratings,” Opt. Lett. 42(15), 3052–3055 (2017).
[Crossref]

Huang, Z.-T.

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Jang, M. S.

S. Kim, M. S. Jang, V. W. Brar, K. W. Mauser, L. Kim, and H. A. Atwater, “Electronically Tunable Perfect Absorption in Graphene,” Nano Lett. 18(2), 971–979 (2018).
[Crossref]

Janner, D.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. De Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015).
[Crossref]

Janssen, G.

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

Jarillo-Herrero, P.

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref]

Jin, Z.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013).
[Crossref]

Kakenov, N.

Kästel, J.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref]

Kaxiras, E.

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref]

Keilmann, F.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Kepaptsoglou, D. M.

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Khosravi Khorashad, L.

X.-T. Kong, L. Khosravi Khorashad, Z. Wang, and A. O. Govorov, “Photothermal Circular Dichroism Induced by Plasmon Resonances in Chiral Metamaterial Absorbers and Bolometers,” Nano Lett. 18(3), 2001–2008 (2018).
[Crossref]

Kim, H.-D.

T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018).
[Crossref]

Kim, L.

S. Kim, M. S. Jang, V. W. Brar, K. W. Mauser, L. Kim, and H. A. Atwater, “Electronically Tunable Perfect Absorption in Graphene,” Nano Lett. 18(2), 971–979 (2018).
[Crossref]

Kim, P.

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
[Crossref]

Kim, S.

S. Kim, M. S. Jang, V. W. Brar, K. W. Mauser, L. Kim, and H. A. Atwater, “Electronically Tunable Perfect Absorption in Graphene,” Nano Lett. 18(2), 971–979 (2018).
[Crossref]

Kim, T.-T.

T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018).
[Crossref]

Kivshar, Y. S.

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017).
[Crossref]

Kocabas, C.

Kong, X.-T.

X.-T. Kong, L. Khosravi Khorashad, Z. Wang, and A. O. Govorov, “Photothermal Circular Dichroism Induced by Plasmon Resonances in Chiral Metamaterial Absorbers and Bolometers,” Nano Lett. 18(3), 2001–2008 (2018).
[Crossref]

Kono, J.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013).
[Crossref]

Kwong, D.-L.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Langguth, L.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref]

Lau, C. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Lee, I.-H.

I.-H. Lee, D. Yoo, P. Avouris, T. Low, and S.-H. Oh, “Graphene acoustic plasmon resonator for ultrasensitive infrared spectroscopy,” Nat. Nanotechnol. 14(4), 313–319 (2019).
[Crossref]

Lee, J.-H.

L. Yang, J.-H. Lee, C. Rathnam, Y. Hou, J.-W. Choi, and K.-B. Lee, “Dual-Enhanced Raman Scattering-Based Characterization of Stem Cell Differentiation Using Graphene-Plasmonic Hybrid Nanoarray,” Nano Lett. 19(11), 8138–8148 (2019).
[Crossref]

Lee, K.-B.

L. Yang, J.-H. Lee, C. Rathnam, Y. Hou, J.-W. Choi, and K.-B. Lee, “Dual-Enhanced Raman Scattering-Based Characterization of Stem Cell Differentiation Using Graphene-Plasmonic Hybrid Nanoarray,” Nano Lett. 19(11), 8138–8148 (2019).
[Crossref]

Lee, Y. H.

T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018).
[Crossref]

Li, C.

Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
[Crossref]

Li, E. P.

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B 85(12), 125431 (2012).
[Crossref]

Li, G.

Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
[Crossref]

Li, H.

H. Xu, M. Zhao, M. Zheng, C. Xiong, B. Zhang, Y. Peng, and H. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D: Appl. Phys. 52(2), 025104 (2019).
[Crossref]

C. Xiong, H. Li, H. Xu, M. Zhao, B. Zhang, C. Liu, and K. Wu, “Coupling effects in single-mode and multimode resonator-coupled system,” Opt. Express 27(13), 17718–17728 (2019).
[Crossref]

C. Liu, H. Li, H. Xu, M. Zhao, C. Xiong, B. Zhang, and K. Wu, “Slow light effect based on tunable plasmon-induced transparency of monolayer black phosphorus,” J. Phys. D: Appl. Phys. 52(40), 405203 (2019).
[Crossref]

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019).
[Crossref]

H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20(40), 25959–25966 (2018).
[Crossref]

Li, J.-H.

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Li, P.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Li, Z.

Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
[Crossref]

Lidorikis, E.

T. J. Echtermeyer, S. Milana, U. Sassi, A. Eiden, M. Wu, E. Lidorikis, and A. C. Ferrari, “Surface Plasmon Polariton Graphene Photodetectors,” Nano Lett. 16(1), 8–20 (2016).
[Crossref]

Limaj, O.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. De Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015).
[Crossref]

Limonov, M. F.

