Abstract

Optical spin splitting has attracted significant attention owing to its potential applications in quantum information and precision metrology. However, it is typically small and cannot be controlled efficiently. Here, we enhance the spin splitting by transmitting higher-order Laguerre–Gaussian (LG) beams through graphene metamaterial slabs. The interaction between LG beams and metamaterial results in an orbital-angular-momentum- (OAM) dependent spin splitting. The upper bound of the OAM-dependent spin splitting is found, which varies with the incident OAM and beam waist. Moreover, the spin splitting can be flexibly tuned by modulating the Fermi energy of the graphene sheets. This tunable spin splitting has potential applications in the development of spin-based applications and the manipulation of mid-infrared waves.

© 2017 Chinese Laser Press

1. INTRODUCTION

Graphene, an atomically thin layer of carbon atoms arranged in a honeycomb lattice, has attracted significant interest owing to its superior electronic and optical properties [13]. The conductivity of graphene is very sensitive to external fields, such that its optoelectronic properties can be precisely tuned [4]. Owing to its unique properties, graphene has been suggested as an alternative to conventional metal-based structures to confine light [5], guide surface plasmon polaritons [6], and manipulate wavefronts [7,8]. The subwavelength metamaterial structures made of graphene sheets show advantages over those made of thin metal layers at frequency and amplitude tunable properties [9]. Recently, the graphene metamaterial has been experimentally realized in the mid-infrared range [10]. The metamaterial experiences an optical topological transition from elliptic to hyperbolic dispersion at a wavelength of 4.5 μm [10].

Spin splitting refers to the spatial separation of two opposite spin components of bounded light beams reflected from or transmitted through an interface between two different media [1114]. The spin splitting phenomenon was first observed experimentally by Hosten and Kwiat in 2008 [11]. In their experiment, a weak measurement was used since the spin splitting of the transmitted beam through an air–glass interface was very small—only a fraction of a wavelength [11,12]. Lately, much larger spin splitting was found by reflected Gaussian beams near Brewster incidence [13]. Götte and coworkers have achieved a spin splitting of ten wavelengths near Brewster incidence by properly choosing the incident polarization state [14]. In 2015, a spin splitting equal nearly to the incident beam waist w0 was demonstrated when a one-dimensional Gaussian beam with w0=10.2μm was reflected from an air–glass interface [15]. For a two-dimensional Gaussian beam, however, the spin splitting could only reach 0.4w0. It was demonstrated that the spin splitting can also be enhanced by metal thin films [16] and metamaterials [17,18]. Recently, the upper bounds of the spin splitting of Gaussian incident beams were found, which were equal to the incident beam waists w0 [19].

Although less investigated, the beam shifts of higher-order Laguerre–Gaussian (LG) beams are very interesting [2022]. When reflected by an interface between two different media, the complex vortex structures of LG beams will interact with the angular Goos–Hänchen (GH) and Imbert–Fedorov shifts, which leads to the orbital-angular-momentum- (OAM) dependent shifts along directions both parallel and perpendicular to the plane of incidence [23]. The OAM-dependent shifts increase linearly with the incident OAM, so that large beam shifts can be achieved [24]. These shifts have been used to steer asymmetric spin splitting [25].

Alternatively, here we theoretically show a symmetric spin splitting dependent on the incident OAM when transmitting higher-order LG beams through a graphene metamaterial slab. The metamaterial is based on the multilayer structure of alternating graphene sheets and Al2O3 layers. As a result of the interaction between graphene metamaterial and a light beam embedded with OAM, the two opposite spin components of the transmitted beam will undergo shifts toward opposite directions, and the shifts depend on the incident OAM . The OAM-dependent spin splitting is bounded by w0||cosθt/[(||+1)1/2cosθi], where θi and θt are the incident and transmitted angles, respectively. By modulating the Fermi energy of the graphene sheets, the spin splitting can be tuned from positive to negative. Also, the splitting can reach its upper bound. The Fermi energy of graphene can be tuned over a wide range by an externally applied bias (electrostatic gating) since the Fermi energy in graphene is related to the carrier concentration [26].

2. THEORY

The graphene-dielectric multilayer structure can be viewed as a metamaterial with effective medium approximation. In the long-wavelength limit, the effective in-plane and out-of-plane permittivities of the metamaterial respectively are [10]

ϵeff,//=ϵd+iσZ0λ2πd,
ϵeff,=ϵd,
where ϵd and h are the permittivity and thickness of the dielectric layer, λ is the wavelength in free space, and Z0 is the vacuum impedance. σ is the optical conductivity of graphene, which is in the form of [1,27]
σ=2e2kBTπ2iw+iτ1ln(2coshEF2kBT)+e24(12+1πtan1wEF2kBT)i2πln(w+2EF)2(w2EF)2+(2kBT)2.

Here, kB is the Boltzmann constant, ω is the frequency of light, EF is the Fermi energy, T=300K is the temperature, and τ is the carrier relaxation lifetime. τ=μEF/(evF2) with vF1×106m/s being the Fermi velocity and μ=10000cm2·V1·s1 being the mobility. As shown by Eq. (1), the real part of the optical conductivity σ raises the absorption of the graphene metamaterial. The image part of σ tunes the real part of the in-plane permittivity of the graphene metamaterial, which can be changed from positive value, zero, to negative value.

