Abstract

Photonic spin Hall effect (PSHE) of type II hyperbolic metamaterials is achieved due to near filed interference, which provides a way to decide the propagation direction of subwavelength beam. In this paper, we propose graphene-based hyperbolic metamaterials (GHMMs), which is composed of the alternating graphene/SiO2 multilayer. The numerical results show that when a dipole emitter is placed at the boundary of the GHMMs, the subwavelength beam with λ/40 full-with half maximum can be excited and propagates along the left or right channel, which is dependent on polarization handedness. In addition, we further demonstrate that the unidirectional propagation angle can be dynamically tuned by changing the external electric field bias applied to graphene.

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

1. Introduction

Hyperbolic metamaterials (HMMs), strongly anisotropic uniaxial artificial engineered electromagnetic materials that enable custom-tailored electromagnetic responses of the medium [18], have drawn great attention in recent years. Such anisotropic metamaterials, whose equi-frequency surface (EFS) is an open hyperboloid due to different signs of the longitudinal (ɛ||) and transverse (ɛ) components of the effective permittivity tensor, can be realized as nanowire arrays [9] and multilayer structures of alternating metal and dielectric [1012]. Many interesting potential applications of HMMs have been demonstrated for negative refraction [11,13,14], sub-diffraction imaging [15], dark hollow light cone [16], biosensing [1719] and photonic spin-hall effect (PSHE) [20]. Recently, graphene has attracted intensive attention in HMMs owing to its tunability of optical properties. Graphene-based HMMs (GHMMs), which is composed of multilayer structure of alternating graphene and dielectric, have been proposed and investigated [2129]. GHMMs structure can be applied to the spontaneous emission enhancement [22], the negative refraction at THz frequencies [24], tunable broadband hyperlens [25], the perfect absorption [26], tunable terahertz amplification [27], epsilon-near-zero material [28], near-field radiative heat transfer [29], and so on.

PSHE is an interesting transport phenomenon that a transverse spin-dependent subwavelength shift happens for the reflection or refraction beam at an optical interface under a circularly polarized light incidence [30,31]. PSHE was first proposed by Onoda et al. in 2004 and experimentally verified by Hosten et al by using the preselection and postselection technique in 2008 [32,33]. This phenomenon originates from spin-orbit coupling of photons and the fundamental law of angular momentum conservation [34]. There has been intensive research about the PSHE, such as magneto-optical modulation in graphene [35], the symmetric and asymmetric spin splitting in monolayer black phosphorus [36], PSHE in metamaterials [3739] and transmission [4044]. However, the PSHE in GHMMs for tunable polarization-controlled routing of subwavelength beam has not yet been studied.

In this work, the GHMMs structure, which consists of alternating graphene/SiO2 multilayer, is proposed to realize dynamically tunable directional subwavelength beam propagation. When a dipole emitter is placed at the boundary of the GHMMs with Type II hyperbolic dispersion, whether excited beam propagates along the left or right channel is dependent on the polarization handedness. This kind of photonic spin Hall effect originates from the near field interference effect. Besides, the unidirectional propagation angle can be dynamically tuned by the external electric field bias applied to graphene. In the previous work of Zhu et al. [45], a symmetric spin splitting dependent on the incident orbital-angular-momentum is achieved by transmitting higher-order Laguerre–Gaussian beams through the GHMMs with epsilon-near-zero region. Differently, directional propagation of the subwavelength beam can be controlled by the dipole handedness in GHMMs with Type II hyperbolic dispersion in our work. Here, all the simulation results based on finite element method (FEM) are conducted to verify our method.

2. Design and theories

The GHMMs structure, which is proposed for tunable polarization-controlled directional propagation of subwavelength beam, is shown in Fig. 1. This structure consists of an alternating graphene/SiO2 multilayer. Bulk plasmon polaritons (BPPs) can be supported and strongly confined inside the GHMMs structure, which originates from the hybridization of short-ranged surface plasmon polaritons (SPPs) in each interface between graphene and SiO2. For BPPs, the absolute value of modal indices is larger than that of SPPs. BPPs can be tailored by controlling the geometry of the metamaterials. This property can be utilized to achieve directional propagation of high-k waves [7]. Here, the period of the multilayer structure is d (= tg + td), the thickness tg of graphene is chosen as 0.35 nm, the thickness td of SiO2 is chosen as 20 nm, and the working wavelength is 7 µm. ɛg and ɛd ( = 1.24) represent the permittivities of graphene and SiO2, respectively. A dipole emitter (for example, an atom, molecule or classical antenna), which is placed in near-field proximity to the interface of the proposed GHMMs structure, emits into extraordinary modes of the metamaterial exhibiting high density of electromagnetic states (DOS) and strong spatial localization, with the directionality of energy propagation controlled by the dipole handedness [20].

 figure: Fig. 1.

Fig. 1. Schematic of the proposed GHMMs structure consisting of alternating graphene/SiO2 multilayer. The thicknesses of the graphene layer and the SiO2 layer are tg, and td, respectively.

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In our work, graphene is characterized by the following surface conductivity σg, which is calculated according to the well-known Kubo formula [46]:

$${\sigma _\textrm{g}} = \frac{{i{e^2}{E_f}}}{{\pi {{\hbar }^2}({\omega + i{\tau^{ - 1}}} )}} + \frac{{i{e^2}}}{{4\pi {\hbar }}}Ln\left[ {\frac{{2{E_f} - ({\omega + i{\tau^{ - 1}}} ){\hbar }}}{{2{E_f} + ({\omega + i{\tau^{ - 1}}} ){\hbar }}}} \right] + \frac{{i2{e^2}{k_B}T}}{{\pi {{\hbar }^2}({\omega + i{\tau^{ - 1}}} )}}Ln\left[ {\exp ( - \frac{{{E_f}}}{{{k_B}T}}) + 1} \right].$$
Where Ef is Fermi level of graphene, τ is electron-phonon relaxation time, e is the charge of an electron, kB is the Boltzmann’s constant, ω is the radian frequency, and ħ is the reduced Planck’s constant. Then the permittivity of monolayer graphene has in-plane component ${\varepsilon _{g,\textrm{||}}} = {\varepsilon _d} + \frac{{i{\sigma _g}{\eta _0}}}{{{k_0}{t_g}}}$ and out-plane component ${\varepsilon _{g, \bot }} = {\varepsilon _d}$, where η0 ( = 377 Ω) is the impedance of air. In our study, T is chosen as 300 K, relaxation time τ is μEf/(evf2), DC mobility μ is 10000 cm2/Vs, Fermi velocity vf is 1×106 m/s. Here, we consider monolayer graphene as a 2D surface current with σg in FEM simulation [47]. Since the conductivity of monolayer graphene depends on chemical potential, the optical properties of our proposed GHMMs structure can be changed by controlling Fermi level of graphene. There are many ways to change the Fermi level of graphene. Such as chemical, molecular doping, and electrical or thermal stimulation [48]. Among the above-mentioned methods, the most efficient and popular way to change the Fermi level of graphene is to apply external electric field bias. For our alternating graphene/SiO2 multilayer structure, we place a gate electrode on all the graphene layers with a bias voltage to tune the Fermi level of each graphene [49]. The relationship between the Fermi level Ef and applied external electric field bias Vg can be expressed as [50]
$${E_f} = \hbar {v_f}\sqrt {\eta \pi |{V_g} + {V_{dirac}}|} .$$
Where η ≈ 9×1016 m-1V-1 is derived from the single capacitor model, Vdirac is offset bias which reflects graphene’s doping and its impurities. Thus, we can modulate the Fermi level of graphene by changing Vg for our multilayer structure.

If the period d of one unit is sufficiently small compared to the operating wavelength, the multilayer structure can be considered as an anisotropic metamaterial. The effective permittivity tensor of the multilayer structure is described as [51]

$${\varepsilon _{eff}} = \left( {\begin{array}{ccc} {{\varepsilon_{\textrm{||}}}}&0&0\\ 0&{{\varepsilon_{\textrm{||}}}}&0\\ 0&0&{{\varepsilon_ \bot }} \end{array}} \right).$$
Where the subscript || and ⊥ mean parallel and vertical components to the graphene sheets, respectively. According to effective medium theory (EMT), ɛ|| and ɛ is given as follow:
$$\left\{ {\begin{array}{c} {{\varepsilon_{\textrm{||}}} = {{({{t_g}{\varepsilon_{g,\textrm{||}}} + {t_d}{\varepsilon_d}} )} \mathord{\left/ {\vphantom {{({{t_g}{\varepsilon_{g,\textrm{||}}} + {t_d}{\varepsilon_d}} )} {({{t_g} + {t_d}} )}}} \right.} {({{t_g} + {t_d}} )}}}\\ {{\varepsilon_ \bot } = {{({{t_g} + {t_d}} ){\varepsilon_{g, \bot }}{\varepsilon_d}} \mathord{\left/ {\vphantom {{({{t_g} + {t_d}} ){\varepsilon_{g, \bot }}{\varepsilon_d}} {({{t_g}{\varepsilon_d} + {t_d}{\varepsilon_{g, \bot }}} )}}} \right.} {({{t_g}{\varepsilon_d} + {t_d}{\varepsilon_{g, \bot }}} )}}} \end{array}} \right..$$

Based on Eq. (4), we calculate the in-plane and out of plane components of effective permittivity under different Vg when the working wavelength λ is 7 µm. Here, we only consider the real part of effective permittivity, and the results are shown in Fig. 2. The black line and red line represent the in-plane and out of plane components of the effective permittivity, respectively. When Vg changes from 0 to 0.277 V, the signs of Re(ɛ||) and Re(ɛ) are both positive and the multilayer structure shows the elliptical dispersion. When Vg changes from 0.277 to 2 V, multilayer structure shows Type II HMM dispersion (Re(ɛ||) < 0 and Re(ɛ) > 0), Re(ɛ||) decreases with increasing Vg. Thus, the GHMMs with Type II dispersion are realized. Besides, Re(ɛ) ( = 1.24) is almost unchanged with Vg. Especially, for Vg = 0.745 V, Re(ɛ||) = -Re(ɛ) = -1.24. In k space, for anisotropic medium, the EFS of TM polarization can be expressed as:

$$\frac{{{k_x}^2 + {k_y}^2}}{{{\varepsilon _ \bot }}} + \frac{{{k_z}^2}}{{{\varepsilon _{\textrm{||}}}}} = {k_0}^2.$$
Here, k0 is the wavevector of light in the vacuum. kx and kz are the wavevector components along X- and Z-directions, respectively. Then, the calculated EFS are plotted in Fig. 2(b) when Vg is 0.2, 0.4, 0.745, and 1.6 V, respectively. The elliptical dispersion under Vg = 0.2 V indicates that high-frequency components (${k_x} > \sqrt {{\varepsilon _d}} {k_0}$) are prohibited to propagate in the multilayer structure; The Type II dispersion under Vg = 0.4, 0.745, and 1.6 V indicates that low-frequency components (${k_x} < \sqrt {{\varepsilon _d}} {k_0}$) are prohibited to propagate in the GHMMs. And their asymptotes for Type II dispersion can be expressed as ${k_z} ={\pm} \sqrt { - \frac{{{\varepsilon _{\textrm{||}}}}}{{{\varepsilon _ \bot }}}} {k_x}$. The direction of light propagation depends on the group velocity. The group velocity demonstrates that the direction of the energy flow is perpendicular to the EFS and can be calculated by ${V_g}(\omega ) = {{\nabla }_k}\omega (k)$. Therefore, for Type II HMM in the kxkz plane, electromagnetic radiation and energy travel preferentially along a cone. The cone angle θ between the splitting beam and optical axis satisfies [52]
$$\theta \approx \arctan \left( {\sqrt { - \frac{{{\mathop{\rm Re}\nolimits} ({\varepsilon_{\textrm{||}}})}}{{{\mathop{\rm Re}\nolimits} ({\varepsilon_ \bot })}}} } \right).$$
Based on Fig. 2(b), the cone angle θ decreases with increasing Vg; and for Vg = 0.745 V, cone angle θ is 45°.

 figure: Fig. 2.

Fig. 2. (a) Re(${\varepsilon _\parallel }$)-Vg and Re(${\varepsilon _ \bot }$)-Vg curves at λ = 7 µm. (b) Calculated EFS for proposed GHMMs structure at Vg = 0.2, 0.4, 0.745, and 1.6 V, respectively.