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017).
[Crossref]

Lin, Q.

Lin, T.-R.

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Liu, C.

C. Xiong, H. Li, H. Xu, M. Zhao, B. Zhang, C. Liu, and K. Wu, “Coupling effects in single-mode and multimode resonator-coupled system,” Opt. Express 27(13), 17718–17728 (2019).
[Crossref]

C. Liu, H. Li, H. Xu, M. Zhao, C. Xiong, B. Zhang, and K. Wu, “Slow light effect based on tunable plasmon-induced transparency of monolayer black phosphorus,” J. Phys. D: Appl. Phys. 52(40), 405203 (2019).
[Crossref]

Liu, J.

Liu, N.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref]

Liu, P.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Liu, Y.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Loh, K. P.

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref]

Low, T.

I.-H. Lee, D. Yoo, P. Avouris, T. Low, and S.-H. Oh, “Graphene acoustic plasmon resonator for ultrasensitive infrared spectroscopy,” Nat. Nanotechnol. 14(4), 313–319 (2019).
[Crossref]

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable Phonon-Induced Transparency in Bilayer Graphene Nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref]

Lu, H.

Z. He, J. Zhao, and H. Lu, “Tunable nonreciprocal reflection and its stability in a non-PT-symmetric plasmonic resonators coupled waveguide systems,” Appl. Phys. Express 13(1), 012009 (2020).
[Crossref]

Lu, T.-C.

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Luan, Y.

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

Martinez, A.

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

Mauser, K. W.

S. Kim, M. S. Jang, V. W. Brar, K. W. Mauser, L. Kim, and H. A. Atwater, “Electronically Tunable Perfect Absorption in Graphene,” Nano Lett. 18(2), 971–979 (2018).
[Crossref]

McGuire, A. F.

J. Horng, H. B. Balch, A. F. McGuire, H.-Z. Tsai, P. R. Forrester, M. F. Crommie, B. Cui, and F. Wang, “Imaging electric field dynamics with graphene optoelectronics,” Nat. Commun. 7(1), 13704 (2016).
[Crossref]

McLeod, A. S.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Meng, H.

J. Guan, S. Xia, Z. Zhang, J. Wu, H. Meng, J. Yue, X. Zhai, L. Wang, and S. Wen, “Two Switchable Plasmonically Induced Transparency Effects in a System with Distinct Graphene Resonators,” Nanoscale Res. Lett. 15(1), 142 (2020).
[Crossref]

Milana, S.

T. J. Echtermeyer, S. Milana, U. Sassi, A. Eiden, M. Wu, E. Lidorikis, and A. C. Ferrari, “Surface Plasmon Polariton Graphene Photodetectors,” Nano Lett. 16(1), 8–20 (2016).
[Crossref]

Min, B.

T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018).
[Crossref]

Novoselov, K. S.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref]

Oh, S. S.

T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018).
[Crossref]

Oh, S.-H.

I.-H. Lee, D. Yoo, P. Avouris, T. Low, and S.-H. Oh, “Graphene acoustic plasmon resonator for ultrasensitive infrared spectroscopy,” Nat. Nanotechnol. 14(4), 313–319 (2019).
[Crossref]

Oulton, R. F.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
[Crossref]

Palik, E. D.

E. D. Palik, Handbook of optical constants of solids (Academic Press, 1985).

Palubski, I. Z.

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

Panoiu, N. C.

Q. Ren, J. W. You, and N. C. Panoiu, “Large enhancement of the effective second-order nonlinearity in graphene metasurfaces,” Phys. Rev. B 99(20), 205404 (2019).
[Crossref]

Peng, Y.

H. Xu, M. Zhao, M. Zheng, C. Xiong, B. Zhang, Y. Peng, and H. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D: Appl. Phys. 52(2), 025104 (2019).
[Crossref]

Pershoguba, S. S.

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Pfau, T.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref]

Pitters, J. L.

P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, and R. A. Wolkow, “Field regulation of single-molecule conductivity by a charged surface atom,” Nature 435(7042), 658–661 (2005).
[Crossref]

Piva, P. G.

P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, and R. A. Wolkow, “Field regulation of single-molecule conductivity by a charged surface atom,” Nature 435(7042), 658–661 (2005).
[Crossref]

Poddubny, A. N.

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017).
[Crossref]

Polini, M.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

Post, K. W.

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

Pruneri, V.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. De Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015).
[Crossref]

Pu, L.

Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
[Crossref]

Qiu, C.

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of Plasmonic Waves in Graphene by Guided-Mode Resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref]

Radko, I. P.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref]

Ramasse, Q. M.