In order to investigate the OAM-dependent spin splitting, we launch a linearly polarized higher-order LG beam obliquely onto a graphene metamaterial from a CaF2 prism, as shown in Fig. 1(a). The incident and transmitted angles are θi and θt, respectively. The local coordinate systems attached to the incident and transmitted beams are (xi,yi,zi) and (xt,yt,zt), respectively. The angular spectrum of a vertically polarized LG beam is E˜i=A[w0(ikix+skiy)/21/2]||exp[(kix2+kiy2)w02/4]|V, where A=w0/(2π||!)1/2, kix and kiy are the transverse wave vector of the incident beam, |V is the vertical polarization state, and s=sign[] denotes the sign of the OAM. According to Ref. [12], the angular spectrum of the transmitted beam is connected with that of the incident beam via Fresnel transmission coefficients. In the first order approximation, it is in form of

E˜t=Atsk[w0(iηktx+skty)2]||exp[(η2ktx2+kty2)w024][δskty|H+(kiηXsktx)|V],
where k=2πn/λ with n being the refractive index of the prism, ktx=ηkix, kty=kiy, and η=cosθt/cosθi. Xs=its/ts and δs=(ηtp/ts)cotθi, with tp,s being Fresnel transmission coefficients for p and s waves and ts being the first derivative of ts. By making an inverse Fourier transformation, we obtain the transmitted light field in real space, which has the following form in circular polarization basis |±=21/2[|H±i|V]:
Et±=its2πw02||!exp[(xt2/η2+yt2)w02]{[1+Xsxt/η±δsytkw02/2][(xt/η+isyt)w0]||||[Xs±isδs]kw0[(xt/η+isyt)w0]|1|}|±.

 

Fig. 1. (a) Schematic of the OAM-dependent spin splitting. A vertically polarized LG beam is coupled into a graphene metamaterial slab through a CaF2 prism. The two opposite spin components of the transmitted beam will separate along the xt axis. (b) The intensity distributions of the RCP and LCP components of the incident and transmitted beams along the xi and xt axes, respectively. (c) The graphene metamaterial composed of alternating graphene sheets and Al2O3 layers.

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The right- and the left-handed circular polarization (RCP and LCP, respectively) components of the transmitted beam are no longer LG modes. They might lose circular symmetry, thus their centroids might shift, as shown in Fig. 1(b). The displacements of the centroids of the RCP and LCP components of the transmitted beam along the xt axis are defined as Δ±=xt|Et±|2dxtdyt/|Et±|2dxtdyt [19]. After some straightforward calculations, we arrive at

Δ±=η[Re(Xs)±Im(δs)]k[1+(||+1)(|Xs|2+|δs|2)/k2w02].

The first term of Eq. (5) is the conventional GH shift originated from the Gaussian envelope [12]. It moves the RCP and LCP components of the transmitted beam together. However, the second term will shift the RCP and LCP components toward opposite directions. The term is OAM dependent, resulting from the coupling between incident OAM and the angular spin splitting σIm(δs) [28]. This OAM-dependent spin splitting is different from the in-plane photonic spin splitting [29], which vanishes for a vertically incident polarization. The spin splitting of the transmitted beam is defined as the distance between the centroids of two opposite spin components, Δ=Δ+Δ, which therefore is equal to the OAM-dependent spin splitting, independent from the GH shift. When the second term of the denominator in Eq. (5) is negligible, the spin splitting Δ is linearly proportional to the incident OAM . Otherwise, the Δ changes nonlinearly with . To maximize the spin splitting Δ, δs should be a pure imaginary number and |δs||Xs|. When |δs|=kw0/(||+1)1/2, the maximum Δ is obtained:

Δup=ηw0||||+1.

Therefore, Δup is the upper bound of the OAM-dependent spin splitting of the transmitted beam, which is determined by the incident OAM, beam waist, and the incident and transmitted angles. It has been already demonstrated that the upper bound of the spin splitting of a reflected Gaussian beam is w0 [19]. In the transmission case, the upper bound of spin splitting along the xt axis should be corrected as ηw0. Therefore, the upper bound of the spin splitting for the Gaussian beam is smaller than those of OAM-dependent spin splitting for LG beams when ||>1. Estimated by the second radial moment of the intensity, the beam size (beam width) of the LG beam is w0(||+1)1/2 [30]. For a fixed w0, the size of the LG beam increases with ||. Thus, the ratio between the upper bound of the spin splitting and the beam size of the LG beam is η||/(||+1), which shows no advantage over the foundational Gaussian beam. However, the OAM-dependent spin splitting is not only physically interesting [12,22], but it also provides an alternative method for the control of optical spin [25]. As will be shown below, when the OAM-dependent spin splitting reaches its upper bound, the RCP and LCP components of the transmitted LG beam are well separated along the xt axis: the two intensity profiles RCP and LCP components are distinguishable according to the Rayleigh criterion [15]. However, the profiles are indistinguishable from each other for the case of Gaussian incident beams [19]. In the following, we will try to tune the spin splitting and approximate its upper bound by using graphene metamaterials.

3. RESULTS

Consider the graphene metamaterial composed of alternating Al2O3 layers and graphene sheets, with the thickness of Al2O3 layers being h=10nm [see Fig. 1(c)]. The real part of the in-plane permittivity Re[ϵeff,//] varies with Fermi energy and can take positive, zero, and negative values. When EF=0.335eV, Re[ϵeff,//] almost vanishes for a wavelength of λ=4.509μm. The graphene metamaterial is displaced on the CaF2 prism, whose reflective index is n=1.39 at λ=4.509μm [10]. The structure can be fabricated by the method provided by Ref. [10].

