Abstract

Both plasmon-phonon-polariton (SPP-PHP) modes and phonon-polariton (PHP) modes supported in graphene-coated hexagon boron nitride (h-BN) single nanowire are presented. The field distributions of the lowest 5 order modes of SPP-PHP modes supported in graphene-coated hexagon boron nitride nanowire pairs (SPP-PHP-GHNP) and the lowest 5 order modes of PHP modes supported in graphene-coated hexagon boron nitride nanowire pairs (GHNP) are also demonstrated and analyzed, respectively. The results of numerical calculation show that SPP-PHP-GHNP mode 0 owns the strongest confinement and lowest loss among the lowest 5 order modes of SPP-PHP-GHNP. Furthermore, the field enhancement of SPP-PHP-GHNP mode 0 can reach over 105 by controlling the geometry parameters of GHNP. Meanwhile, the influence of tuning the Fermi level of graphene on the field enhancement is also presented in the paper. The proposed structure may improve the development of graphene-h-BN-based optoelectronic devices.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

In recent years, graphene-based structure has attracted numerous attention for its various applications including absorber [1], plasmonically induced transparency [2], isolator [3], filter [4], demultiplexing [5], switch [6], slow light [7], nanofocusing [8], Fano resonance [9], sensor [10], Kerr nonlinearity [11] and splitter [12]. Besides, many hexagon boron nitride (h-BN)-based devices have also been proposed in different fields such as quantum emitter [13], nanofocusing [14], optical imaging [15], hybrid waveguide [16] and absorption [17] in the past few years.

As we know, surface plasmon polariton (SPP) mode can be supported in graphene and phonon polariton (PHP) mode can be supported in h-BN [18,19]. Recently, researchers have demonstrated that hybrid SPP-PHP mode can be supported by graphene-h-BN system [20,21]. And a lot of graphene-h-BN hybrid structures have been proposed and discussed in different applications including absorption [22] and switch [23] in the past several years. Apart from that, Xu et al. reported an in-plane pressure sensor and a tunneling pressure sensor based on graphene-h-BN heterostructures [24]. Zhu et al. discussed a tapered graphene-h-BN hybrid structure and its application of nanofocusing [25]. Brar et al. experimentally investigated the hybrid surface-phonon-plasmon polariton modes in the graphene-h-BN sheets [26]. Barnard et al. proposed an infrared emitter consisting of graphene encapsulated h-BN [27]. Wu et al. discussed the nonlinear surface-phonon-plasmon-polaritons in the structure of a graphene sandwiched by a nonlinear material and h-BN [28].

In this paper, a graphene-coated h-BN nanowire pairs (GHNP) structure is firstly proposed. Both hybrid SPP-PHP modes and PHP modes can be supported in the proposed GHNP structure. The electric field distribution |E| and z-component of electric field EZ for the SPP-PHP modes and PHP modes supported in the GHNP structure are illustrated by the numerical calculation. The dependencies of the real part of the effective index and ratio between the real part and imaginary part of the effective index for the SPP-PHP modes and PHP modes supported in the GHNP on the Fermi level of graphene, the distance between the two graphene-coated h-BN nanowire (GHN) waveguides, the radius of substrate and the thickness of h-BN are also presented, respectively. Furthermore, the field enhancement is defined and the relationships between the field enhancement and the four parameters above are also discussed.

2. Graphene-coated h-BN nanowire pairs

The scheme of the GHNP structure is shown in Fig. 1(a). The proposed structure could be implemented by the following steps. First, graphene flake could be prepared by chemical vapour deposition (CVD) and exfoliation methods [20]. h-BN film can be obtained by exfoliation techniques [14]. Then, graphene flake and h-BN film could be transferred and wrapped around the silica substrate by micromanipulation [29]. Finally, both graphene and h-BN could be spontaneously wrapped around the silica substrate and the proposed graphene-coated hexagon boron nitride nanowire waveguide could be achieved [29]. The thickness of h-BN is th-BN. In the simulation, h-BN is modelled as an anisotropic material with permittivities [21]:

εa(r)=ε,a(r)+ε,a(r)(ωLO,a(r))2(ωTO,a(r))2(ωTO,a(r))2ω2iωΓa(r),
where εa and εr are the out-of-plane (in radial direction) dielectric permittivity and in-plane (in azimuthal direction and z direction) dielectric permittivity of h-BN, respectively. ε∞,a = 2.95, ε∞,r = 4.87, ωLO,a = 830 cm−1, ωTO,a = 780 cm−1, ωLO,r = 1610 cm−1, ωTO,r = 1370 cm−1, Γa = 4 cm−1, Γr = 5 cm−1. Figure 1(b) shows the dielectric permittivity of h-BN versus wavenumber in the range of 500 cm−1 to 2000 cm−1. Here, wavenumber is defined as 1/λ, where λ is the wavelength. In this paper, we only discuss the upper Reststrahlen band where the in-plane dielectric permittivity of h-BN is negative and out-of-plane one is positive [21]. The conductivity of the graphene, σg can be expressed as σg = σinter + σintra, where σinter and σintra represent the interband part and intraband part, respectively [30]. And they can expressed as [30]:
{σinter=e24{0.5+arctan(ω2Ef2kBT)πi2πln[(ω+2Ef)2(ω2Ef)2+(2kBT)2]},σintra=2ie2kBTπ2(ω+iτ)ln[2cosh(Ef2kBT)],
where is the reduced Planck’s constant, e is the electron charge, T = 300 K is the environment temperature. τ = 0.5 ps is the relaxation time. Ef is the Fermi level of graphene. ω and kB are the angular frequency and Boltzmann constant, respectively. The permittivity of graphene in radial direction can be expressed as εg_r = 2.5. And the permittivities of graphene in azimuthal direction and z direction can be expressed as εg_ar = εg_z = 2.5 + g/ωε0t [31], where ε0 is the dielectric constant in vacuum. t = 0.5 nm is the thickness of graphene. The dielectric permittivity of the silica substrate and air (the surrounding media) are assumed to be εsi = 3.9, εair = 1, respectively [32].

 

Fig. 1 (a) Schematics of the GHNP structure. (b) The out-of-plane dielectric permittivity and in-plane dielectric permittivity of h-BN versus wavenumber.