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Rao, Y.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Rathnam, C.

L. Yang, J.-H. Lee, C. Rathnam, Y. Hou, J.-W. Choi, and K.-B. Lee, “Dual-Enhanced Raman Scattering-Based Characterization of Stem Cell Differentiation Using Graphene-Plasmonic Hybrid Nanoarray,” Nano Lett. 19(11), 8138–8148 (2019).
[Crossref]

Ren, Q.

Q. Ren, J. W. You, and N. C. Panoiu, “Large enhancement of the effective second-order nonlinearity in graphene metasurfaces,” Phys. Rev. B 99(20), 205404 (2019).
[Crossref]

Rezeq, M.

P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, and R. A. Wolkow, “Field regulation of single-molecule conductivity by a charged surface atom,” Nature 435(7042), 658–661 (2005).
[Crossref]

Rodin, A. S.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Rodrigo, D.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. De Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015).
[Crossref]

Rodriguez, F. J.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref]

Rybin, M. V.

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017).
[Crossref]

Sassi, U.

T. J. Echtermeyer, S. Milana, U. Sassi, A. Eiden, M. Wu, E. Lidorikis, and A. C. Ferrari, “Surface Plasmon Polariton Graphene Photodetectors,” Nano Lett. 16(1), 8–20 (2016).
[Crossref]

Seabourne, C. R.

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Shen, N.-H.

Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019).
[Crossref]

Shi, G.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013).
[Crossref]

Shi, Z.

Shu, J.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013).
[Crossref]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of Plasmonic Waves in Graphene by Guided-Mode Resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref]

Soukoulis, C. M.

Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019).
[Crossref]

Sun, B.

Sun, Z.

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

Taniguchi, T.

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref]

Thévenaz, L.

L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2(8), 474–481 (2008).
[Crossref]

Thiemens, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Thygesen, K. S.

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Tong, S.

Tsai, H.-Z.

J. Horng, H. B. Balch, A. F. McGuire, H.-Z. Tsai, P. R. Forrester, M. F. Crommie, B. Cui, and F. Wang, “Imaging electric field dynamics with graphene optoelectronics,” Nat. Commun. 7(1), 13704 (2016).
[Crossref]

Vajtai, R.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013).
[Crossref]

Vakil, A.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref]

Wagner, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Wang, F.

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

J. Horng, H. B. Balch, A. F. McGuire, H.-Z. Tsai, P. R. Forrester, M. F. Crommie, B. Cui, and F. Wang, “Imaging electric field dynamics with graphene optoelectronics,” Nat. Commun. 7(1), 13704 (2016).
[Crossref]

Wang, L.

Wang, X.

Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
[Crossref]

Wang, Z.

X.-T. Kong, L. Khosravi Khorashad, Z. Wang, and A. O. Govorov, “Photothermal Circular Dichroism Induced by Plasmon Resonances in Chiral Metamaterial Absorbers and Bolometers,” Nano Lett. 18(3), 2001–2008 (2018).
[Crossref]

Watanabe, K.

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref]

Wei, Z.

Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019).
[Crossref]

Weiss, T.

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref]

Wen, S.

Winther, K. T.

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Wolkow, R. A.

P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, and R. A. Wolkow, “Field regulation of single-molecule conductivity by a charged surface atom,” Nature 435(7042), 658–661 (2005).
[Crossref]

Wong, C. W.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Wu, H.

Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019).
[Crossref]

Wu, J.

J. Guan, S. Xia, Z. Zhang, J. Wu, H. Meng, J. Yue, X. Zhai, L. Wang, and S. Wen, “Two Switchable Plasmonically Induced Transparency Effects in a System with Distinct Graphene Resonators,” Nanoscale Res. Lett. 15(1), 142 (2020).
[Crossref]

Wu, J. S.

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

Wu, K.

C. Liu, H. Li, H. Xu, M. Zhao, C. Xiong, B. Zhang, and K. Wu, “Slow light effect based on tunable plasmon-induced transparency of monolayer black phosphorus,” J. Phys. D: Appl. Phys. 52(40), 405203 (2019).
[Crossref]

C. Xiong, H. Li, H. Xu, M. Zhao, B. Zhang, C. Liu, and K. Wu, “Coupling effects in single-mode and multimode resonator-coupled system,” Opt. Express 27(13), 17718–17728 (2019).
[Crossref]

Wu, M.

T. J. Echtermeyer, S. Milana, U. Sassi, A. Eiden, M. Wu, E. Lidorikis, and A. C. Ferrari, “Surface Plasmon Polariton Graphene Photodetectors,” Nano Lett. 16(1), 8–20 (2016).
[Crossref]

Wu, Y.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Xia, F.