The spin splitting of the transmitted beam Δ will change with incident angle θi and the thickness of metamaterial d, as shown by Fig. 2(a), where Δ is normalized to its upper bound Δup. In the calculations, the incident OAM is =1, the beam waist is w0=180μm, the Fermi energy of the graphene sheets is EF=0.335eV, and the wavelength is λ=4.509μm. In this situation, the effective in-plane permittivity of the graphene metamaterial is ϵeff,//=0.001+0.086i. When the incident angle θi changes from 10° to 45°, the spin splitting Δ can always approach the upper bound Δup by modulating d. When θi=33° and d=7.5μm, Δ is up to 0.994Δup. The dependences of normalized spin splitting Δ/Δup on the incident angle θi for w0=90μm (red color), 225 μm (blue color), and 450 μm (green color) are shown respectively in Fig. 2(b), where the thickness of metamaterial is fixed on 7.5 μm. The maximum value of Δ/Δup changes slightly with the beam waist w0. For the beam waist ranging from 90 to 450 μm, Δ/Δup is larger than 0.95, which indicates that Δ is close to its upper bound Δup over a wide range of w0.

 

Fig. 2. (a) Changes of the normalized OAM-dependent spin splitting Δ/Δup with the incident angle θi and thickness of metamaterial d when w0=180μm. (b) The dependences of Δ/Δup on θi for w0=90μm (red color), 225 μm (blue color), and 450 μm (green color). In our calculations, =1, EF=0.335eV, d=7.5μm, and λ=4.509μm.

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For the incident beams carried with different values of OAM, the spin splitting of the transmitted beams Δ are different. According to Eq. (6), the upper bounds of the OAM-dependent spin splitting Δup increases with the OAM ||. The change of Δup with is shown in Fig. 3(a), where the spin splitting Δ is also shown. Δ is opposite in sign for negative and positive OAM , and Δ vanishes when =0. Δ and Δup are identical for the cases of =±1 since the parameters θi=33° and d=7.5μm are optimized for these cases, as mentioned above. However, Δ is smaller than Δup when ||>1, and the difference increases with ||, as shown by Fig. 3(a).

 

Fig. 3. (a) Changes of the spin splitting Δ (red dots) and its upper bounds Δup (blue dots) with the incident OAM for θi=33° and d=7.5μm. (b) The normalized spin splitting Δ/Δup changing with the incident angle θi for OAM =±10 (red color), ±5 (blue color), ±1 (green color), and 0 (black color).

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The spin splitting Δ for ||>1 can be increased by slightly changing the incident angle θi. Figure 3(b) shows the normalized spin splitting Δ/Δup changing with the incident angle θi for OAM =10 (red lines), 5 (blue lines), 1 (green lines), and 0 (black line). For a Gaussian incident beam (=0), the spin splitting vanishes for all the incident angles. However, when 0, the spin splitting |Δ| increases with the incident angle θi and decreases gradually after reaching peak. The incident angle of the splitting peak decreases with the increase of ||. For all , the spin splitting can reach more than 0.99 of their upper bounds.

The spin splitting of the transmitted beam can be flexibly tuned by modulating the Fermi energy of the graphene sheets. The normalized spin splitting Δ/Δup changing with Fermi energy EF for different thicknesses of the graphene metamaterial d are shown in Fig. 4(a), where the incident OAM =3 (solid lines) and =3 (dashed lines). For each situation, there are two peaks in the pattern of the spin splitting: a positive peak and a negative peak. The positive and negative peaks are separated by a zero point, which is located around EF=0.31eV. When d=7.2 and 9.0 μm, the spin splitting |Δ| reach their upper bounds Δup at EF=0.336 and 0.297 eV, respectively. When d=8.3μm, however, the spin splitting Δ is smaller than Δup. Interestingly, the absolute values of the spin splitting |Δ| for positive and negative peaks are identically equal to 0.82Δup. To show the change of the spin splitting with the Fermi energy EF more clearly, the intensity profiles of the RCP (solid lines) and LCP (dotted lines) components of the transmitted beam along xt are shown in Fig. 4(b) for EF=0.275eV (red color), 0.299 eV (blue color), 0.318 eV (green color), 0.356 eV (pink color), and 0.4 eV (black color) when the thickness of the graphene metamaterial is d=8.3μm. The intensity profiles of the RCP and LCP components are overlapped when EF=0.318eV, indicating the spin splitting Δ=0. The giant spin splitting is evident in cases of EF=0.299 and 0.356 eV, where the two opposite spin components are well separated.

 

Fig. 4. (a) Dependences of the normalized spin splitting Δ/Δup on the Fermi energy EF for =3 and d=7.2μm (red color), 8.3 μm (blue color), and 9.0 μm (green color). (b) The normalized intensities of the RCP (solid lines) and LCP (dotted lines) components of the transmitted beams along the xt axis for d=8.3μm and EF=0.275eV (red color), 0.299 eV (blue color), 0.318 eV (green color), 0.356 eV (pink color), and 0.4 eV (black color).

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The spin splitting will change with the wavelength λ owing to the dispersion of the graphene metamaterial. Figure 5 plots the spin splitting Δ as a function of wavelength λ for different values of Fermi energy EF. From Fig. 5, one can see that the spin splitting for each EF almost vanishes in the short wavelength range (λ<3μm). However, Δ will increase suddenly and reach peak value. After that, it decreases sharply until reaching a negative peak. Then it will increase gradually. It is worth noticing that the magnitudes of the positive and negative peaks are different. The spin splitting undergoes blueshift when the Fermi energy EF increases. This phenomenon can be explained by the move of the zero points of the real part of the in-plane permittivity, Re[ϵeff,//], as shown in the inset of Fig. 5, where the changing of Re[ϵeff,//] with wavelength λ for different values of Fermi energy EF are shown.