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3. Method and numerical analysis

For a graphene/h-BN film/silica substrate structure, the modal dispersion within the upper Reststrahlen band can be expressed as [21,25]:

β=ΨthBN{arctan[εair+i(β/k0)Z0σgεrΨ]+arctan(εsiεrΨ)+πL},
where σg is the conductivity of graphene, εsi and εair are the dielectric permittivity of silica substrate and air (the surrounding media), respectively. k0 is the propagation constant in vacuum, Z0≈377Ω is the free space impedance [25]. th-BN is the thickness of h-BN, L = 0, 1, 2, 3…, Ψ=εa/εr/i, where εa and εr are the out-of-plane dielectric permittivity and in-plane dielectric permittivity of h-BN, respectively. And for the graphene-coated h-BN single nanowire structure, the modal dispersion can be approximately written as [33]:
βZ2=β2(M/R0)2,
where R0 is the effective radius of the proposed graphene-coated h-BN single nanowire structure, and M = 0, 1, 2, 3…. In our work, the finite-element method (FEM) software COMSOL Multiphysics is used for the numerical calculation of the proposed structures. In the COMSOL FEM model, the mode analysis solver is used to finish the numerical calculation. Mode analysis is a two dimensional eigenvalue solver and it can compute the propagation constants at waveguide cross sections for a given wavenumber in electromagnetics. The size of surrounding media (air) is set as 10000 nm*10000 nm, the mesh size of graphene and h-BN are both extremely fine.

The electric field distribution |E| and the z-component of electric field EZ for the lowest 3 order modes (M = 0, 1, 2) of the plasmon-phonon-polariton mode (L = 0) supported in the graphene-coated h-BN single nanowire (SPP-PHP-GHN) are shown in Fig. 2(a). Here, the wavenumber is set as 1450 cm−1. Without special explication, the parameters of the GHN are set as follows: the radius of silica substrate R = 90 nm, the Fermi level of graphene Ef = 0.5 eV, the thickness of h-BN th-BN = 10 nm. The real part of the effective index (Re(neff)) and ratio of real part to imaginary part of the effective index (Re(neff) / Im(neff)) for the lowest 3 order modes of SPP-PHP-GHN (SPP-PHP-GHN mode 0, mode 1 and mode 2) are also presented in Figs. 3(a) and 3(b), respectively. Here, the effective refractive index neff is defined as neff = βz/k0, where βz is the propagation constant in z direction and k0 is the propagation constant in vacuum. One can see that the both Re(neff) and Re(neff) / Im(neff) for SPP-PHP-GHN mode 0, mode 1 and mode 2 increase as the wavenumber increases from 1450 to 1550 cm−1. Besides, we can find that Re(neff) and Re(neff) / Im(neff) for SPP-PHP-GHN mode 2 owes the smallest Re(neff) and Re(neff) / Im(neff) among these 3 order modes. Higher order phonon-polariton modes (L = 1, 2, 3…) are not affected by the plasmon-phonon-polariton coupling [21,25]. The electric field distribution |E| and z-component of electric field EZ for the lowest 3 order modes (M = 0, 1, 2) of the phonon-polariton modes (L = 1) supported in the graphene-coated h-BN nanowire (PHP-GHN) are shown in Fig. 2(b). Here, the wavenumber is set as 1450 cm−1. Moreover, Re (neff) and Re (neff) / Im (neff) for the lowest 3 order modes of PHP-GHN (PHP-GHN mode 0, mode 1 and mode 2) are described in Figs. 3(c) and 3(d), respectively. Here we can observe that Re(neff) for them increase with the wavenumber increasing from 1450 to 1550 cm−1 while Re (neff) / Im (neff) for them reach a peak first and then drop gradually with rising the wavenumber from 1450 to 1550 cm−1. Apart from that, larger Re(neff) and Re(neff) / Im(neff) reflects the stronger field confinement and lower propagation loss of the plasmon-phonon-polariton modes and phonon-polariton modes supported in the proposed waveguide, respectively [34,35]. As is shown in Figs. 3(c) and 3(d), Re (neff) and Re(neff) / Im(neff) for PHP-GHN mode 0, mode 1 and mode 2 show a rapid upward trend and a rapid downward trend when the wavenumber increases to approach 1550 cm−1. This is because the Re (εr) of h-BN shows a nonlinear change in this range of wavenumber. Consequently, stronger field confinement but higher propagation loss are achieved among these 3 order modes as wavenumber increases to approach 1550 cm−1. However, as is shown in Figs. 3(a) and 3(b), Re(neff) and Re(neff) / Im(neff) for the lowest 3 order modes of SPP-PHP-GHN display a relatively slow upward trend as wavenumber increases. This is because that phonon-polariton modes couple to the plasmon-polariton modes. And both stronger field confinement and lower loss can be achieved among these 3 orders modes as wavenumber increases. For the plasmon polariton modes supported in graphene-coated silica substrate nanowire structure, the eigen equation can be derived from [36]. Especially, for the lowest order mode of plasmon polariton modes supported in graphene-coated silica substrate nanowire structure, the dispersion equation can be written as [36]:

ε1μ1I1(μ1R0)I0(μ1R0)+ε2μ2K1(μ2R0)K0(μ2R0)=σgjω,
where ε1 is the permittivity of silica substrate, ε2 is the permittivity of air (the surrounding media), σg is the conductivity of the graphene. μ1=βg2ω2ε1μ0,μ2=βg2ω2ε2μ0, Im(μ1R0) and Km(μ2R0) are the modified Bessel functions of the first and second kind (m = 0, 1). R0 is the radius of the silica substrate. The effective refractive index for the lowest order mode of plasmon polariton modes supported in graphene-coated silica substrate nanowire structure can be calculated by βg/k0. Here, k0 is the propagation constant in vacuum. Then, the dependences of the effective refractive index for the lowest order mode of plasmon polariton modes supported in graphene-coated silica substrate nanowire structure on the wavenumber can be calculated by solving the Eq. (5). And the influences of plasmon-phonon-polariton coupling on the effective refractive index for the lowest 3 order modes of SPP-PHP-GHN versus wavenumber could be understood.

 

Fig. 2 (a) The electric field distribution |E| (V/m) and the z-component of electric field EZ (V/m) for the lowest 3 order modes of SPP-PHP-GHN. (b) The electric field distribution |E| (V/m) and the z-component of electric field EZ (V/m) for the lowest 3 order modes of PHP-GHN.

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Fig. 3 (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 3 order modes of SPP-PHP-GHN versus wavenumber. (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 3 order modes of PHP-GHN versus wavenumber.