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To achieve unidirectional subwavelength beam propagation based on photonic spin Hall effect, we utilize GHMMs with Type II dispersion based on the near-field interference effect [53]. As shown in Fig. 1, if an elliptically polarized emitter is placed in near-field proximity to the interface of the proposed GHMMs structure, its emission will be coupled to the high local DOS modes. Here, we discuss a 2D case in which a 2D emitter with a dipolar moment is defined ${ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textbf{p}}} }$ = [px, pz] for simplify considerations. Near-field interference effect will happen due to the linear superposition of the two orthogonal dipole orientations px and pz. All possible plane wave modes (high-frequency components) in GHMMs can be excited by the dipole with an efficiency proportional to the strength of the interaction ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textbf {p}}} }{\; }\cdot{\; }\mathop{{{\textbf E}_{\textbf k}}}\limits^\rightharpoonup $, where $\mathop{{{\textbf E}_{\textbf k}}}\limits^\rightharpoonup$ (= [Ex, Ez]) is the electric field of k-th mode at emitter location. The coupling efficiency C to high LDOS mode is given by [20]

$$C{\sim }{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textrm {p}}} }\cdot{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\rm E}} }{\; }{\; }={p_x}{E_x} + {p_z}{E_z}.$$
Where translational symmetry is assumed along the y axis. Under the paraxial propagation condition, the electric field of k-th mode in the GHMMs close to the boundary satisfies ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textbf {E}}} } \approx {E_x}{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {x}} } - ({{{{k_x}} \mathord{\left/ {\vphantom {{{k_x}} {{k_z}}}} \right.} {{k_z}}}} ){E_x}{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\boldsymbol z}} }$, where kx and kz (= $i\sqrt {{k_x}^2 - {k_0}^2}$) are the mode wave vectors in the x and z directions, respectively. The superposition of different components with $|{{k_x}} |\gg {k_0}$ make up the subwavelength high DOS modes which decide the propagation direction of beam in GHMMs with Type II HMM dispersion. Therefore, for GHMMs with Type II HMM dispersion, the electric field of the subwavelength mode near dipole can be approximated with ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textbf {E}}} } \approx {E_x}\approx {E_x}{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {x}} } \mp i{E_x}{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\boldsymbol z}} }$, where the upper sign applies to the left channel (x < xdipole) and the lower sign applies to the right channel (x > x dipole) [53]. Thus, the coupling efficiency C also can be expressed as
$$C{\sim }{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textrm {p}}} } \cdot {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textrm {E}}} } = {p_x}{E_x} \mp i{p_z}{E_x}.$$
Based on Eq. (8), coupling efficiency C is equal to zero when dipolar moment ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textbf {p}}} } = p[1,i]$ (left-handed circular (LHC) polarization) for right channel or dipolar moment ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textbf {p}}} } = p[1, - i]$ (right-handed circular (RHC) polarization) for left channel, due to destructive near-field interference. So, the emission of the dipole can be directionally guided along the opposite directions in GHMMs through controlling the spin of emitted photons and subwavelength beam directional propagation can be controlled by polarization handedness. Besides, the unidirectional propagation angle can also be tuned by applied external electric field bias based on Eq. (6).

3. Results and discussions

To verify the proposed way to dynamically tune directional subwavelength beam propagation, we put an elliptically polarized emitter in near-field proximity to the interface of the proposed GHMMs structure and conduct the FEM simulation based on commercial software COMSOL Multiphysics. When Vg = 0.745 V, as shown in Fig. 3, (y) component of the magnetic field distributions Hy and intensity of |Hy|2 are displayed under the dipole excitations with different polarizations. The distributions of Hy under horizontal linear, vertical linear, LHC and RHC polarizations are depicted in Figs. 3(a), (c), (e) and (g), respectively. Figures 3(b), (d), (f), and (h) shows the intensity distributions of |Hy|2 at z = 0.143λ from the GHMMs structure boundary in the z direction corresponding to Figs. 3(a), (c), (e), and (g), respectively. When the dipole excites horizontally linear polarization as shown in Fig. 3(a), the field distribution of Hy exhibits even symmetry (Hy(x) = Hy(-x)). When the dipole excites vertically linear polarization as shown in Fig. 3(c), the field distribution of Hy exhibits odd symmetry (Hy(x) = -Hy(-x)). Based on Eq. (8), no near-field interference happens for the both linear polarizations. For the case of Figs. 3(a) and (c), dipolar moment ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textbf {p}}} }$ can be considered as [1,0] and [0,1], and the corresponding coupling efficiency C are approximately equal to pxEx and ${\mp} $ipzEx, respectively. Therefore, the field distribution of Hy for the left and right channels is symmetrical in Fig. 3(a), while the field distribution of Hy is antisymmetric in Fig. 3(c). When the dipole excites LHC polarized light as shown in Fig. 3(e), the field distribution of Hy shows that the left channel is open and the right channel is closed. Conversely, when the dipole excites RHC polarized light as shown in Fig. 3(g), the field distribution of Hy shows the left channel is closed and the right channel is open. This is because the destructive interference condition is satisfied and the coupling efficiency C of right or left channel is absent based on Eq. (8), respectively. So, the intensity of |Hy|2 in Figs. 3(f) and (h) clearly shows the strong unidirectionality of the confined subwavelength beam due to near field interference based on photonic spin Hall effect. Besides, the lateral confinement of the beam is about λ/40 full-with half maximum.

 figure: Fig. 3.

Fig. 3. Field distribution of Hy in GHMMs structure when the dipole emitter excites with (a) horizontal linear polarization ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textrm {p}}} } = [{1,0} ]$, (c) vertical linear polarization ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textrm {p}}} } = [{0,1} ]$, (e) LHC polarization ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textrm {p}}} } = [{1,i} ]$ and (g) RHC polarization ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textrm {p}}} } = [{1, - i} ]$, respectively. Their distributions of normalized |Hy|2 at z = 0.143λ from the GHMMs structure boundary in the z direction are shown in (b), (d), (f) and (h), which are corresponding with (a), (c), (e) and (g).