 

Fig. 5. Spin splitting Δ changing with the wavelength λ when EF=0.3eV (red color), 0.335 eV (blue color), 0.38 eV (green color), and 0.45 eV (black color). The inset shows the real part of in-plane permittivity of the graphene metamaterial Re[ϵeff,//] changing with λ for different values of EF.

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From Fig. 5, one can conclude that the giant spin splitting is associated with the near-zero Re[ϵeff,//]. In these cases, however, the image part of the in-plane permittivity, Im[ϵeff,//], is nonzero, which causes loss. Specially, at the upper-bounded spin splitting, the energy transmissivity is of the order of 105. It is worth pointing out that the energy transmissivity is of the same order of magnitude when a reflected Gaussian beam reaches its upper-bounded spin splitting at Brewster incidence [19], and this upper-bounded spin splitting has been experimentally measured [29]. Therefore, the low-energy transmissivity will not prevent the experimental measurement of giant spin splitting of the transmitted beam through graphene metamaterial.

4. CONCLUSION

We have theoretically demonstrated the tunable OAM-dependent spin splitting by transmitting higher-order LG beams through graphene metamaterials. The upper bound of the OAM-dependent spin splitting is ηw0||/[(||+1)1/2], which increases with the incident OAM ||. The Fermi energy of the graphene sheets can change the effective permittivity of the graphene metamaterial, which therefore tune the spin splitting. The spin splitting can be tuned from positive to negative values and can reach its upper bound. These findings provide an effective method for the flexible control of the spin splitting and therefore facilitate the development of spin-based applications and the manipulation of the mid-infrared waves.

Funding

National Natural Science Foundation of China (NSFC) (61505069, 61675092, 61705086); Guangzhou Science and Technology Program key projects (2017A010102006, 2017A030313375).

REFERENCES

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2. J.-M. Poumirol, P. Q. Liu, T. M. Slipchenko, A. Y. Nikitin, L. Martin-Moreno, J. Faist, and A. B. Kuzmenko, “Electrically controlled terahertz magneto-optical phenomena in continuous and patterned graphene,” Nat. Commun. 8, 14626 (2017). [CrossRef]  

3. 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, 682–686 (2015). [CrossRef]  

4. T. Q. Tran, S. Lee, H. Heo, and S. Kim, “Tunable wide-angle tunneling in graphene-assisted frustrated total internal reflection,” Sci. Rep. 6, 19975 (2016). [CrossRef]  

5. A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014). [CrossRef]  

6. D. Smirnova, S. H. Mousavi, Z. Wang, Y. S. Kivshar, and A. B. Khanikaev, “Trapping and guiding surface plasmons in curved graphene landscapes,” ACS Photon. 3, 875–880 (2016). [CrossRef]  

7. H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015). [CrossRef]  

8. N. Mohammadi Estakhri and A. Alù, “Wave-front transformation with gradient metasurfaces,” Phys. Rev. X 6, 41008 (2016). [CrossRef]  

9. X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8, 10388–10397 (2016). [CrossRef]  

10. Y. Chang, C. Liu, C. Liu, S. Zhang, and S. R. Marder, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016). [CrossRef]  

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

12. K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15, 14001 (2013). [CrossRef]  

13. H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 43806 (2011). [CrossRef]  

14. J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for giant transverse optical beam shifts,” Phys. Rev. Lett. 112, 233901 (2014). [CrossRef]  

15. J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air–glass interface,” Appl. Phys. Lett. 107, 111105 (2015). [CrossRef]  

16. X. Tan and X. Zhu, “Enhancing photonic spin Hall effect via long-range surface plasmon resonance,” Opt. Lett. 41, 2478–2481 (2016). [CrossRef]  

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

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24. X. Wang, H. Wang, and F. Zheng, “Properties of group delay for photon tunneling through dispersive metamaterial barriers,” Opt. Commun. 382, 371–376 (2017). [CrossRef]  

25. J. Zhang, Z. Luo, H. Luo, and S. Wen, “Steering asymmetric spin splitting in photonic spin Hall effect by orbital angular momentum,” Acta Opt. Sin. 33, 1126002 (2013). [CrossRef]  

26. X. Liu, Z. Chen, E. P. J. Parrott, B. S.-Y. Ung, J. Xu, and E. Pickwell-MacPherson, “Graphene based terahertz light modulator in total internal reflection geometry,” Adv. Opt. Mater. 3, 1600697 (2016). [CrossRef]  

27. J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Towards nano-optical tweezers with graphene plasmons: Numerical investigation of trapping 10-nm particles with mid-infrared light,” Sci. Rep. 6, 38086 (2016). [CrossRef]  

28. W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, Y. Luo, and Z. Chen, “Large spatial and angular spin splitting in a thin anisotropic ϵ-near-zero metamaterial,” Opt. Express 25, 5196–5205 (2017). [CrossRef]  

29. X. Qiu, Z. Zhang, L. Xie, J. Qiu, F. Gao, and J. Du, “Incident-polarization-sensitive and large in-plane-photonic-spin-splitting at the Brewster angle,” Opt. Lett. 40, 1018–1021 (2015). [CrossRef]  