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable Phonon-Induced Transparency in Bilayer Graphene Nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref]

Xia, H.

H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20(40), 25959–25966 (2018).
[Crossref]

Xia, S.

Xiao, B.

Xiao, X.

Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
[Crossref]

Xie, Z.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Xiong, C.

H. Xu, M. Zhao, M. Zheng, C. Xiong, B. Zhang, Y. Peng, and H. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D: Appl. Phys. 52(2), 025104 (2019).
[Crossref]

C. Xiong, H. Li, H. Xu, M. Zhao, B. Zhang, C. Liu, and K. Wu, “Coupling effects in single-mode and multimode resonator-coupled system,” Opt. Express 27(13), 17718–17728 (2019).
[Crossref]

C. Liu, H. Li, H. Xu, M. Zhao, C. Xiong, B. Zhang, and K. Wu, “Slow light effect based on tunable plasmon-induced transparency of monolayer black phosphorus,” J. Phys. D: Appl. Phys. 52(40), 405203 (2019).
[Crossref]

H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20(40), 25959–25966 (2018).
[Crossref]

Xu, H.

C. Liu, H. Li, H. Xu, M. Zhao, C. Xiong, B. Zhang, and K. Wu, “Slow light effect based on tunable plasmon-induced transparency of monolayer black phosphorus,” J. Phys. D: Appl. Phys. 52(40), 405203 (2019).
[Crossref]

C. Xiong, H. Li, H. Xu, M. Zhao, B. Zhang, C. Liu, and K. Wu, “Coupling effects in single-mode and multimode resonator-coupled system,” Opt. Express 27(13), 17718–17728 (2019).
[Crossref]

H. Xu, M. Zhao, M. Zheng, C. Xiong, B. Zhang, Y. Peng, and H. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D: Appl. Phys. 52(2), 025104 (2019).
[Crossref]

H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20(40), 25959–25966 (2018).
[Crossref]

Xu, Q.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013).
[Crossref]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of Plasmonic Waves in Graphene by Guided-Mode Resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref]

Xue, W.

Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
[Crossref]

Yan, H.

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable Phonon-Induced Transparency in Bilayer Graphene Nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref]

Yang, J.-H.

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Yang, L.

L. Yang, J.-H. Lee, C. Rathnam, Y. Hou, J.-W. Choi, and K.-B. Lee, “Dual-Enhanced Raman Scattering-Based Characterization of Stem Cell Differentiation Using Graphene-Plasmonic Hybrid Nanoarray,” Nano Lett. 19(11), 8138–8148 (2019).
[Crossref]

Yao, B.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Yao, J.

X. Zhao, L. Zhu, C. Yuan, and J. Yao, “Tunable plasmon-induced transparency in a grating-coupled double-layer graphene hybrid system at far-infrared frequencies,” Opt. Lett. 41(23), 5470–5473 (2016).
[Crossref]

X. Zhao, C. Yuan, L. Zhu, and J. Yao, “Graphene-based tunable terahertz plasmon-induced transparency metamaterial,” Nanoscale 8(33), 15273–15280 (2016).
[Crossref]

Yoo, D.

I.-H. Lee, D. Yoo, P. Avouris, T. Low, and S.-H. Oh, “Graphene acoustic plasmon resonator for ultrasensitive infrared spectroscopy,” Nat. Nanotechnol. 14(4), 313–319 (2019).
[Crossref]

You, J. W.

Q. Ren, J. W. You, and N. C. Panoiu, “Large enhancement of the effective second-order nonlinearity in graphene metasurfaces,” Phys. Rev. B 99(20), 205404 (2019).
[Crossref]

Yu, M.

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Yu, M.-W.

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

Yuan, C.

X. Zhao, L. Zhu, C. Yuan, and J. Yao, “Tunable plasmon-induced transparency in a grating-coupled double-layer graphene hybrid system at far-infrared frequencies,” Opt. Lett. 41(23), 5470–5473 (2016).
[Crossref]

X. Zhao, C. Yuan, L. Zhu, and J. Yao, “Graphene-based tunable terahertz plasmon-induced transparency metamaterial,” Nanoscale 8(33), 15273–15280 (2016).
[Crossref]

Yue, J.

J. Guan, S. Xia, Z. Zhang, J. Wu, H. Meng, J. Yue, X. Zhai, L. Wang, and S. Wen, “Two Switchable Plasmonically Induced Transparency Effects in a System with Distinct Graphene Resonators,” Nanoscale Res. Lett. 15(1), 142 (2020).
[Crossref]

Zan, R.

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Zeng, J.

H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20(40), 25959–25966 (2018).
[Crossref]

Zentgraf, T.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
[Crossref]

Zhai, X.

Zhang, B.