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Furthermore, the numerical calculation results of the GHNP structure shown in Fig. 1(a) are presented. Without special explication, the parameters of the GHNP are set as follows: the radius of silica substrate R = 90 nm, the Fermi level of graphene Ef = 0.5 eV, the thickness of h-BN th-BN = 10 nm, the distance between the two GHN waveguides D = 10 nm. Figures 4(a) and 4(b) illustrate the field distributions of the lowest 5 order modes of the plasmon-phonon-polariton modes supported in the graphene-coated h-BN nanowire pairs (SPP-PHP-GHNP mode 0, mode 1, mode 2, mode 3 and mode 4) and the lowest 5 order modes of the phonon-polariton modes supported in the graphene-coated h-BN nanowire pairs (PHP-GHNP mode 0, mode 1, mode 2, mode 3 and mode 4), respectively. Here, the wavenumber is set as 1450 cm−1. The orders of these modes discussed above can be explicated and derived from [34]. Besides, Re (neff) and Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP and the lowest 5 order modes of PHP-GHNP are described in Figs. 5(a)-5(d), respectively. Figures 5(a) and 5(b) show that both Re (neff) and Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP increase with rising the wavenumber from 1450 to 1550 cm−1. It is worth noting that SPP-PHP-GHNP mode 0 owns the largest Re (neff) and Re (neff) / Im (neff) among these 5 order modes, which leads to a strongest confinement and lowest loss. And its performance of low loss is better than the results in [33,35]. As is shown in Figs. 5(c) and 5(d), Re (neff) for the lowest 5 order modes of PHP-GHNP rise as the wavenumber increases from 1450 to 1550 cm−1 while Re (neff) / Im (neff) for them firstly show a upward trend and then decline with increasing the wavenumber from 1450 to 1550 cm−1. Besides, as is shown in Figs. 5(c) and 5(d), Re(neff) and Re(neff) / Im(neff) for lowest 5 order modes of PHP-GHNP display a quick upward trend and a rapid downward trend when the wavenumber increases to approach 1550 cm−1. Similarly, this is owing to the nonlinear change of Re (εr) of h-BN in this range of wavenumber. And stronger field confinement but higher loss are achieved among these 5 order modes by increasing the wavenumber to approach 1550 cm−1. But as is shown in Figs. 5(a) and 5(b), Re(neff) and Re(neff) / Im(neff) for lowest 5 order modes of SPP-PHP-GHNP increase relatively slowly with the increasing of wavenumber. This is also because of the plasmon-phonon-polariton coupling as discussed above. And both stronger field confinement and lower propagation loss can be realized among these 5 order modes with the increasing of wavenumber. Here, one can see that Re(neff) and Re(neff) / Im(neff) for lowest 5 order modes of SPP-PHP-GHNP and PHP-GHNP show the similar trend compared with Re(neff) and Re(neff) / Im(neff) for lowest 5 order modes of SPP-PHP-GHN and PHP-GHN as shown in Figs. 3(a)-3(d) when wavenumber increases from 1450 to 1550 cm−1.

 

Fig. 4 (a) The electric field distribution |E| (V/m) and the z-component of electric field EZ (V/m) for the lowest 5 order modes of SPP-PHP-GHNP. (b) The electric field distribution |E| (V/m) and the z-component of electric field EZ (V/m) for the lowest 5 order modes of PHP-GHNP.

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Fig. 5 (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP versus wavenumber. (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP versus wavenumber.

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Next, the dependencies of Re (neff) and Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP and PHP-GHNP on the Fermi level of graphene Ef are shown in Figs. 6(a)-6(d), respectively. Here, the wavenumber is set as 1500 cm−1. Figure 6(a) illustrates that Re (neff) for the lowest 5 order modes of SPP-PHP-GHNP drop as Ef increases. However, Re (neff) / Im (neff) for them increase with the rising of Ef as shown in Fig. 6(b). Here, it is obvious that SPP-PHP-GHNP mode 0 displays a larger Re (neff) and Re (neff) / Im (neff) than the other 4 order modes, which means that SPP-PHP-GHNP mode 0 remains the strongest confinement and lowest loss with the increasing of Ef. As is presented in Fig. 6(c), Re (neff) for the lowest 5 order modes of PHP-GHNP show a downward trend when Ef increases from 0.3 to 0.8 eV. Whereas Re (neff) / Im (neff) increase and hit a peak as Ef increases from 0.3 to 0.4 eV and then decrease gradually with the increasing of Ef from 0.4 to 0.8 eV as shown in Fig. 6(d). Moreover, as is shown in Figs. 6(a) and 6(b), the influences of Ef on the Re(neff) and Re(neff) / Im(neff) for the lowest 5 order modes of SPP-PHP-GHNP are obvious owing to the coupling between the plasmon polariton modes and phonon-polariton modes. And we can find that lower propagation loss but weaker field confinement can be realized among these 5 order modes by increasing Ef. Besides, the relationship between Ef and the effective index for the lowest order mode of plasmon polariton modes supported in graphene-coated silica substrate nanowire structure can also be derived by solving the Eq. (5). And the influences of plasmon-phonon-polariton coupling on the effective refractive index for the lowest 5 order modes of SPP-PHP-GHNP versus Ef could be understood. However, as is illustrated in Figs. 6(c) and 6(d), the influences of Ef on the Re(neff) and Re(neff) / Im(neff) for lowest 5 order modes of PHP-GHNP are not obvious compared with lowest 5 order modes of SPP-PHP-GHNP. This is because high order phonon-polariton modes are almost not influenced by the plasmon-phonon-polariton coupling.

 

Fig. 6 Dependencies of (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP on the Fermi level of graphene. Dependencies of (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP on the Fermi level of graphene.

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Figures 7(a) and 7(b) illustrate that both Re (neff) and Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP display a upward trend when the radius of substrate R increases from 30 to 130 nm. The wavenumber is set as 1500 cm−1. Here, one can see that the SPP-PHP-GHNP mode 0 shows the larger Re (neff) and Re (neff) / Im (neff) than the other 4 order modes, which indicates that the SPP-PHP-GHNP mode 0 has stronger confinement and lower loss than the other 4 order modes. Similarly, as is shown in Figs. 7(c) and 7(d), both Re (neff) and Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP increase with the increasing of R from 30 to 130 nm. Here, the wavenumber is set as 1500 cm−1. One can find that PHP-GHNP mode 0 and mode 1 own the larger Re (neff) and Re (neff) / Im (neff) among these lowest 5 order modes.

 

Fig. 7 Dependencies of (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP on the radius of substrate. Dependencies of (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP on the radius of substrate.

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The dependencies of Re (neff) and Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP and PHP-GHNP on the distance between the two GHN waveguides D are shown in Figs. 8(a)-8(d), respectively. Here, the wavenumber is set as 1500 cm−1. In Figs. 8(a) and 8(b), we can see that the influences of D on Re (neff) and Re (neff) / Im (neff) for the SPP-PHP-GHNP mode 1, mode 2 and mode 4 are not obvious compared with SPP-PHP-GHNP mode 0 and mode 3. This is because the fields of SPP-PHP-GHNP mode 1, mode 2 and mode 4 are relatively far from the area between the two GHN waveguides as shown in Fig. 4(a) [34]. Similarly, one can find that the dependencies of Re (neff) and Re (neff) / Im (neff) for the PHP-GHNP mode 3 and mode 4 on D are not obvious compared with PHP-GHNP mode 0, mode 1 and mode 2 as shown in Figs. 8(c) and 8(d). This can also be explained by observing the field distributions of the lowest 5 order modes of PHP-GHNP shown in Fig. 4(b). In Fig. 4(b), we can find that the fields of PHP-GHNP mode 3 and mode 4 are more far from the area between the two GHN waveguides than PHP-GHNP mode 0, mode 1 and mode 2.