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References

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  1. F. H. L. Koppens, D. E. Chang, and F. J. García De Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
    [Crossref]
  2. J.-M. Poumirol, P. Q. Liu, T. M. Slipchenko, A. Y. Nikitin, L. Martin-Moreno, J. Faist, and A. B. Kuzmenko, “Electrically controlled terahertz magneto-optical phenomena in continuous and patterned graphene,” Nat. Commun. 8, 14626 (2017).
    [Crossref]
  3. 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, 682–686 (2015).
    [Crossref]
  4. T. Q. Tran, S. Lee, H. Heo, and S. Kim, “Tunable wide-angle tunneling in graphene-assisted frustrated total internal reflection,” Sci. Rep. 6, 19975 (2016).
    [Crossref]
  5. A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
    [Crossref]
  6. D. Smirnova, S. H. Mousavi, Z. Wang, Y. S. Kivshar, and A. B. Khanikaev, “Trapping and guiding surface plasmons in curved graphene landscapes,” ACS Photon. 3, 875–880 (2016).
    [Crossref]
  7. H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015).
    [Crossref]
  8. N. Mohammadi Estakhri and A. Alù, “Wave-front transformation with gradient metasurfaces,” Phys. Rev. X 6, 41008 (2016).
    [Crossref]
  9. X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8, 10388–10397 (2016).
    [Crossref]
  10. Y. Chang, C. Liu, C. Liu, S. Zhang, and S. R. Marder, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
    [Crossref]
  11. O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319, 787–790 (2008).
    [Crossref]
  12. K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15, 14001 (2013).
    [Crossref]
  13. H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 43806 (2011).
    [Crossref]
  14. J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for giant transverse optical beam shifts,” Phys. Rev. Lett. 112, 233901 (2014).
    [Crossref]
  15. J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air–glass interface,” Appl. Phys. Lett. 107, 111105 (2015).
    [Crossref]
  16. X. Tan and X. Zhu, “Enhancing photonic spin Hall effect via long-range surface plasmon resonance,” Opt. Lett. 41, 2478–2481 (2016).
    [Crossref]
  17. T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6, 30762 (2016).
    [Crossref]
  18. W. Zhu and W. She, “Enhanced spin Hall effect of transmitted light through a thin epsilon-near-zero slab,” Opt. Lett. 40, 2961–2964 (2015).
    [Crossref]
  19. W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass–air interface,” Sci. Rep. 7, 1150 (2017).
    [Crossref]
  20. K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos–Hänchen and Imbert–Fedorov shifts of polarized vortex beams,” Opt. Lett. 34, 389–391 (2009).
    [Crossref]
  21. M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
    [Crossref]
  22. A. Aiello, “Goos–Hänchen and Imbert–Fedorov shifts: a novel perspective,” New J. Phys. 14, 013058 (2012).
    [Crossref]
  23. Z. Xiao, H. Luo, and S. Wen, “Goos–Hänchen and Imbert–Fedorov shifts of vortex beams at air left-handed-material interfaces,” Phys. Rev. A 85, 33–35 (2012).
    [Crossref]
  24. X. Wang, H. Wang, and F. Zheng, “Properties of group delay for photon tunneling through dispersive metamaterial barriers,” Opt. Commun. 382, 371–376 (2017).
    [Crossref]
  25. J. Zhang, Z. Luo, H. Luo, and S. Wen, “Steering asymmetric spin splitting in photonic spin Hall effect by orbital angular momentum,” Acta Opt. Sin. 33, 1126002 (2013).
    [Crossref]
  26. X. Liu, Z. Chen, E. P. J. Parrott, B. S.-Y. Ung, J. Xu, and E. Pickwell-MacPherson, “Graphene based terahertz light modulator in total internal reflection geometry,” Adv. Opt. Mater. 3, 1600697 (2016).
    [Crossref]
  27. J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Towards nano-optical tweezers with graphene plasmons: Numerical investigation of trapping 10-nm particles with mid-infrared light,” Sci. Rep. 6, 38086 (2016).
    [Crossref]
  28. W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, Y. Luo, and Z. Chen, “Large spatial and angular spin splitting in a thin anisotropic ϵ-near-zero metamaterial,” Opt. Express 25, 5196–5205 (2017).
    [Crossref]
  29. X. Qiu, Z. Zhang, L. Xie, J. Qiu, F. Gao, and J. Du, “Incident-polarization-sensitive and large in-plane-photonic-spin-splitting at the Brewster angle,” Opt. Lett. 40, 1018–1021 (2015).
    [Crossref]
  30. C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
    [Crossref]

2017 (4)

J.-M. Poumirol, P. Q. Liu, T. M. Slipchenko, A. Y. Nikitin, L. Martin-Moreno, J. Faist, and A. B. Kuzmenko, “Electrically controlled terahertz magneto-optical phenomena in continuous and patterned graphene,” Nat. Commun. 8, 14626 (2017).
[Crossref]

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass–air interface,” Sci. Rep. 7, 1150 (2017).
[Crossref]

X. Wang, H. Wang, and F. Zheng, “Properties of group delay for photon tunneling through dispersive metamaterial barriers,” Opt. Commun. 382, 371–376 (2017).
[Crossref]

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, Y. Luo, and Z. Chen, “Large spatial and angular spin splitting in a thin anisotropic ϵ-near-zero metamaterial,” Opt. Express 25, 5196–5205 (2017).
[Crossref]

2016 (9)

X. Liu, Z. Chen, E. P. J. Parrott, B. S.-Y. Ung, J. Xu, and E. Pickwell-MacPherson, “Graphene based terahertz light modulator in total internal reflection geometry,” Adv. Opt. Mater. 3, 1600697 (2016).
[Crossref]

J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Towards nano-optical tweezers with graphene plasmons: Numerical investigation of trapping 10-nm particles with mid-infrared light,” Sci. Rep. 6, 38086 (2016).
[Crossref]