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To verify the unidirectional propagation angle can be tuned by applied external electric field bias, we calculate the field distribution of Hy under different Vg: (a) Vg = 0.2 V, (b) Vg = 0.4 V, (c) Vg = 0.8 V and (d) Vg = 1.6 V, shown as Fig. 4. Here, we take the RHC polarized light (${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textrm {p}}} } = [{1, - i} ]$) as a case to illustrate. And other parameters are the same with Fig. 3(g). According to Fig. 2(a), when Vg = 0.2 V, the multilayer structure shows the elliptical dispersion; when Vg = 0.4, 0.8, and 1.6 V, the multilayer structure is Type II GHMMs. The electromagnetic wave is quickly dissipated in the elliptical dispersion region, and the electromagnetic wave can directionally propagate along the right channel in the Type II HMM region under RHC polarized light. And the unidirectional propagation angle is decided by Eq. (6). The propagation angles of subwavelength beam are θ = 31.36°, 46.45°, and 56.01° when Vg varies from 0.4 to 1.6 V, respectively. And the theoretical values of the angle are 30.32°, 46.25° and 55.35° based on the Eq. (6), which are almost identical to the simulation results. It is believed our proposed design pave a possible way to tune the propagation direction by changing Vg.

 figure: Fig. 4.

Fig. 4. Field distribution of Hy in GHMMs structure with (a) Vg = 0.2 V, (b) Vg = 0.4 V, (c) Vg = 0.8 V and (d) Vg = 1.6 V, respectively, when dipole excites RHC polarization. Other parameters are the same with Fig. 3(g).

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Then, we calculate the offset angle in the range of 0.3 to 2 V, and other parameters are the same with Fig. 4. As shown in Fig. 5, the black curve represents the theoretical calculation result and the red dots represent the simulation results. It is obviously that the theoretical and the simulated values are almost identical. Therefore, the offset angle of the left or right channel beam can be well controlled by regulating the applied voltage of graphene. Besides, it is possible to achieve broadband directional subwavelength beam propagation based on PSHE, because graphene/SiO2 multilayer can be tuned to GHMMs with Type II hyperbolic dispersion by changing Fermi level under different wavelengths [25].

 figure: Fig. 5.

Fig. 5. Offset angle under different Vg. The black curve is the analytical result and the red dots are the simulation results. Other parameters are the same with Fig. 4

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The proposed GHMMs multilayer structure consisting of alternating graphene/SiO2 is feasible at the current level of fabrication technology. The preparation procedure of the proposed multilayer structure is as follows: SiO2 layer is first coated on a dielectric substrate through thermal evaporation, and then the high-quality graphene sheets prepared using chemical vapor deposition (CVD) method are coated on the top of the SiO2 layer. For CVD, the number of layers can be controlled precisely by regulating the flow radio of CH4 and H2, the reaction pressure, the temperature and reaction time [54]. And the large-area high-quality graphene films have also been demonstrated experimentally in other work by applying optimized liquid precursor chemical vapor deposition method [55,56]. Finally, the multilayer structure is realized by stacking of many graphene/SiO2 layers on the dielectric substrate.

4. Conclusion

In general, we propose the GHMMs structure, which consists of periodic stacking of graphene layers and SiO2 layers, to achieve directional subwavelength beam propagation based on PSHE. The PSHE effect is due to near field interference between high-frequency components in GHMMs with Type II hyperbolic dispersion. The propagation direction of subwavelength beam (about λ/40 full-with half maximum) is decided by polarization handedness, and the unidirectional propagation angles can be tuned by changing external electric field bias applied to graphene. All the design is verified by FEM and it is believed that our findings provide a new way to control the subwavelength beam unidirectional propagation dynamically.

Funding

National Natural Science Foundation of China (1148081606193050); Fundamental Research Funds for the Central Universities (JUSRP115A15, JUSRP21935, JUSRP51628B); Undergraduate Innovation Training Program of Jiangnan University of China (1148088201191487).

Disclosures

The authors declare no conflicts of interest.

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28. K. Halterman and J. M. Elson, “Near-perfect absorption in epsilon-near-zero structures with hyperbolic dispersion,” Opt. Express 22(6), 7337–7348 (2014). [CrossRef]  

29. Q.-M. Zhao, T.-B. Wang, D.-J. Zhang, W.-X. Liu, T.-B. Yu, Q.-H. Liao, and N.-H. Liu, “Contribution of terahertz waves to near-field radiative heat transfer between graphene-based hyperbolic metamaterials,” Chin. Phys. B 27(9), 094401 (2018). [CrossRef]  

30. K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015). [CrossRef]  

31. X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017). [CrossRef]  

32. M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004). [CrossRef]  

33. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008). [CrossRef]  

34. K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006). [CrossRef]  

35. T. Tang, J. Li, L. Luo, P. Sun, and J. Yao, “Magneto-Optical Modulation of Photonic Spin Hall Effect of Graphene in Terahertz Region,” Adv. Opt. Mater. 6(7), 1701212 (2018). [CrossRef]  

36. H. Lin, B. Chen, S. Yang, W. Zhu, J. Yu, H. Guan, H. Lu, Y. Luo, and Z. Chen, “Photonic spin Hall effect of monolayer black phosphorus in the Terahertz region,” Nanophotonics 7(12), 1929–1937 (2018). [CrossRef]  

37. H. Chen, S. Zhou, G. Rui, and Q. Zhan, “Magnified photonic spin-Hall effect with curved hyperbolic metamaterials,” J. Appl. Phys. 124(23), 233104 (2018). [CrossRef]  

38. T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6(1), 30762 (2016). [CrossRef]  

39. Y. Liu, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6(1), 51–70 (2017). [CrossRef]  

40. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006). [CrossRef]  

41. D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009). [CrossRef]  

42. X. Zhou, X. Ling, Z. Zhang, H. Luo, and S. Wen, “Observation of spin Hall effect in photon tunneling via weak measurements,” Sci. Rep. 4(1), 7388 (2015). [CrossRef]  

43. K. Y. Bliokh, C. Samlan, C. Prajapati, G. Puentes, N. K. Viswanathan, and F. Nori, “Spin-Hall effect and circular birefringence of a uniaxial crystal plate,” Optica 3(10), 1039 (2016). [CrossRef]  

44. O. Takayama and G. Puentes, “Enhanced spin Hall effect of light by transmission in a polymer,” Opt. Lett. 43(6), 1343 (2018). [CrossRef]  