C. Liu, H. Li, H. Xu, M. Zhao, C. Xiong, B. Zhang, and K. Wu, “Slow light effect based on tunable plasmon-induced transparency of monolayer black phosphorus,” J. Phys. D: Appl. Phys. 52(40), 405203 (2019).
[Crossref]

H. Xu, M. Zhao, M. Zheng, C. Xiong, B. Zhang, Y. Peng, and H. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D: Appl. Phys. 52(2), 025104 (2019).
[Crossref]

C. Xiong, H. Li, H. Xu, M. Zhao, B. Zhang, C. Liu, and K. Wu, “Coupling effects in single-mode and multimode resonator-coupled system,” Opt. Express 27(13), 17718–17728 (2019).
[Crossref]

H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20(40), 25959–25966 (2018).
[Crossref]

Zhang, F.

Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019).
[Crossref]

Zhang, L. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Zhang, Q.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013).
[Crossref]

Zhang, S.

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018).
[Crossref]

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
[Crossref]

Zhang, X.

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
[Crossref]

Zhang, Z.

J. Guan, S. Xia, Z. Zhang, J. Wu, H. Meng, J. Yue, X. Zhai, L. Wang, and S. Wen, “Two Switchable Plasmonically Induced Transparency Effects in a System with Distinct Graphene Resonators,” Nanoscale Res. Lett. 15(1), 142 (2020).
[Crossref]

Zhao, J.

Z. He, J. Zhao, and H. Lu, “Tunable nonreciprocal reflection and its stability in a non-PT-symmetric plasmonic resonators coupled waveguide systems,” Appl. Phys. Express 13(1), 012009 (2020).
[Crossref]

Zhao, M.

H. Xu, M. Zhao, M. Zheng, C. Xiong, B. Zhang, Y. Peng, and H. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D: Appl. Phys. 52(2), 025104 (2019).
[Crossref]

C. Xiong, H. Li, H. Xu, M. Zhao, B. Zhang, C. Liu, and K. Wu, “Coupling effects in single-mode and multimode resonator-coupled system,” Opt. Express 27(13), 17718–17728 (2019).
[Crossref]

C. Liu, H. Li, H. Xu, M. Zhao, C. Xiong, B. Zhang, and K. Wu, “Slow light effect based on tunable plasmon-induced transparency of monolayer black phosphorus,” J. Phys. D: Appl. Phys. 52(40), 405203 (2019).
[Crossref]

H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20(40), 25959–25966 (2018).
[Crossref]

Zhao, Q.

Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019).
[Crossref]

Zhao, R.

T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018).
[Crossref]

Zhao, X.

X. Zhao, L. Zhu, C. Yuan, and J. Yao, “Tunable plasmon-induced transparency in a grating-coupled double-layer graphene hybrid system at far-infrared frequencies,” Opt. Lett. 41(23), 5470–5473 (2016).
[Crossref]

X. Zhao, C. Yuan, L. Zhu, and J. Yao, “Graphene-based tunable terahertz plasmon-induced transparency metamaterial,” Nanoscale 8(33), 15273–15280 (2016).
[Crossref]

Zhao, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Zheng, M.

H. Xu, M. Zhao, M. Zheng, C. Xiong, B. Zhang, Y. Peng, and H. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D: Appl. Phys. 52(2), 025104 (2019).
[Crossref]

H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20(40), 25959–25966 (2018).
[Crossref]

Zhu, L.

X. Zhao, L. Zhu, C. Yuan, and J. Yao, “Tunable plasmon-induced transparency in a grating-coupled double-layer graphene hybrid system at far-infrared frequencies,” Opt. Lett. 41(23), 5470–5473 (2016).
[Crossref]

X. Zhao, C. Yuan, L. Zhu, and J. Yao, “Graphene-based tunable terahertz plasmon-induced transparency metamaterial,” Nanoscale 8(33), 15273–15280 (2016).
[Crossref]

Zikovsky, J.

P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, and R. A. Wolkow, “Field regulation of single-molecule conductivity by a charged surface atom,” Nature 435(7042), 658–661 (2005).
[Crossref]

ACS Nano (3)

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[Crossref]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of Plasmonic Waves in Graphene by Guided-Mode Resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref]

F. S. Hage, T. P. Hardcastle, M. N. Gjerding, D. M. Kepaptsoglou, C. R. Seabourne, K. T. Winther, R. Zan, J. A. Amani, H. C. Hofsaess, U. Bangert, K. S. Thygesen, and Q. M. Ramasse, “Local Plasmon Engineering in Doped Graphene,” ACS Nano 12(2), 1837–1848 (2018).
[Crossref]

Acs Photonics (1)