T. Q. Tran, S. Lee, H. Heo, and S. Kim, “Tunable wide-angle tunneling in graphene-assisted frustrated total internal reflection,” Sci. Rep. 6, 19975 (2016).
[Crossref]

N. Mohammadi Estakhri and A. Alù, “Wave-front transformation with gradient metasurfaces,” Phys. Rev. X 6, 41008 (2016).
[Crossref]

X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8, 10388–10397 (2016).
[Crossref]

Y. Chang, C. Liu, C. Liu, S. Zhang, and S. R. Marder, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

D. Smirnova, S. H. Mousavi, Z. Wang, Y. S. Kivshar, and A. B. Khanikaev, “Trapping and guiding surface plasmons in curved graphene landscapes,” ACS Photon. 3, 875–880 (2016).
[Crossref]

X. Tan and X. Zhu, “Enhancing photonic spin Hall effect via long-range surface plasmon resonance,” Opt. Lett. 41, 2478–2481 (2016).
[Crossref]

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

2015 (5)

W. Zhu and W. She, “Enhanced spin Hall effect of transmitted light through a thin epsilon-near-zero slab,” Opt. Lett. 40, 2961–2964 (2015).
[Crossref]

H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015).
[Crossref]

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, 682–686 (2015).
[Crossref]

X. Qiu, Z. Zhang, L. Xie, J. Qiu, F. Gao, and J. Du, “Incident-polarization-sensitive and large in-plane-photonic-spin-splitting at the Brewster angle,” Opt. Lett. 40, 1018–1021 (2015).
[Crossref]

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air–glass interface,” Appl. Phys. Lett. 107, 111105 (2015).
[Crossref]

2014 (2)

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for giant transverse optical beam shifts,” Phys. Rev. Lett. 112, 233901 (2014).
[Crossref]

2013 (2)

K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15, 14001 (2013).
[Crossref]

J. Zhang, Z. Luo, H. Luo, and S. Wen, “Steering asymmetric spin splitting in photonic spin Hall effect by orbital angular momentum,” Acta Opt. Sin. 33, 1126002 (2013).
[Crossref]

2012 (2)

A. Aiello, “Goos–Hänchen and Imbert–Fedorov shifts: a novel perspective,” New J. Phys. 14, 013058 (2012).
[Crossref]

Z. Xiao, H. Luo, and S. Wen, “Goos–Hänchen and Imbert–Fedorov shifts of vortex beams at air left-handed-material interfaces,” Phys. Rev. A 85, 33–35 (2012).
[Crossref]

2011 (2)

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 43806 (2011).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. García De Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

2010 (1)

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

2009 (1)

2008 (1)

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

2005 (1)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref]

Aiello, A.

K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15, 14001 (2013).
[Crossref]

A. Aiello, “Goos–Hänchen and Imbert–Fedorov shifts: a novel perspective,” New J. Phys. 14, 013058 (2012).
[Crossref]

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

Alonso-González, P.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

Alù, A.

N. Mohammadi Estakhri and A. Alù, “Wave-front transformation with gradient metasurfaces,” Phys. Rev. X 6, 41008 (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, 682–686 (2015).
[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, 682–686 (2015).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15, 14001 (2013).
[Crossref]

K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos–Hänchen and Imbert–Fedorov shifts of polarized vortex beams,” Opt. Lett. 34, 389–391 (2009).
[Crossref]

Carrega, M.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. García De Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

Chang, Y.

Y. Chang, C. Liu, C. Liu, S. Zhang, and S. R. Marder, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

Chen, S.

H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015).
[Crossref]

Chen, Z.

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass–air interface,” Sci. Rep. 7, 1150 (2017).
[Crossref]

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, Y. Luo, and Z. Chen, “Large spatial and angular spin splitting in a thin anisotropic ϵ-near-zero metamaterial,” Opt. Express 25, 5196–5205 (2017).
[Crossref]

X. Liu, Z. Chen, E. P. J. Parrott, B. S.-Y. Ung, J. Xu, and E. Pickwell-MacPherson, “Graphene based terahertz light modulator in total internal reflection geometry,” Adv. Opt. Mater. 3, 1600697 (2016).
[Crossref]

Cheng, H.

H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015).
[Crossref]

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, 682–686 (2015).
[Crossref]

Dennis, M. R.

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for giant transverse optical beam shifts,” Phys. Rev. Lett. 112, 233901 (2014).
[Crossref]

Du, J.

Faist, J.

J.-M. Poumirol, P. Q. Liu, T. M. Slipchenko, A. Y. Nikitin, L. Martin-Moreno, J. Faist, and A. B. Kuzmenko, “Electrically controlled terahertz magneto-optical phenomena in continuous and patterned graphene,” Nat. Commun. 8, 14626 (2017).
[Crossref]

Fan, D.

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 43806 (2011).
[Crossref]

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, 682–686 (2015).
[Crossref]

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, 682–686 (2015).
[Crossref]

Gao, F.

Gao, P.

X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8, 10388–10397 (2016).
[Crossref]

Gao, Y.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

García De Abajo, F. J.

F. H. L. Koppens, D. E. Chang, and F. J. García De Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

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, 682–686 (2015).
[Crossref]

Gong, Q.

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air–glass interface,” Appl. Phys. Lett. 107, 111105 (2015).
[Crossref]

Götte, J. B.

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for giant transverse optical beam shifts,” Phys. Rev. Lett. 112, 233901 (2014).
[Crossref]

Guan, H.

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass–air interface,” Sci. Rep. 7, 1150 (2017).
[Crossref]

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, Y. Luo, and Z. Chen, “Large spatial and angular spin splitting in a thin anisotropic ϵ-near-zero metamaterial,” Opt. Express 25, 5196–5205 (2017).
[Crossref]

He, X.