 

Fig. 8 Dependencies of (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP on the distance between the two GHN waveguides. Dependencies of (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP on the distance between the two GHN waveguides.

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Figures 9(a)-9(d) illustrate Re (neff) and Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP and PHP-GHNP versus the thickness of h-BN th-BN. Here, the wavenumber is set as 1500 cm−1 and R is fixed at 90 nm. As is presented in Figs. 9(a) and 9(b), both Re (neff) and Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP decline as th-BN increases from 5 to 15 nm. It is obvious that SPP-PHP-GHNP mode 0 shows the larger Re (neff) (stronger confinement) and larger Re (neff) / Im (neff) (lower loss) among these 5 order modes. Besides, Re (neff) for the lowest 5 order modes of PHP-GHNP decrease with the rising of th-BN while Re (neff) / Im (neff) for them display a upward trend as th-BN increases from 5 to 15 nm as shown in Figs. 9(c) and 9(d).

 

Fig. 9 Dependencies of (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP on the thickness of h-BN. Here, R is fixed at 90 nm. Dependencies of (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP on the thickness of h-BN. Here, R is fixed at 90 nm.

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Finally, the field enhancement of the SPP-PHP-GHNP mode 0 is demonstrated because of its strong confinement as discussed above. The field enhancement is defined by the ratio of electric field distribution |E| at the inner surface of graphene (x = D/2) to that at the outer surface of graphene (x = D/2 + 2R + 2t + 2th-BN) [37]. The dependencies of field enhancement of the SPP-PHP-GHNP mode 0 on the Fermi level of graphene Ef, the radius of substrate R, the distance between the two GHN waveguides D, and the thickness of h-BN th-BN are shown in Figs. 10(a)-10(d), respectively. Here, the wavenumber is set as 1550 cm−1. A field enhancement, over 105, can be realized by tuning Ef and R. Figure 10(a) shows that the field enhancement declines as Ef increases from 0.3 to 0.8 eV. On the contrary, the field enhancement rises as R increases from 30 to 130 nm as shown in Fig. 10(b). Figure 10(c) illustrates that the field enhancement increases and reaches the peak when D increases from 4 to 6 nm and then decreases gradually as D increases from 6 to 14 nm. In Fig. 10(d), we can see that the influence of th-BN on the field enhancement is not obvious compared with the other three parameters.

 

Fig. 10 Dependencies of field enhancement of the SPP-PHP-GHNP mode 0 on (a) the Fermi level of graphene. (b) the radius of substrate. (c) the distance between the two GHN waveguides. (d) the thickness of h-BN (Here R is fixed at 90 nm).

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4. Conclusion

In this paper, the graphene-coated h-BN nanowire pairs structure is proposed and demonstrated. Firstly, the lowest 3 order modes of SPP-PHP modes and PHP modes supported in the graphene-coated hexagon boron nitride single nanowire is discussed. Then, we demonstrated the dependencies of Re (neff) and Re (neff) / Im (neff) for the first 5 order modes of SPP-PHP-GHNP and PHP-GHNP on the Fermi level of graphene Ef, the distance between the two GHN waveguides D, the radius of substrate R, and the thickness of h-BN th-BN. The results indicate that SPP-PHP-GHNP mode 0 remains the strongest confinement and lowest loss among the lowest 5 order modes of SPP-PHP-GHNP with the change of Ef, R, D or th-BN. Finally, we discussed the dependencies of field enhancement of SPP-PHP-GHNP mode 0 on Ef, D, R and th-BN. A field enhancement over 105 can be achieved by controlling Ef or changing R. Moreover, the results show that the field enhancement is less dependent on th-BN than the other three parameters discussed above. The proposed structure may have a promising application in graphene-h-BN-based optical devices.

Funding

Fundamental Research Funds for the Central Universities (W17RC00020); China Postdoctoral Science Foundation (2018M631327).

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12. J. Yang, H. Xin, Y. Han, D. Chen, J. Zhang, J. Huang, and Z. Zhang, “Ultra-compact beam splitter and filter based on a graphene plasmon waveguide,” Appl. Opt. 56(35), 9814–9821 (2017). [CrossRef]   [PubMed]  

13. A. W. Schell, T. T. Tran, H. Takashima, S. Takeuchi, and I. Aharonovich, “Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers,” APL Photonics 1(9), 091302 (2016). [CrossRef]  

14. A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016). [CrossRef]  

15. P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015). [CrossRef]   [PubMed]  

16. Y. Xu, N. Premkumar, Y. Yang, and B. A. Lail, “Hybrid surface phononic waveguide using hyperbolic boron nitride,” Opt. Express 24(15), 17183–17192 (2016). [CrossRef]   [PubMed]  

17. B. Zhao and Z. M. Zhang, “Resonance perfect absorption by exciting hyperbolic phonon polaritons in 1D hBN gratings,” Opt. Express 25(7), 7791–7796 (2017). [CrossRef]   [PubMed]  

18. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009). [CrossRef]  

19. S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014). [CrossRef]   [PubMed]  

20. S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015). [CrossRef]   [PubMed]  

21. A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015). [CrossRef]   [PubMed]  

22. J. Wu, L. Jiang, J. Guo, X. Dai, Y. Xiang, and S. Wen, “Turnable perfect absorption at infrared frequencies by a Graphene-hBN Hyper Crystal,” Opt. Express 24(15), 17103–17114 (2016). [CrossRef]   [PubMed]  

23. A. Farmani, M. Yavarian, A. Alighanbari, M. Miri, and M. H. Sheikhi, “Tunable graphene plasmonic Y-branch switch in the terahertz region using hexagonal boron nitride with electric and magnetic biasing,” Appl. Opt. 56(32), 8931–8940 (2017). [CrossRef]   [PubMed]  

24. Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011). [CrossRef]  

25. B. Zhu, G. Ren, B. Wu, Y. Gao, H. Li, and S. Jian, “Nanofocusing of hybrid plasmons-phonons-polaritons in a graphene-hexagonal boron nitride heterostructure,” Opt. Lett. 41(19), 4578–4581 (2016). [CrossRef]   [PubMed]  