45. W. Zhu, M. Jiang, H. Guan, J. Yu, H. Lu, J. Zhang, and Z. Chen, “Tunable spin splitting of Laguerre–Gaussian beams in graphene metamaterials,” Photonics Res. 5(6), 684–688 (2017). [CrossRef]  

46. Z. P. Su, Y. K. Wang, X. Luo, H. Luo, C. Zhang, M. X. Li, T. Sang, and G. F. Yang, “A tunable THz absorber consisting of an elliptical graphene disk array,” Phys. Chem. Chem. Phys. 20, 14358 (2018). [CrossRef]  

47. A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012). [CrossRef]  

48. B. Guo, L. Fang, B. Zhang, and J. R. Gong, “Graphene doping: a review,” Insci. J. 1(2), 80–89 (2011). [CrossRef]  

49. A. A. Sayem, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Ultrathin ultra-broadband electro-absorption modulator based on few-layer graphene based anisotropic metamaterial,” Opt. Commun. 384, 50–58 (2017). [CrossRef]  

50. B. Janaszek, A. Tyszka-Zawadzka, and P. Szczepański, “Tunable graphene-based hyperbolic metamaterial operating in SCLU telecom bands,” Opt. Express 24(21), 24129–24136 (2016). [CrossRef]  

51. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006). [CrossRef]  

52. B. Wood, J. Pendry, and D. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006). [CrossRef]  

53. F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013). [CrossRef]  

54. Z. Q. Tu, Z. C. Liu, Y. F. Li, F. Yang, L. Q. Zhang, Z. Zhao, C. M. Xu, S. F. Wu, H. W. Liu, H. T. Yang, and P. Richard, “Controllable growth of 1-7 layers of graphene by chemical vapour deposition,” Carbon 73, 252–258 (2014). [CrossRef]  

55. Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. G. de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013). [CrossRef]  

56. X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009). [CrossRef]  

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    [Crossref]
  29. Q.-M. Zhao, T.-B. Wang, D.-J. Zhang, W.-X. Liu, T.-B. Yu, Q.-H. Liao, and N.-H. Liu, “Contribution of terahertz waves to near-field radiative heat transfer between graphene-based hyperbolic metamaterials,” Chin. Phys. B 27(9), 094401 (2018).
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  30. K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
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  31. X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
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  41. D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
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  44. O. Takayama and G. Puentes, “Enhanced spin Hall effect of light by transmission in a polymer,” Opt. Lett. 43(6), 1343 (2018).
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  45. W. Zhu, M. Jiang, H. Guan, J. Yu, H. Lu, J. Zhang, and Z. Chen, “Tunable spin splitting of Laguerre–Gaussian beams in graphene metamaterials,” Photonics Res. 5(6), 684–688 (2017).
    [Crossref]
  46. Z. P. Su, Y. K. Wang, X. Luo, H. Luo, C. Zhang, M. X. Li, T. Sang, and G. F. Yang, “A tunable THz absorber consisting of an elliptical graphene disk array,” Phys. Chem. Chem. Phys. 20, 14358 (2018).
    [Crossref]
  47. A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
    [Crossref]
  48. B. Guo, L. Fang, B. Zhang, and J. R. Gong, “Graphene doping: a review,” Insci. J. 1(2), 80–89 (2011).
    [Crossref]
  49. A. A. Sayem, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Ultrathin ultra-broadband electro-absorption modulator based on few-layer graphene based anisotropic metamaterial,” Opt. Commun. 384, 50–58 (2017).
    [Crossref]
  50. B. Janaszek, A. Tyszka-Zawadzka, and P. Szczepański, “Tunable graphene-based hyperbolic metamaterial operating in SCLU telecom bands,” Opt. Express 24(21), 24129–24136 (2016).
    [Crossref]
  51. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
    [Crossref]
  52. B. Wood, J. Pendry, and D. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
    [Crossref]
  53. F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
    [Crossref]
  54. Z. Q. Tu, Z. C. Liu, Y. F. Li, F. Yang, L. Q. Zhang, Z. Zhao, C. M. Xu, S. F. Wu, H. W. Liu, H. T. Yang, and P. Richard, “Controllable growth of 1-7 layers of graphene by chemical vapour deposition,” Carbon 73, 252–258 (2014).
    [Crossref]
  55. Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. G. de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
    [Crossref]
  56. X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
    [Crossref]

2020 (1)

Z. Guo, H. Jiang, and H. Chen, “Hyperbolic metamaterials: From dispersion manipulation to applications,” J. Appl. Phys. 127(7), 071101 (2020).
[Crossref]

2019 (2)

O. Takayama and A. V. Lavrinenko, “Optics with hyperbolic materials,” J. Opt. Soc. Am. B 36(8), F38 (2019).
[Crossref]

L.-M. Ye, X.-J. Yi, T.-B. Wang, Y. Zhao, T.-B. Yu, Q.-H. Liao, and N.-H. Liu, “Enhancement and modulation of spontaneous emission near graphene-based hyperbolic metamaterials,” Mater. Res. Express 6(12), 125803 (2019).
[Crossref]

2018 (9)

E. Shkondin, T. Repän, M. E. Aryaee Panah, A. V. Lavrinenko, and O. Takayama, “High aspect ratio plasmonic nanotrench structures with large active surface area for label-free mid-infrared molecular absorption sensing,” ACS Appl. Nano Mater. 1(3), 1212–1218 (2018).
[Crossref]

T. Guo, L. Zhu, P.-Y. Chen, and C. Argyropoulos, “Tunable terahertz amplification based on photoexcited active graphene hyperbolic metamaterials,” Opt. Mater. Express 8(12), 3941–3952 (2018).
[Crossref]

Q.-M. Zhao, T.-B. Wang, D.-J. Zhang, W.-X. Liu, T.-B. Yu, Q.-H. Liao, and N.-H. Liu, “Contribution of terahertz waves to near-field radiative heat transfer between graphene-based hyperbolic metamaterials,” Chin. Phys. B 27(9), 094401 (2018).
[Crossref]

T. Tang, J. Li, L. Luo, P. Sun, and J. Yao, “Magneto-Optical Modulation of Photonic Spin Hall Effect of Graphene in Terahertz Region,” Adv. Opt. Mater. 6(7), 1701212 (2018).
[Crossref]