X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8, 10388–10397 (2016).
[Crossref]

Heo, H.

T. Q. Tran, S. Lee, H. Heo, and S. Kim, “Tunable wide-angle tunneling in graphene-assisted frustrated total internal reflection,” Sci. Rep. 6, 19975 (2016).
[Crossref]

Hermosa, N.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

Hillenbrand, R.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

Hone, J.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

Hosten, O.

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

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, 682–686 (2015).
[Crossref]

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, 682–686 (2015).
[Crossref]

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, 682–686 (2015).
[Crossref]

Khanikaev, A. B.

D. Smirnova, S. H. Mousavi, Z. Wang, Y. S. Kivshar, and A. B. Khanikaev, “Trapping and guiding surface plasmons in curved graphene landscapes,” ACS Photon. 3, 875–880 (2016).
[Crossref]

Kim, S.

T. Q. Tran, S. Lee, H. Heo, and S. Kim, “Tunable wide-angle tunneling in graphene-assisted frustrated total internal reflection,” Sci. Rep. 6, 19975 (2016).
[Crossref]

Kivshar, Y. S.

D. Smirnova, S. H. Mousavi, Z. Wang, Y. S. Kivshar, and A. B. Khanikaev, “Trapping and guiding surface plasmons in curved graphene landscapes,” ACS Photon. 3, 875–880 (2016).
[Crossref]

K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos–Hänchen and Imbert–Fedorov shifts of polarized vortex beams,” Opt. Lett. 34, 389–391 (2009).
[Crossref]

Koppens, F. H. L.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. García De Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

Kuzmenko, A. B.

J.-M. Poumirol, P. Q. Liu, T. M. Slipchenko, A. Y. Nikitin, L. Martin-Moreno, J. Faist, and A. B. Kuzmenko, “Electrically controlled terahertz magneto-optical phenomena in continuous and patterned graphene,” Nat. Commun. 8, 14626 (2017).
[Crossref]

Kwiat, P.

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

Lee, S.

T. Q. Tran, S. Lee, H. Heo, and S. Kim, “Tunable wide-angle tunneling in graphene-assisted frustrated total internal reflection,” Sci. Rep. 6, 19975 (2016).
[Crossref]

Li, C.

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

Li, J.

H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015).
[Crossref]

Li, Y.

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air–glass interface,” Appl. Phys. Lett. 107, 111105 (2015).
[Crossref]

Li, Z.

H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015).
[Crossref]

Liu, C.

Y. Chang, C. Liu, C. Liu, S. Zhang, and S. R. Marder, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

Y. Chang, C. Liu, C. Liu, S. Zhang, and S. R. Marder, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

Liu, M. K.

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, 682–686 (2015).
[Crossref]

Liu, P. Q.

J.-M. Poumirol, P. Q. Liu, T. M. Slipchenko, A. Y. Nikitin, L. Martin-Moreno, J. Faist, and A. B. Kuzmenko, “Electrically controlled terahertz magneto-optical phenomena in continuous and patterned graphene,” Nat. Commun. 8, 14626 (2017).
[Crossref]

Liu, W.

J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Towards nano-optical tweezers with graphene plasmons: Numerical investigation of trapping 10-nm particles with mid-infrared light,” Sci. Rep. 6, 38086 (2016).
[Crossref]

H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015).
[Crossref]

Liu, X.

X. Liu, Z. Chen, E. P. J. Parrott, B. S.-Y. Ung, J. Xu, and E. Pickwell-MacPherson, “Graphene based terahertz light modulator in total internal reflection geometry,” Adv. Opt. Mater. 3, 1600697 (2016).
[Crossref]

Löffler, W.

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for giant transverse optical beam shifts,” Phys. Rev. Lett. 112, 233901 (2014).
[Crossref]

Lu, H.

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass–air interface,” Sci. Rep. 7, 1150 (2017).
[Crossref]

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, Y. Luo, and Z. Chen, “Large spatial and angular spin splitting in a thin anisotropic ϵ-near-zero metamaterial,” Opt. Express 25, 5196–5205 (2017).
[Crossref]

Lundeberg, M. B.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

Luo, H.

J. Zhang, Z. Luo, H. Luo, and S. Wen, “Steering asymmetric spin splitting in photonic spin Hall effect by orbital angular momentum,” Acta Opt. Sin. 33, 1126002 (2013).
[Crossref]

Z. Xiao, H. Luo, and S. Wen, “Goos–Hänchen and Imbert–Fedorov shifts of vortex beams at air left-handed-material interfaces,” Phys. Rev. A 85, 33–35 (2012).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 43806 (2011).
[Crossref]

Luo, L.

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

Luo, Y.

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass–air interface,” Sci. Rep. 7, 1150 (2017).
[Crossref]

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, Y. Luo, and Z. Chen, “Large spatial and angular spin splitting in a thin anisotropic ϵ-near-zero metamaterial,” Opt. Express 25, 5196–5205 (2017).
[Crossref]

Luo, Z.

J. Zhang, Z. Luo, H. Luo, and S. Wen, “Steering asymmetric spin splitting in photonic spin Hall effect by orbital angular momentum,” Acta Opt. Sin. 33, 1126002 (2013).
[Crossref]

Ma, Q.

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, 682–686 (2015).
[Crossref]

Marder, S. R.

Y. Chang, C. Liu, C. Liu, S. Zhang, and S. R. Marder, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

Martin-Moreno, L.