26. V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014). [CrossRef]   [PubMed]  

27. H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016). [CrossRef]  

28. Y. Wu, L. Jiang, H. Xu, X. Dai, Y. Xiang, and D. Fan, “Hybrid nonlinear surface-phonon-plasmon-polaritons at the interface of nolinear medium and graphene-covered hexagonal boron nitride crystal,” Opt. Express 24(3), 2109–2124 (2016). [CrossRef]   [PubMed]  

29. W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014). [CrossRef]   [PubMed]  

30. S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016). [CrossRef]   [PubMed]  

31. 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]   [PubMed]  

32. H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015). [CrossRef]   [PubMed]  

33. Y. Zhou, D.-X. Qi, and Y.-K. Wang, “Phonon polaritons in cylindrically curved h-BN,” Opt. Express 25(15), 17606–17615 (2017). [CrossRef]   [PubMed]  

34. B. Zhu, G. Ren, Y. Yang, Y. Gao, B. Wu, Y. Lian, J. Wang, and S. Jian, “Field enhancement and gradient force in the graphene-coated nanowire pairs,” Plasmonics 10(4), 839–845 (2015). [CrossRef]  

35. Z.-W. Zhao, H.-W. Wu, and Y. Zhou, “Surface-confined edge phonon polaritons in hexagonal boron nitride thin films and nanoribbons,” Opt. Express 24(20), 22930–22942 (2016). [CrossRef]   [PubMed]  

36. Y. Gao, G. Ren, B. Zhu, H. Liu, Y. Lian, and S. Jian, “Analytical model for plasmon modes in graphene-coated nanowire,” Opt. Express 22(20), 24322–24331 (2014). [CrossRef]   [PubMed]  

37. R. Xing and S. Jian, “Numerical analysis on the multilayer nanoring waveguide pair,” IEEE Photonics Technol. Lett. 28(24), 2779–2782 (2016). [CrossRef]  

References

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  1. A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
    [Crossref]
  2. X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
    [Crossref]
  3. B. Zhu, G. Ren, M. J. Cryan, Y. Gao, Y. Yang, B. Wu, Y. Lian, and S. Jian, “Magnetically tunable non-reciprocal plasmons resonator based on graphene-coated nanowire,” Opt. Mater. Express 5(10), 2174–2183 (2015).
    [Crossref]
  4. V. Dmitriev and C. Monte do Nascimento, “Planar THz electromagnetic graphene pass-band filter with low polarization and angle of incidence dependencies,” Appl. Opt. 54(6), 1515–1520 (2015).
    [Crossref] [PubMed]
  5. E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
    [Crossref]
  6. Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
    [Crossref] [PubMed]
  7. R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
    [Crossref] [PubMed]
  8. W. Liu, B. Wang, S. Ke, C. Qin, H. Long, K. Wang, and P. Lu, “Enhanced plasmonic nanofocusing of terahertz waves in tapered graphene multilayers,” Opt. Express 24(13), 14765–14780 (2016).
    [Crossref] [PubMed]
  9. Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
    [Crossref]
  10. H. Xu, L. Wu, X. Dai, Y. Gao, and Y. Xiang, “An ultra-high sensitivity surface plasmon resonance sensor based on graphene-aluminum-graphene sandwich-like structure,” J. Appl. Phys. 120(5), 053101 (2016).
    [Crossref]
  11. T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
    [Crossref]
  12. J. Yang, H. Xin, Y. Han, D. Chen, J. Zhang, J. Huang, and Z. Zhang, “Ultra-compact beam splitter and filter based on a graphene plasmon waveguide,” Appl. Opt. 56(35), 9814–9821 (2017).
    [Crossref] [PubMed]
  13. A. W. Schell, T. T. Tran, H. Takashima, S. Takeuchi, and I. Aharonovich, “Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers,” APL Photonics 1(9), 091302 (2016).
    [Crossref]
  14. A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
    [Crossref]
  15. P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
    [Crossref] [PubMed]
  16. Y. Xu, N. Premkumar, Y. Yang, and B. A. Lail, “Hybrid surface phononic waveguide using hyperbolic boron nitride,” Opt. Express 24(15), 17183–17192 (2016).
    [Crossref] [PubMed]
  17. B. Zhao and Z. M. Zhang, “Resonance perfect absorption by exciting hyperbolic phonon polaritons in 1D hBN gratings,” Opt. Express 25(7), 7791–7796 (2017).
    [Crossref] [PubMed]
  18. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
    [Crossref]
  19. S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
    [Crossref] [PubMed]
  20. S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
    [Crossref] [PubMed]
  21. A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
    [Crossref] [PubMed]
  22. J. Wu, L. Jiang, J. Guo, X. Dai, Y. Xiang, and S. Wen, “Turnable perfect absorption at infrared frequencies by a Graphene-hBN Hyper Crystal,” Opt. Express 24(15), 17103–17114 (2016).
    [Crossref] [PubMed]
  23. A. Farmani, M. Yavarian, A. Alighanbari, M. Miri, and M. H. Sheikhi, “Tunable graphene plasmonic Y-branch switch in the terahertz region using hexagonal boron nitride with electric and magnetic biasing,” Appl. Opt. 56(32), 8931–8940 (2017).
    [Crossref] [PubMed]
  24. Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
    [Crossref]
  25. B. Zhu, G. Ren, B. Wu, Y. Gao, H. Li, and S. Jian, “Nanofocusing of hybrid plasmons-phonons-polaritons in a graphene-hexagonal boron nitride heterostructure,” Opt. Lett. 41(19), 4578–4581 (2016).
    [Crossref] [PubMed]
  26. V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
    [Crossref] [PubMed]
  27. H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
    [Crossref]
  28. Y. Wu, L. Jiang, H. Xu, X. Dai, Y. Xiang, and D. Fan, “Hybrid nonlinear surface-phonon-plasmon-polaritons at the interface of nolinear medium and graphene-covered hexagonal boron nitride crystal,” Opt. Express 24(3), 2109–2124 (2016).
    [Crossref] [PubMed]
  29. W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
    [Crossref] [PubMed]
  30. S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
    [Crossref] [PubMed]
  31. 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] [PubMed]
  32. H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
    [Crossref] [PubMed]
  33. Y. Zhou, D.-X. Qi, and Y.-K. Wang, “Phonon polaritons in cylindrically curved h-BN,” Opt. Express 25(15), 17606–17615 (2017).
    [Crossref] [PubMed]
  34. B. Zhu, G. Ren, Y. Yang, Y. Gao, B. Wu, Y. Lian, J. Wang, and S. Jian, “Field enhancement and gradient force in the graphene-coated nanowire pairs,” Plasmonics 10(4), 839–845 (2015).
    [Crossref]
  35. Z.-W. Zhao, H.-W. Wu, and Y. Zhou, “Surface-confined edge phonon polaritons in hexagonal boron nitride thin films and nanoribbons,” Opt. Express 24(20), 22930–22942 (2016).
    [Crossref] [PubMed]
  36. Y. Gao, G. Ren, B. Zhu, H. Liu, Y. Lian, and S. Jian, “Analytical model for plasmon modes in graphene-coated nanowire,” Opt. Express 22(20), 24322–24331 (2014).
    [Crossref] [PubMed]
  37. R. Xing and S. Jian, “Numerical analysis on the multilayer nanoring waveguide pair,” IEEE Photonics Technol. Lett. 28(24), 2779–2782 (2016).
    [Crossref]