T.-T. Kim, H.-D. Kim, R. Zhao, S. S. Oh, T. Ha, D. S. Chung, Y. H. Lee, B. Min, and S. Zhang, “Electrically Tunable Slow Light Using Graphene Metamaterials,” Acs Photonics 5(5), 1800–1807 (2018).
[Crossref]

Adv. Opt. Mater. (1)

Y. Fan, N.-H. Shen, F. Zhang, Q. Zhao, H. Wu, Q. Fu, Z. Wei, H. Li, and C. M. Soukoulis, “Graphene Plasmonics: A Platform for 2D Optics,” Adv. Opt. Mater. 7(3), 1800537 (2019).
[Crossref]

Appl. Phys. Express (1)

Z. He, J. Zhao, and H. Lu, “Tunable nonreciprocal reflection and its stability in a non-PT-symmetric plasmonic resonators coupled waveguide systems,” Appl. Phys. Express 13(1), 012009 (2020).
[Crossref]

J. Phys. D: Appl. Phys. (2)

H. Xu, M. Zhao, M. Zheng, C. Xiong, B. Zhang, Y. Peng, and H. Li, “Dual plasmon-induced transparency and slow light effect in monolayer graphene structure with rectangular defects,” J. Phys. D: Appl. Phys. 52(2), 025104 (2019).
[Crossref]

C. Liu, H. Li, H. Xu, M. Zhao, C. Xiong, B. Zhang, and K. Wu, “Slow light effect based on tunable plasmon-induced transparency of monolayer black phosphorus,” J. Phys. D: Appl. Phys. 52(40), 405203 (2019).
[Crossref]

J. Phys.: Conf. Ser. (1)

L. A. Falkovsky, “Optical properties of graphene,” J. Phys.: Conf. Ser. 129, 012004 (2008).
[Crossref]

Nano Lett. (8)

H. Yan, T. Low, F. Guinea, F. Xia, and P. Avouris, “Tunable Phonon-Induced Transparency in Bilayer Graphene Nanoribbons,” Nano Lett. 14(8), 4581–4586 (2014).
[Crossref]

L. Yang, J.-H. Lee, C. Rathnam, Y. Hou, J.-W. Choi, and K.-B. Lee, “Dual-Enhanced Raman Scattering-Based Characterization of Stem Cell Differentiation Using Graphene-Plasmonic Hybrid Nanoarray,” Nano Lett. 19(11), 8138–8148 (2019).
[Crossref]

H. Li, J.-H. Li, K.-B. Hong, M.-W. Yu, Y.-C. Chung, C.-Y. Hsu, J.-H. Yang, C.-W. Cheng, Z.-T. Huang, K.-P. Chen, T.-R. Lin, S. Gwo, and T.-C. Lu, “Plasmonic Nanolasers Enhanced by Hybrid Graphene–Insulator–Metal Structures,” Nano Lett. 19(8), 5017–5024 (2019).
[Crossref]

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and Active Control of Propagating Surface Plasmon Polaritons in Graphene,” Nano Lett. 13(8), 3698–3702 (2013).
[Crossref]

T. J. Echtermeyer, S. Milana, U. Sassi, A. Eiden, M. Wu, E. Lidorikis, and A. C. Ferrari, “Surface Plasmon Polariton Graphene Photodetectors,” Nano Lett. 16(1), 8–20 (2016).
[Crossref]

X.-T. Kong, L. Khosravi Khorashad, Z. Wang, and A. O. Govorov, “Photothermal Circular Dichroism Induced by Plasmon Resonances in Chiral Metamaterial Absorbers and Bolometers,” Nano Lett. 18(3), 2001–2008 (2018).
[Crossref]

S. Kim, M. S. Jang, V. W. Brar, K. W. Mauser, L. Kim, and H. A. Atwater, “Electronically Tunable Perfect Absorption in Graphene,” Nano Lett. 18(2), 971–979 (2018).
[Crossref]

F. Hu, Y. Luan, Z. Fei, I. Z. Palubski, M. D. Goldflam, S. Dai, J. S. Wu, K. W. Post, G. Janssen, M. M. Fogler, and D. N. Basov, “Imaging the Localized Plasmon Resonance Modes in Graphene Nanoribbons,” Nano Lett. 17(9), 5423–5428 (2017).
[Crossref]

Nanomaterials (1)

Z. He, W. Xue, W. Cui, C. Li, Z. Li, L. Pu, J. Feng, X. Xiao, X. Wang, and G. Li, “Tunable Fano Resonance and Enhanced Sensing in a Simple Au/TiO2 Hybrid Metasurface,” Nanomaterials 10(4), 687 (2020).
[Crossref]

Nanoscale (1)