H. Lin, B. Chen, S. Yang, W. Zhu, J. Yu, H. Guan, H. Lu, Y. Luo, and Z. Chen, “Photonic spin Hall effect of monolayer black phosphorus in the Terahertz region,” Nanophotonics 7(12), 1929–1937 (2018).
[Crossref]

H. Chen, S. Zhou, G. Rui, and Q. Zhan, “Magnified photonic spin-Hall effect with curved hyperbolic metamaterials,” J. Appl. Phys. 124(23), 233104 (2018).
[Crossref]

O. Takayama, J. Sukham, R. Malureanu, A. V. Lavrinenko, and G. Puentes, “Photonic spin Hall effect in hyperbolic metamaterials at visible wavelengths,” Opt. Lett. 43(19), 4602–4605 (2018).
[Crossref]

O. Takayama and G. Puentes, “Enhanced spin Hall effect of light by transmission in a polymer,” Opt. Lett. 43(6), 1343 (2018).
[Crossref]

Z. P. Su, Y. K. Wang, X. Luo, H. Luo, C. Zhang, M. X. Li, T. Sang, and G. F. Yang, “A tunable THz absorber consisting of an elliptical graphene disk array,” Phys. Chem. Chem. Phys. 20, 14358 (2018).
[Crossref]

2017 (4)

A. A. Sayem, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Ultrathin ultra-broadband electro-absorption modulator based on few-layer graphene based anisotropic metamaterial,” Opt. Commun. 384, 50–58 (2017).
[Crossref]

W. Zhu, M. Jiang, H. Guan, J. Yu, H. Lu, J. Zhang, and Z. Chen, “Tunable spin splitting of Laguerre–Gaussian beams in graphene metamaterials,” Photonics Res. 5(6), 684–688 (2017).
[Crossref]

Y. Liu, Y. Ke, H. Luo, and S. Wen, “Photonic spin Hall effect in metasurfaces: a brief review,” Nanophotonics 6(1), 51–70 (2017).
[Crossref]

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

2016 (4)

T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6(1), 30762 (2016).
[Crossref]

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref]

B. Janaszek, A. Tyszka-Zawadzka, and P. Szczepański, “Tunable graphene-based hyperbolic metamaterial operating in SCLU telecom bands,” Opt. Express 24(21), 24129–24136 (2016).
[Crossref]

K. Y. Bliokh, C. Samlan, C. Prajapati, G. Puentes, N. K. Viswanathan, and F. Nori, “Spin-Hall effect and circular birefringence of a uniaxial crystal plate,” Optica 3(10), 1039 (2016).
[Crossref]

2015 (4)

X. Zhou, X. Ling, Z. Zhang, H. Luo, and S. Wen, “Observation of spin Hall effect in photon tunneling via weak measurements,” Sci. Rep. 4(1), 7388 (2015).
[Crossref]

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

2014 (4)

K. Halterman and J. M. Elson, “Near-perfect absorption in epsilon-near-zero structures with hyperbolic dispersion,” Opt. Express 22(6), 7337–7348 (2014).
[Crossref]

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
[Crossref]

P. Shekhar, J. Atkinson, and Z. Jacob, “Hyperbolic metamaterials: fundamentals and applications,” Nano Convergence 1(1), 14 (2014).
[Crossref]

Z. Q. Tu, Z. C. Liu, Y. F. Li, F. Yang, L. Q. Zhang, Z. Zhao, C. M. Xu, S. F. Wu, H. W. Liu, H. T. Yang, and P. Richard, “Controllable growth of 1-7 layers of graphene by chemical vapour deposition,” Carbon 73, 252–258 (2014).
[Crossref]

2013 (8)

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. G. de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
[Crossref]

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[Crossref]

M. A. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013).
[Crossref]

K. Sreekanth, A. De Luca, and G. Strangi, “Negative refraction in graphene-based hyperbolic metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[Crossref]

T. Zhang, L. Chen, and X. Li, “Graphene-based tunable broadband hyperlens for far-field subdiffraction imaging at mid-infrared frequencies,” Opt. Express 21(18), 20888–20899 (2013).
[Crossref]

I. S. Nefedov, C. A. Valagiannopoulos, and L. A. Melnikov, “Perfect absorption in graphene multilayers,” J. Opt. 15(11), 114003 (2013).
[Crossref]

2012 (2)

H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336(6078), 205–209 (2012).
[Crossref]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
[Crossref]

2011 (2)

B. Guo, L. Fang, B. Zhang, and J. R. Gong, “Graphene doping: a review,” Insci. J. 1(2), 80–89 (2011).
[Crossref]

C. Yan, D. H. Zhang, D. Li, H. Bian, Z. Xu, and Y. Wang, “Metal nanorod-based metamaterials for beam splitting and a subdiffraction-limited dark hollow light cone,” J. Opt. 13(8), 085102 (2011).
[Crossref]

2009 (3)

A. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. Wurtz, R. Atkinson, R. Pollard, V. Podolskiy, and A. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref]

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[Crossref]

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

2008 (2)

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref]

2007 (2)

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref]

2006 (5)

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[Crossref]

B. Wood, J. Pendry, and D. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006).
[Crossref]

2004 (2)

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84(13), 2244–2246 (2004).
[Crossref]

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

2003 (1)

D. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref]

Ajayan, P. M.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. G. de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
[Crossref]

Alapan, Y.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref]

Alekseyev, L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[Crossref]

Alekseyev, L. V.

An, J.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
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Argyropoulos, C.

Aryaee Panah, M. E.

E. Shkondin, T. Repän, M. E. Aryaee Panah, A. V. Lavrinenko, and O. Takayama, “High aspect ratio plasmonic nanotrench structures with large active surface area for label-free mid-infrared molecular absorption sensing,” ACS Appl. Nano Mater. 1(3), 1212–1218 (2018).
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Atkinson, J.

P. Shekhar, J. Atkinson, and Z. Jacob, “Hyperbolic metamaterials: fundamentals and applications,” Nano Convergence 1(1), 14 (2014).
[Crossref]

Atkinson, R.

A. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. Wurtz, R. Atkinson, R. Pollard, V. Podolskiy, and A. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref]

Banerjee, S. K.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Bartal, G.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref]

Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Belov, P. A.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
[Crossref]

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[Crossref]

Bian, H.