2018 (1)

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
[Crossref] [PubMed]

2017 (4)

2016 (12)

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
[Crossref] [PubMed]

B. Zhu, G. Ren, B. Wu, Y. Gao, H. Li, and S. Jian, “Nanofocusing of hybrid plasmons-phonons-polaritons in a graphene-hexagonal boron nitride heterostructure,” Opt. Lett. 41(19), 4578–4581 (2016).
[Crossref] [PubMed]

H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
[Crossref]

Y. Wu, L. Jiang, H. Xu, X. Dai, Y. Xiang, and D. Fan, “Hybrid nonlinear surface-phonon-plasmon-polaritons at the interface of nolinear medium and graphene-covered hexagonal boron nitride crystal,” Opt. Express 24(3), 2109–2124 (2016).
[Crossref] [PubMed]

J. Wu, L. Jiang, J. Guo, X. Dai, Y. Xiang, and S. Wen, “Turnable perfect absorption at infrared frequencies by a Graphene-hBN Hyper Crystal,” Opt. Express 24(15), 17103–17114 (2016).
[Crossref] [PubMed]

A. W. Schell, T. T. Tran, H. Takashima, S. Takeuchi, and I. Aharonovich, “Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers,” APL Photonics 1(9), 091302 (2016).
[Crossref]

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

H. Xu, L. Wu, X. Dai, Y. Gao, and Y. Xiang, “An ultra-high sensitivity surface plasmon resonance sensor based on graphene-aluminum-graphene sandwich-like structure,” J. Appl. Phys. 120(5), 053101 (2016).
[Crossref]

Y. Xu, N. Premkumar, Y. Yang, and B. A. Lail, “Hybrid surface phononic waveguide using hyperbolic boron nitride,” Opt. Express 24(15), 17183–17192 (2016).
[Crossref] [PubMed]

W. Liu, B. Wang, S. Ke, C. Qin, H. Long, K. Wang, and P. Lu, “Enhanced plasmonic nanofocusing of terahertz waves in tapered graphene multilayers,” Opt. Express 24(13), 14765–14780 (2016).
[Crossref] [PubMed]

Z.-W. Zhao, H.-W. Wu, and Y. Zhou, “Surface-confined edge phonon polaritons in hexagonal boron nitride thin films and nanoribbons,” Opt. Express 24(20), 22930–22942 (2016).
[Crossref] [PubMed]

R. Xing and S. Jian, “Numerical analysis on the multilayer nanoring waveguide pair,” IEEE Photonics Technol. Lett. 28(24), 2779–2782 (2016).
[Crossref]

2015 (10)

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
[Crossref] [PubMed]

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
[Crossref]

B. Zhu, G. Ren, M. J. Cryan, Y. Gao, Y. Yang, B. Wu, Y. Lian, and S. Jian, “Magnetically tunable non-reciprocal plasmons resonator based on graphene-coated nanowire,” Opt. Mater. Express 5(10), 2174–2183 (2015).
[Crossref]

V. Dmitriev and C. Monte do Nascimento, “Planar THz electromagnetic graphene pass-band filter with low polarization and angle of incidence dependencies,” Appl. Opt. 54(6), 1515–1520 (2015).
[Crossref] [PubMed]

T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

B. Zhu, G. Ren, Y. Yang, Y. Gao, B. Wu, Y. Lian, J. Wang, and S. Jian, “Field enhancement and gradient force in the graphene-coated nanowire pairs,” Plasmonics 10(4), 839–845 (2015).
[Crossref]

2014 (5)

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
[Crossref]

Y. Gao, G. Ren, B. Zhu, H. Liu, Y. Lian, and S. Jian, “Analytical model for plasmon modes in graphene-coated nanowire,” Opt. Express 22(20), 24322–24331 (2014).
[Crossref] [PubMed]

2013 (1)

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

2012 (2)

A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (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] [PubMed]

2011 (1)

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

2009 (1)

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Aharonovich, I.

A. W. Schell, T. T. Tran, H. Takashima, S. Takeuchi, and I. Aharonovich, “Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers,” APL Photonics 1(9), 091302 (2016).
[Crossref]

Alighanbari, A.

Alonso-Gonzalez, P.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Andersen, T.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

Atwater, H.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Avouris, P.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Bao, J.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Barnard, H. R.

H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
[Crossref]

Basov, D. N.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Brar, V. W.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Caldwell, J. D.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

Casanova, F.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Castro Neto, A. H.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Chen, B.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Chen, D.

Chen, H.

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

Chen, H.-S.

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
[Crossref] [PubMed]

Chen, J.-H.

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
[Crossref]

Chen, Z.-X.

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
[Crossref]

Choi, M.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Christensen, T.

T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

Cryan, M. J.

Dai, S.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Dai, T.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
[Crossref] [PubMed]

Dai, X.

Dmitriev, V.

Dolado, I.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Dominguez, G.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Fan, D.

Fang, N. X.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Fang, W.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Farmani, A.

Fei, Z.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Fogler, M. M.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Forati, E.

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

Fung, K. H.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Gannett, W.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Gao, H.

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

Gao, W.

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] [PubMed]

Gao, Y.

Gaussmann, F.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

Goldflam, M. D.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

Gu, M.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Guinea, F.

A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
[Crossref]

Guo, J.

Guo, Z.

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

Han, X.

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
[Crossref] [PubMed]

Han, Y.

Hanson, G. W.

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

Hao, R.

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
[Crossref] [PubMed]

Hillenbrand, R.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Hossain, M. M.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Hu, W.

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
[Crossref]

Hu, Z.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Hu, Z.-D.

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
[Crossref]

Huang, J.

Hueso, L. E.

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

Jablan, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Jang, M. S.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Janssen, G. C. A. M.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

Jarillo-Herrero, P.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Jauho, A.-P.

T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

Jian, S.

Jiang, J.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
[Crossref] [PubMed]

Jiang, L.

Jiang, X.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
[Crossref] [PubMed]

Jin, J.-M.

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
[Crossref] [PubMed]

Ke, S.

Keilmann, F.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

Kim, L. B.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Kim, S.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
[Crossref] [PubMed]

Kretinin, A. V.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

Kumar, A.

A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
[Crossref] [PubMed]

Lail, B. A.