X. Zhao, C. Yuan, L. Zhu, and J. Yao, “Graphene-based tunable terahertz plasmon-induced transparency metamaterial,” Nanoscale 8(33), 15273–15280 (2016).
[Crossref]

Nanoscale Res. Lett. (1)

J. Guan, S. Xia, Z. Zhang, J. Wu, H. Meng, J. Yue, X. Zhai, L. Wang, and S. Wen, “Two Switchable Plasmonically Induced Transparency Effects in a System with Distinct Graphene Resonators,” Nanoscale Res. Lett. 15(1), 142 (2020).
[Crossref]

Nanotechnology (1)

Z. Chen, P. Li, S. Zhang, Y. Chen, P. Liu, and H. Duan, “Enhanced extraordinary optical transmission and refractive-index sensing sensitivity in tapered plasmonic nanohole arrays,” Nanotechnology 30(33), 335201 (2019).
[Crossref]

Nat. Commun. (2)

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref]

J. Horng, H. B. Balch, A. F. McGuire, H.-Z. Tsai, P. R. Forrester, M. F. Crommie, B. Cui, and F. Wang, “Imaging electric field dynamics with graphene optoelectronics,” Nat. Commun. 7(1), 13704 (2016).
[Crossref]

Nat. Mater. (2)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref]

N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. 8(9), 758–762 (2009).
[Crossref]

Nat. Nanotechnol. (1)

I.-H. Lee, D. Yoo, P. Avouris, T. Low, and S.-H. Oh, “Graphene acoustic plasmon resonator for ultrasensitive infrared spectroscopy,” Nat. Nanotechnol. 14(4), 313–319 (2019).
[Crossref]

Nat. Photonics (5)

B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J. Flor Flores, Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Broadband gate-tunable terahertz plasmons in graphene heterostructures,” Nat. Photonics 12(1), 22–28 (2018).
[Crossref]

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11(9), 543–554 (2017).
[Crossref]

L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2(8), 474–481 (2008).
[Crossref]

Nature (3)

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, “Unconventional superconductivity in magic-angle graphene superlattices,” Nature 556(7699), 43–50 (2018).
[Crossref]

P. G. Piva, G. A. DiLabio, J. L. Pitters, J. Zikovsky, M. Rezeq, S. Dogel, W. A. Hofer, and R. A. Wolkow, “Field regulation of single-molecule conductivity by a charged surface atom,” Nature 435(7042), 658–661 (2005).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Photonics Res. (1)

S. Xia, X. Zhai, L. Wang, and S. Wen, “Plasmonically induced transparency in double-layered graphene nanoribbons,” Photonics Res. 6(7), 692–702 (2018).
[Crossref]

Phys. Chem. Chem. Phys. (1)

H. Xu, M. Zhao, C. Xiong, B. Zhang, M. Zheng, J. Zeng, H. Xia, and H. Li, “Dual plasmonically tunable slow light based on plasmon-induced transparency in planar graphene ribbon metamaterials,” Phys. Chem. Chem. Phys. 20(40), 25959–25966 (2018).
[Crossref]

Phys. Rev. B (4)

C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B 85(12), 125431 (2012).
[Crossref]

T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B 80(19), 195415 (2009).
[Crossref]

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Q. Ren, J. W. You, and N. C. Panoiu, “Large enhancement of the effective second-order nonlinearity in graphene metasurfaces,” Phys. Rev. B 99(20), 205404 (2019).
[Crossref]

Phys. Rev. Lett. (2)

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
[Crossref]

M. Farhat, S. Guenneau, and H. Bağcı, “Exciting graphene surface plasmon polaritons through light and sound interplay,” Phys. Rev. Lett. 111(23), 237404 (2013).
[Crossref]

Proc. IEEE (1)

H. A. Haus and W. Huang, “Coupled-Mode Theory “ Proc,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

Science (2)

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. De Abajo, V. Pruneri, and H. Altug, “Mid-Infrared Plasmonic Biosensing with Graphene,” Science 349(6244), 165–168 (2015).
[Crossref]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref]

Other (1)

E. D. Palik, Handbook of optical constants of solids (Academic Press, 1985).

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Figures (6)