C. Yan, D. H. Zhang, D. Li, H. Bian, Z. Xu, and Y. Wang, “Metal nanorod-based metamaterials for beam splitting and a subdiffraction-limited dark hollow light cone,” J. Opt. 13(8), 085102 (2011).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh, C. Samlan, C. Prajapati, G. Puentes, N. K. Viswanathan, and F. Nori, “Spin-Hall effect and circular birefringence of a uniaxial crystal plate,” Optica 3(10), 1039 (2016).
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K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

Bliokh, Y. P.

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

Cai, W.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Capolino, F.

Chen, B.

H. Lin, B. Chen, S. Yang, W. Zhu, J. Yu, H. Guan, H. Lu, Y. Luo, and Z. Chen, “Photonic spin Hall effect of monolayer black phosphorus in the Terahertz region,” Nanophotonics 7(12), 1929–1937 (2018).
[Crossref]

Chen, H.

Z. Guo, H. Jiang, and H. Chen, “Hyperbolic metamaterials: From dispersion manipulation to applications,” J. Appl. Phys. 127(7), 071101 (2020).
[Crossref]

H. Chen, S. Zhou, G. Rui, and Q. Zhan, “Magnified photonic spin-Hall effect with curved hyperbolic metamaterials,” J. Appl. Phys. 124(23), 233104 (2018).
[Crossref]

Chen, L.

Chen, P.-Y.

Chen, Z.

H. Lin, B. Chen, S. Yang, W. Zhu, J. Yu, H. Guan, H. Lu, Y. Luo, and Z. Chen, “Photonic spin Hall effect of monolayer black phosphorus in the Terahertz region,” Nanophotonics 7(12), 1929–1937 (2018).
[Crossref]

W. Zhu, M. Jiang, H. Guan, J. Yu, H. Lu, J. Zhang, and Z. Chen, “Tunable spin splitting of Laguerre–Gaussian beams in graphene metamaterials,” Photonics Res. 5(6), 684–688 (2017).
[Crossref]

Colombo, L.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

de Abajo, F. J. G.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. G. de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
[Crossref]

de Leon, N. P.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref]

De Luca, A.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref]

K. Sreekanth, A. De Luca, and G. Strangi, “Negative refraction in graphene-based hyperbolic metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
[Crossref]

Devlin, R. C.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref]

Dibos, A.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref]

Dogariu, A.

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[Crossref]

ElKabbash, M.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref]

Elson, J. M.

Engheta, N.

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[Crossref]

Evans, P.

A. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. Wurtz, R. Atkinson, R. Pollard, V. Podolskiy, and A. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref]

Fang, L.

B. Guo, L. Fang, B. Zhang, and J. R. Gong, “Graphene doping: a review,” Insci. J. 1(2), 80–89 (2011).
[Crossref]

Fang, Z.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. G. de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
[Crossref]

Ferrari, L.

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

Filonov, D. S.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
[Crossref]

Franz, K. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[Crossref]

Garcia-Vidal, F. J.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
[Crossref]

Ginzburg, P.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
[Crossref]

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Gmachl, C.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[Crossref]

Gong, J. R.

B. Guo, L. Fang, B. Zhang, and J. R. Gong, “Graphene doping: a review,” Insci. J. 1(2), 80–89 (2011).
[Crossref]

Guan, H.

H. Lin, B. Chen, S. Yang, W. Zhu, J. Yu, H. Guan, H. Lu, Y. Luo, and Z. Chen, “Photonic spin Hall effect of monolayer black phosphorus in the Terahertz region,” Nanophotonics 7(12), 1929–1937 (2018).
[Crossref]

W. Zhu, M. Jiang, H. Guan, J. Yu, H. Lu, J. Zhang, and Z. Chen, “Tunable spin splitting of Laguerre–Gaussian beams in graphene metamaterials,” Photonics Res. 5(6), 684–688 (2017).
[Crossref]

Guclu, C.

Guinea, F.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
[Crossref]

Guo, B.

B. Guo, L. Fang, B. Zhang, and J. R. Gong, “Graphene doping: a review,” Insci. J. 1(2), 80–89 (2011).
[Crossref]

Guo, T.

Guo, Z.

Z. Guo, H. Jiang, and H. Chen, “Hyperbolic metamaterials: From dispersion manipulation to applications,” J. Appl. Phys. 127(7), 071101 (2020).
[Crossref]

Gurkan, U. A.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref]

Haefner, D.

D. Haefner, S. Sukhov, and A. Dogariu, “Spin hall effect of light in spherical geometry,” Phys. Rev. Lett. 102(12), 123903 (2009).
[Crossref]

Halas, N. J.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, and F. J. G. de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7(3), 2388–2395 (2013).
[Crossref]

Halterman, K.

Hendren, W.

A. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. Wurtz, R. Atkinson, R. Pollard, V. Podolskiy, and A. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref]

High, A. A.

A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
[Crossref]

Hinczewski, M.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref]

Hoffman, A. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[Crossref]

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref]

Howard, S. S.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[Crossref]

Huang, K.

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
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Ilker, E.

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref]

Iorsh, I.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

Iorsh, I. V.

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[Crossref]

Jacob, Z.

P. Shekhar, J. Atkinson, and Z. Jacob, “Hyperbolic metamaterials: fundamentals and applications,” Nano Convergence 1(1), 14 (2014).
[Crossref]

H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kretzschmar, and V. M. Menon, “Topological transitions in metamaterials,” Science 336(6078), 205–209 (2012).
[Crossref]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref]

Jahangir, I.

A. A. Sayem, M. R. C. Mahdy, I. Jahangir, and M. S. Rahman, “Ultrathin ultra-broadband electro-absorption modulator based on few-layer graphene based anisotropic metamaterial,” Opt. Commun. 384, 50–58 (2017).
[Crossref]

Janaszek, B.

Jiang, H.

Z. Guo, H. Jiang, and H. Chen, “Hyperbolic metamaterials: From dispersion manipulation to applications,” J. Appl. Phys. 127(7), 071101 (2020).
[Crossref]

Jiang, M.

W. Zhu, M. Jiang, H. Guan, J. Yu, H. Lu, J. Zhang, and Z. Chen, “Tunable spin splitting of Laguerre–Gaussian beams in graphene metamaterials,” Photonics Res. 5(6), 684–688 (2017).
[Crossref]

Jung, I.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
[Crossref]

Kabashin, A.

A. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. Wurtz, R. Atkinson, R. Pollard, V. Podolskiy, and A. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
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Z. Q. Tu, Z. C. Liu, Y. F. Li, F. Yang, L. Q. Zhang, Z. Zhao, C. M. Xu, S. F. Wu, H. W. Liu, H. T. Yang, and P. Richard, “Controllable growth of 1-7 layers of graphene by chemical vapour deposition,” Carbon 73, 252–258 (2014).
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T. Tang, J. Li, L. Luo, P. Sun, and J. Yao, “Magneto-Optical Modulation of Photonic Spin Hall Effect of Graphene in Terahertz Region,” Adv. Opt. Mater. 6(7), 1701212 (2018).
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D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84(13), 2244–2246 (2004).
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L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
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X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
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Poddubny, A. N.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortuño, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
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A. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. Wurtz, R. Atkinson, R. Pollard, V. Podolskiy, and A. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
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A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
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A. A. High, R. C. Devlin, A. Dibos, M. Polking, D. S. Wild, J. Perczel, N. P. de Leon, M. D. Lukin, and H. Park, “Visible-frequency hyperbolic metasurface,” Nature 522(7555), 192–196 (2015).
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Puentes, G.

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X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
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E. Shkondin, T. Repän, M. E. Aryaee Panah, A. V. Lavrinenko, and O. Takayama, “High aspect ratio plasmonic nanotrench structures with large active surface area for label-free mid-infrared molecular absorption sensing,” ACS Appl. Nano Mater. 1(3), 1212–1218 (2018).
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Z. Q. Tu, Z. C. Liu, Y. F. Li, F. Yang, L. Q. Zhang, Z. Zhao, C. M. Xu, S. F. Wu, H. W. Liu, H. T. Yang, and P. Richard, “Controllable growth of 1-7 layers of graphene by chemical vapour deposition,” Carbon 73, 252–258 (2014).
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K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
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F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
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X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
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Rye, P.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. 84(13), 2244–2246 (2004).
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Zhu, W.

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ACS Appl. Nano Mater. (1)

E. Shkondin, T. Repän, M. E. Aryaee Panah, A. V. Lavrinenko, and O. Takayama, “High aspect ratio plasmonic nanotrench structures with large active surface area for label-free mid-infrared molecular absorption sensing,” ACS Appl. Nano Mater. 1(3), 1212–1218 (2018).
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ACS Nano (1)

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[Crossref]

Adv. Opt. Mater. (1)

T. Tang, J. Li, L. Luo, P. Sun, and J. Yao, “Magneto-Optical Modulation of Photonic Spin Hall Effect of Graphene in Terahertz Region,” Adv. Opt. Mater. 6(7), 1701212 (2018).
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Appl. Phys. Lett. (2)

K. Sreekanth, A. De Luca, and G. Strangi, “Negative refraction in graphene-based hyperbolic metamaterials,” Appl. Phys. Lett. 103(2), 023107 (2013).
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Carbon (1)

Z. Q. Tu, Z. C. Liu, Y. F. Li, F. Yang, L. Q. Zhang, Z. Zhao, C. M. Xu, S. F. Wu, H. W. Liu, H. T. Yang, and P. Richard, “Controllable growth of 1-7 layers of graphene by chemical vapour deposition,” Carbon 73, 252–258 (2014).
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Chin. Phys. B (1)

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Insci. J. (1)

B. Guo, L. Fang, B. Zhang, and J. R. Gong, “Graphene doping: a review,” Insci. J. 1(2), 80–89 (2011).
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J. Appl. Phys. (2)

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Figures (5)

Fig. 1.
Fig. 1. Schematic of the proposed GHMMs structure consisting of alternating graphene/SiO2 multilayer. The thicknesses of the graphene layer and the SiO2 layer are tg, and td, respectively.
Fig. 2.
Fig. 2. (a) Re(${\varepsilon _\parallel }$)-Vg and Re(${\varepsilon _ \bot }$)-Vg curves at λ = 7 µm. (b) Calculated EFS for proposed GHMMs structure at Vg = 0.2, 0.4, 0.745, and 1.6 V, respectively.
Fig. 3.
Fig. 3. Field distribution of Hy in GHMMs structure when the dipole emitter excites with (a) horizontal linear polarization ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textrm {p}}} } = [{1,0} ]$, (c) vertical linear polarization ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textrm {p}}} } = [{0,1} ]$, (e) LHC polarization ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textrm {p}}} } = [{1,i} ]$ and (g) RHC polarization ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over {\textrm {p}}} } = [{1, - i} ]$, respectively. Their distributions of normalized |Hy|2 at z = 0.143λ from the GHMMs structure boundary in the z direction are shown in (b), (d), (f) and (h), which are corresponding with (a), (c), (e) and (g).
Fig. 4.
Fig. 4. Field distribution of Hy in GHMMs structure with (a) Vg = 0.2 V, (b) Vg = 0.4 V, (c) Vg = 0.8 V and (d) Vg = 1.6 V, respectively, when dipole excites RHC polarization. Other parameters are the same with Fig. 3(g).
Fig. 5.
Fig. 5. Offset angle under different Vg. The black curve is the analytical result and the red dots are the simulation results. Other parameters are the same with Fig. 4

Equations (8)

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σ g = i e 2 E f π 2 ( ω + i τ 1 ) + i e 2 4 π L n [ 2 E f ( ω + i τ 1 ) 2 E f + ( ω + i τ 1 ) ] + i 2 e 2 k B T π 2 ( ω + i τ 1 ) L n [ exp ( E f k B T ) + 1 ] .
E f = v f η π | V g + V d i r a c | .
ε e f f = ( ε || 0 0 0 ε || 0 0 0 ε ) .
{ ε || = ( t g ε g , || + t d ε d ) / ( t g ε g , || + t d ε d ) ( t g + t d ) ( t g + t d ) ε = ( t g + t d ) ε g , ε d / ( t g + t d ) ε g , ε d ( t g ε d + t d ε g , ) ( t g ε d + t d ε g , ) .
k x 2 + k y 2 ε + k z 2 ε || = k 0 2 .
θ arctan ( Re ( ε || ) Re ( ε ) ) .
C p E = p x E x + p z E z .
C p E = p x E x i p z E x .

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