Lawton, L. M.

H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
[Crossref]

Lewin, M.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

Li, E.-P.

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
[Crossref] [PubMed]

Li, H.

Li, P.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

Li, W.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Li, X.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
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Li, Y.

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Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
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X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
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S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
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W. Liu, B. Wang, S. Ke, C. Qin, H. Long, K. Wang, and P. Lu, “Enhanced plasmonic nanofocusing of terahertz waves in tapered graphene multilayers,” Opt. Express 24(13), 14765–14780 (2016).
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Liu, X.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
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Liu, Y.

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
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Lopez, J. J.

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
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Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
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Lu, Y.-Q.

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S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
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S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
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S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
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Monte do Nascimento, C.

Mortensen, N. A.

T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
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H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
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A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
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A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
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P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
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Peng, X.-L.

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
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Qi, D.-X.

Qin, C.

Qin, Y.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
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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).
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Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
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S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
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Rodin, A. S.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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A. W. Schell, T. T. Tran, H. Takashima, S. Takeuchi, and I. Aharonovich, “Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers,” APL Photonics 1(9), 091302 (2016).
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A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
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Shen, Y. R.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
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V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
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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).
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A. W. Schell, T. T. Tran, H. Takashima, S. Takeuchi, and I. Aharonovich, “Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers,” APL Photonics 1(9), 091302 (2016).
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P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
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S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
[Crossref] [PubMed]

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
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Thiemens, M.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
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S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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Tong, L.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
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A. W. Schell, T. T. Tran, H. Takashima, S. Takeuchi, and I. Aharonovich, “Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers,” APL Photonics 1(9), 091302 (2016).
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A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
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S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
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S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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Wang, G.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
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W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
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B. Zhu, G. Ren, Y. Yang, Y. Gao, B. Wu, Y. Lian, J. Wang, and S. Jian, “Field enhancement and gradient force in the graphene-coated nanowire pairs,” Plasmonics 10(4), 839–845 (2015).
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X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
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Wang, K.

Wang, T.

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
[Crossref] [PubMed]

Wang, Y.-K.

Watanabe, K.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6(1), 7507 (2015).
[Crossref] [PubMed]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
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S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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Wu, B.

Wu, H.-W.

Wu, J.

Wu, L.

H. Xu, L. Wu, X. Dai, Y. Gao, and Y. Xiang, “An ultra-high sensitivity surface plasmon resonance sensor based on graphene-aluminum-graphene sandwich-like structure,” J. Appl. Phys. 120(5), 053101 (2016).
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Wu, Z.-J.

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
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Wubs, M.

T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
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Xia, X.

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
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Xiao, S.

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
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Xiao, Y.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
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S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
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Xu, H.

Y. Wu, L. Jiang, H. Xu, X. Dai, Y. Xiang, and D. Fan, “Hybrid nonlinear surface-phonon-plasmon-polaritons at the interface of nolinear medium and graphene-covered hexagonal boron nitride crystal,” Opt. Express 24(3), 2109–2124 (2016).
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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).
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Y. Xu, N. Premkumar, Y. Yang, and B. A. Lail, “Hybrid surface phononic waveguide using hyperbolic boron nitride,” Opt. Express 24(15), 17183–17192 (2016).
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[Crossref] [PubMed]

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

Yan, W.

T. Christensen, W. Yan, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Kerr nonlinearity and plasmonic bistability in graphene nanoribbons,” Phys. Rev. B 92(12), 121407 (2015).
[Crossref]

Yan, X.

S. Xiao, T. Wang, Y. Liu, C. Xu, X. Han, and X. Yan, “Tunable light trapping and absorption enhancement with graphene ring arrays,” Phys. Chem. Chem. Phys. 18(38), 26661–26669 (2016).
[Crossref] [PubMed]

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
[Crossref]

Yang, J.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
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J. Yang, H. Xin, Y. Han, D. Chen, J. Zhang, J. Huang, and Z. Zhang, “Ultra-compact beam splitter and filter based on a graphene plasmon waveguide,” Appl. Opt. 56(35), 9814–9821 (2017).
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Yang, Y.

Yavarian, M.

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A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
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Yu, B.

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
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Yu, H.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
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Yuan, L.

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
[Crossref]

Yuan, Y.

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
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Zeng, C.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
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Zettl, A.

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
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Zhang, F.

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
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Zhang, J.

Zhang, Q.

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
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H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
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Zhang, X.-J.

Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
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Zhang, X.-M.

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
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Zhang, Z.

Zhang, Z. M.

Zhao, B.

Zhao, Z.-W.

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Zhu, B.

Zhu, S.-E.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
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H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
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ACS Photonics (1)

A. Y. Nikitin, E. Yoxall, M. Schnell, S. Vélez, I. Dolado, P. Alonso-Gonzalez, F. Casanova, L. E. Hueso, and R. Hillenbrand, “Nanofocusing of hyperbolic phonon polaritons in a tapered boron nitride slab,” ACS Photonics 3(6), 924–929 (2016).
[Crossref]

APL Photonics (1)

A. W. Schell, T. T. Tran, H. Takashima, S. Takeuchi, and I. Aharonovich, “Non-linear excitation of quantum emitters in hexagonal boron nitride multiplayers,” APL Photonics 1(9), 091302 (2016).
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Appl. Opt. (3)

Appl. Phys. Lett. (5)

Y. Xu, Z. Guo, H. Chen, Y. Yuan, J. Lou, X. Lin, H. Gao, H. Chen, and B. Yu, “In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures,” Appl. Phys. Lett. 99(13), 133109 (2011).
[Crossref]

H. R. Barnard, E. Zossimova, N. H. Mahlmeister, L. M. Lawton, I. J. Luxmoore, and G. R. Nash, “Boron nitride encapsulated graphene infrared emitters,” Appl. Phys. Lett. 108(13), 131110 (2016).
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E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
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A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
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Z.-X. Chen, J.-H. Chen, Z.-J. Wu, W. Hu, X.-J. Zhang, and Y.-Q. Lu, “Tunable Fano resonance in hybrid graphene-metal gratings,” Appl. Phys. Lett. 104(16), 161114 (2014).
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IEEE Photonics Technol. Lett. (1)

R. Xing and S. Jian, “Numerical analysis on the multilayer nanoring waveguide pair,” IEEE Photonics Technol. Lett. 28(24), 2779–2782 (2016).
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J. Appl. Phys. (1)

H. Xu, L. Wu, X. Dai, Y. Gao, and Y. Xiang, “An ultra-high sensitivity surface plasmon resonance sensor based on graphene-aluminum-graphene sandwich-like structure,” J. Appl. Phys. 120(5), 053101 (2016).
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Nano Lett. (3)