Fig. 1.
Fig. 1. (a) The tunable plasmonic graphene-based device. The inset is the right view of this device, and it is the theoretical regulated schematic diagram between the voltage and Fermi level of graphene. (b) The front view of one unit of the periodic device.
Fig. 2.
Fig. 2. (a) The optical transmission spectrum of the plasmonic graphene-based structure. (b) The equivalent coupled mode model of this device. (c-e) The electric field distribution of bright mode (c), dark mode (d) and plasmonically induced transparency at 5 THz (e). (f-g) The electric field distribution of plasmonically induced transparency at dip1 (f, 4.31 THz), dip2 (g, 6.57 THz), respectively. At this time, the Fermi level is equal to 0.8 eV.
Fig. 3.
Fig. 3. (a) The real part of the propagation constant. (b) The imaginary part of the propagation constant. (c) The real part of the effective index. (d) The imaginary part of the effective index. Fermi level EF = 0.6 eV, 0.7 eV, 0.8 eV, 0.9 eV.
Fig. 4.
Fig. 4. (a) The evolutionary relationship between the internal loss quality factor and frequency, where Fermi level of the graphene monolayer is 0.6 eV, 0.7 eV, 0.8 eV, 0.9 eV. (b) The evolution of the resonant frequency with the Fermi level at the resonant dip and peak. dip1, peak1 and dip2 are the low frequency trough, PIT peak and high frequency trough, respectively. (c-d) The value of total quality factor and internal loss quality factor, respectively.
Fig. 5.
Fig. 5. (a-b) The numerical calculation and theoretical fitting curve of the optical transmission and reflection. The blue solid line is the FDTD numerical result, and the red dotted line is the coupled mode theory data. Fermi level of the graphene monolayer is 0.6 eV, 0.7 eV, 0.8 eV, 0.9 eV.
Fig. 6.
Fig. 6. (a-d) The trend of phase and group delay (ps) against frequency, respectively. Fermi level is equal to 0.6 eV, 0.7 eV, 0.8 eV, 0.9 eV.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

σ = i e 2 E F π 2 ( ω + i τ 1 ) ,
( γ 1 i μ 12 i μ 21 γ 2 ) ( a 1 a 2 ) = ( γ o 1 1 / 2 0 0 γ o 2 1 / 2 ) ( A 1 + i n + A 1 i n A 2 + i n + A 2 i n ) ,
A 2 + i n = A 1 + o u t e i φ , A 1 i n = A 2 o u t e i φ
A n + o u t = A n + i n γ o n 1 / 2 a n , A n o u t = A n i n γ o n 1 / 2 a n ( n = 1 , 2 )
t = A 2 + o u t A 1 + i n = e i φ + ( γ o 1 γ 2 e i φ + γ 1 γ o 2 e i φ + ( γ o 1 γ o 2 ) 1 / 2 e 2 i φ χ 1 + ( γ o 1 γ o 2 ) 1 / 2 χ 2 ) ( γ 1 γ 2 χ 1 χ 2 ) 1 ,
r = A 1 o u t A 1 + i n = ( γ o 1 γ 2 + γ o 2 γ 1 e 2 i φ + ( γ o 1 γ o 2 ) 1 / 2 χ 1 e i φ + ( γ o 1 γ o 2 ) 1 / 2 χ 2 e i φ ) ( γ 1 γ 2 χ 1 χ 2 ) 1 .
{ E x = i 1 ω ε 0 ε H y z , E z = β ω ε 0 ε H y 2 H y z 2 + ( k 0 2 ε β 2 ) H y = 0 ,
{ H y 1 = A e i β x e k 1 z E x 1 = i A 1 ω ε 0 ε 1 k 1 e i β x e k 1 z E z 1 = A β ω ε 0 ε 1 e i β x e k 1 z ,
{ H y 3 = D e i β x e k 3 z E x 3 = i D 1 ω ε 0 ε 3 k 3 e i β x e k 3 z E z 3 = D β ω ε 0 ε 3 e i β x e k 3 z .
{ H y 2 = B e i β x e k 2 z + C e i β x e k 2 z E x 2 = i B 1 ω ε 0 ε 2 k 2 e i β x e k 2 z + i C 1 ω ε 0 ε 2 k 2 e i β x e k 2 z E z 2 = B β ω ε 0 ε 2 e i β x e k 2 z C β ω ε 0 ε 2 e i β x e k 2 z .
{ z = d : k 1 ε 1 1 + i σ ω ε 0 k 1 ε 1 = B k 2 ε 2 e k 2 d + C k 2 ε 2 e k 2 d B e k 2 d + C e k 2 d z = 0 : k 3 ε 3 1 + i σ ω ε 0 k 3 ε 3 = B k 2 ε 2 + C k 2 ε 2 B + C .
e 2 k 2 d = k 1 ε 1 k 2 ε 2 ( 1 + i σ ω ε 0 k 1 ε 1 ) k 1 ε 1 + k 2 ε 2 ( 1 + i σ ω ε 0 k 1 ε 1 ) k 3 ε 3 k 2 ε 2 ( 1 + i σ ω ε 0 k 3 ε 3 ) k 3 ε 3 + k 2 ε 2 ( 1 + i σ ω ε 0 k 3 ε 3 ) .
E F = v F ( π ε 0 ε g r a t i n g V g d s u b e ) 1 / 2

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