V. W. Brar, M. S. Jang, M. Sherrott, S. Kim, J. J. Lopez, L. B. Kim, M. Choi, and H. Atwater, “Hybrid surface-phonon-plasmon polariton modes in graphene/monolayer h-BN heterostructures,” Nano Lett. 14(7), 3876–3880 (2014).
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A. Kumar, T. Low, K. H. Fung, P. Avouris, and N. X. Fang, “Tunable light-matter interaction and the role of hyperbolicity in graphene-hBN system,” Nano Lett. 15(5), 3172–3180 (2015).
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Nat. Commun. (1)

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Nat. Nanotechnol. (1)

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S.-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nat. Nanotechnol. 10(8), 682–686 (2015).
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Opt. Express (8)

Y. Wu, L. Jiang, H. Xu, X. Dai, Y. Xiang, and D. Fan, “Hybrid nonlinear surface-phonon-plasmon-polaritons at the interface of nolinear medium and graphene-covered hexagonal boron nitride crystal,” Opt. Express 24(3), 2109–2124 (2016).
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J. Wu, L. Jiang, J. Guo, X. Dai, Y. Xiang, and S. Wen, “Turnable perfect absorption at infrared frequencies by a Graphene-hBN Hyper Crystal,” Opt. Express 24(15), 17103–17114 (2016).
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Y. Zhou, D.-X. Qi, and Y.-K. Wang, “Phonon polaritons in cylindrically curved h-BN,” Opt. Express 25(15), 17606–17615 (2017).
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Z.-W. Zhao, H.-W. Wu, and Y. Zhou, “Surface-confined edge phonon polaritons in hexagonal boron nitride thin films and nanoribbons,” Opt. Express 24(20), 22930–22942 (2016).
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B. Zhao and Z. M. Zhang, “Resonance perfect absorption by exciting hyperbolic phonon polaritons in 1D hBN gratings,” Opt. Express 25(7), 7791–7796 (2017).
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Plasmonics (2)

X. Xia, J. Wang, F. Zhang, Z.-D. Hu, C. Liu, X. Yan, and L. Yuan, “Multi-mode plasmonically induced transparency in dual coupled graphene-integrated ring resonators,” Plasmonics 10(6), 1409–1415 (2015).
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B. Zhu, G. Ren, Y. Yang, Y. Gao, B. Wu, Y. Lian, J. Wang, and S. Jian, “Field enhancement and gradient force in the graphene-coated nanowire pairs,” Plasmonics 10(4), 839–845 (2015).
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Sci. Rep. (3)

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5(1), 8443 (2015).
[Crossref] [PubMed]

Y. Li, H. Yu, X. Qiu, T. Dai, J. Jiang, G. Wang, Q. Zhang, Y. Qin, J. Yang, and X. Jiang, “Graphene-based nonvolatile terahertz switch with asymmetric electrodes,” Sci. Rep. 8(1), 1562 (2018).
[Crossref] [PubMed]

R. Hao, X.-L. Peng, E.-P. Li, Y. Xu, J.-M. Jin, X.-M. Zhang, and H.-S. Chen, “Improved slow light capacity in graphene-based waveguide,” Sci. Rep. 5(1), 15335 (2015).
[Crossref] [PubMed]

Science (1)

S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watanabe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. Castro Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride,” Science 343(6175), 1125–1129 (2014).
[Crossref] [PubMed]

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Figures (10)

Fig. 1
Fig. 1 (a) Schematics of the GHNP structure. (b) The out-of-plane dielectric permittivity and in-plane dielectric permittivity of h-BN versus wavenumber.
Fig. 2
Fig. 2 (a) The electric field distribution |E| (V/m) and the z-component of electric field EZ (V/m) for the lowest 3 order modes of SPP-PHP-GHN. (b) The electric field distribution |E| (V/m) and the z-component of electric field EZ (V/m) for the lowest 3 order modes of PHP-GHN.
Fig. 3
Fig. 3 (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 3 order modes of SPP-PHP-GHN versus wavenumber. (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 3 order modes of PHP-GHN versus wavenumber.
Fig. 4
Fig. 4 (a) The electric field distribution |E| (V/m) and the z-component of electric field EZ (V/m) for the lowest 5 order modes of SPP-PHP-GHNP. (b) The electric field distribution |E| (V/m) and the z-component of electric field EZ (V/m) for the lowest 5 order modes of PHP-GHNP.
Fig. 5
Fig. 5 (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP versus wavenumber. (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP versus wavenumber.
Fig. 6
Fig. 6 Dependencies of (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP on the Fermi level of graphene. Dependencies of (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP on the Fermi level of graphene.
Fig. 7
Fig. 7 Dependencies of (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP on the radius of substrate. Dependencies of (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP on the radius of substrate.
Fig. 8
Fig. 8 Dependencies of (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP on the distance between the two GHN waveguides. Dependencies of (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP on the distance between the two GHN waveguides.
Fig. 9
Fig. 9 Dependencies of (a) Re (neff) (b) Re (neff) / Im (neff) for the lowest 5 order modes of SPP-PHP-GHNP on the thickness of h-BN. Here, R is fixed at 90 nm. Dependencies of (c) Re (neff) (d) Re (neff) / Im (neff) for the lowest 5 order modes of PHP-GHNP on the thickness of h-BN. Here, R is fixed at 90 nm.
Fig. 10
Fig. 10 Dependencies of field enhancement of the SPP-PHP-GHNP mode 0 on (a) the Fermi level of graphene. (b) the radius of substrate. (c) the distance between the two GHN waveguides. (d) the thickness of h-BN (Here R is fixed at 90 nm).

Equations (5)

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ε a ( r ) = ε , a ( r ) + ε , a ( r ) ( ω L O , a ( r ) ) 2 ( ω T O , a ( r ) ) 2 ( ω T O , a ( r ) ) 2 ω 2 i ω Γ a ( r ) ,
{ σ inter = e 2 4 { 0.5 + arc tan ( ω 2 E f 2 k B T ) π i 2 π ln [ ( ω + 2 E f ) 2 ( ω 2 E f ) 2 + ( 2 k B T ) 2 ] } , σ intra = 2 i e 2 k B T π 2 ( ω + i τ ) ln [ 2 cos h ( E f 2 k B T ) ] ,
β = Ψ t h B N { arc tan [ ε a i r + i ( β / k 0 ) Z 0 σ g ε r Ψ ] + arc tan ( ε s i ε r Ψ ) + π L } ,
β Z 2 = β 2 ( M / R 0 ) 2 ,
ε 1 μ 1 I 1 ( μ 1 R 0 ) I 0 ( μ 1 R 0 ) + ε 2 μ 2 K 1 ( μ 2 R 0 ) K 0 ( μ 2 R 0 ) = σ g j ω ,

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