J.-M. Poumirol, P. Q. Liu, T. M. Slipchenko, A. Y. Nikitin, L. Martin-Moreno, J. Faist, and A. B. Kuzmenko, “Electrically controlled terahertz magneto-optical phenomena in continuous and patterned graphene,” Nat. Commun. 8, 14626 (2017).
[Crossref]

Merano, M.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

Mohammadi Estakhri, N.

N. Mohammadi Estakhri and A. Alù, “Wave-front transformation with gradient metasurfaces,” Phys. Rev. X 6, 41008 (2016).
[Crossref]

Mousavi, S. H.

D. Smirnova, S. H. Mousavi, Z. Wang, Y. S. Kivshar, and A. B. Khanikaev, “Trapping and guiding surface plasmons in curved graphene landscapes,” ACS Photon. 3, 875–880 (2016).
[Crossref]

Nikitin, A. Y.

J.-M. Poumirol, P. Q. Liu, T. M. Slipchenko, A. Y. Nikitin, L. Martin-Moreno, J. Faist, and A. B. Kuzmenko, “Electrically controlled terahertz magneto-optical phenomena in continuous and patterned graphene,” Nat. Commun. 8, 14626 (2017).
[Crossref]

Parrott, E. P. J.

X. Liu, Z. Chen, E. P. J. Parrott, B. S.-Y. Ung, J. Xu, and E. Pickwell-MacPherson, “Graphene based terahertz light modulator in total internal reflection geometry,” Adv. Opt. Mater. 3, 1600697 (2016).
[Crossref]

Paterson, C.

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref]

Pickwell-MacPherson, E.

X. Liu, Z. Chen, E. P. J. Parrott, B. S.-Y. Ung, J. Xu, and E. Pickwell-MacPherson, “Graphene based terahertz light modulator in total internal reflection geometry,” Adv. Opt. Mater. 3, 1600697 (2016).
[Crossref]

Polini, M.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

Poumirol, J.-M.

J.-M. Poumirol, P. Q. Liu, T. M. Slipchenko, A. Y. Nikitin, L. Martin-Moreno, J. Faist, and A. B. Kuzmenko, “Electrically controlled terahertz magneto-optical phenomena in continuous and patterned graphene,” Nat. Commun. 8, 14626 (2017).
[Crossref]

Principi, A.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

Qin, S.

J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Towards nano-optical tweezers with graphene plasmons: Numerical investigation of trapping 10-nm particles with mid-infrared light,” Sci. Rep. 6, 38086 (2016).
[Crossref]

Qiu, J.

Qiu, X.

Ren, J. L.

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air–glass interface,” Appl. Phys. Lett. 107, 111105 (2015).
[Crossref]

Shadrivov, I. V.

She, W.

Shi, W.

X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8, 10388–10397 (2016).
[Crossref]

Shu, W.

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 43806 (2011).
[Crossref]

Slipchenko, T. M.

J.-M. Poumirol, P. Q. Liu, T. M. Slipchenko, A. Y. Nikitin, L. Martin-Moreno, J. Faist, and A. B. Kuzmenko, “Electrically controlled terahertz magneto-optical phenomena in continuous and patterned graphene,” Nat. Commun. 8, 14626 (2017).
[Crossref]

Smirnova, D.

D. Smirnova, S. H. Mousavi, Z. Wang, Y. S. Kivshar, and A. B. Khanikaev, “Trapping and guiding surface plasmons in curved graphene landscapes,” ACS Photon. 3, 875–880 (2016).
[Crossref]

Tan, X.

Tang, J.

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass–air interface,” Sci. Rep. 7, 1150 (2017).
[Crossref]

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, Y. Luo, and Z. Chen, “Large spatial and angular spin splitting in a thin anisotropic ϵ-near-zero metamaterial,” Opt. Express 25, 5196–5205 (2017).
[Crossref]

Tang, T.

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

Taniguchi, 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, 682–686 (2015).
[Crossref]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

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, 682–686 (2015).
[Crossref]

Tian, J.

H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015).
[Crossref]

Tran, T. Q.

T. Q. Tran, S. Lee, H. Heo, and S. Kim, “Tunable wide-angle tunneling in graphene-assisted frustrated total internal reflection,” Sci. Rep. 6, 19975 (2016).
[Crossref]

Ung, B. S.-Y.

X. Liu, Z. Chen, E. P. J. Parrott, B. S.-Y. Ung, J. Xu, and E. Pickwell-MacPherson, “Graphene based terahertz light modulator in total internal reflection geometry,” Adv. Opt. Mater. 3, 1600697 (2016).
[Crossref]

Vignale, G.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

Wagner, 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, 682–686 (2015).
[Crossref]

Wang, B.

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air–glass interface,” Appl. Phys. Lett. 107, 111105 (2015).
[Crossref]

Wang, H.

X. Wang, H. Wang, and F. Zheng, “Properties of group delay for photon tunneling through dispersive metamaterial barriers,” Opt. Commun. 382, 371–376 (2017).
[Crossref]

Wang, X.

X. Wang, H. Wang, and F. Zheng, “Properties of group delay for photon tunneling through dispersive metamaterial barriers,” Opt. Commun. 382, 371–376 (2017).
[Crossref]

Wang, Z.

D. Smirnova, S. H. Mousavi, Z. Wang, Y. S. Kivshar, and A. B. Khanikaev, “Trapping and guiding surface plasmons in curved graphene landscapes,” ACS Photon. 3, 875–880 (2016).
[Crossref]

Watanabe, K.

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, 682–686 (2015).
[Crossref]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

Wen, S.

J. Zhang, Z. Luo, H. Luo, and S. Wen, “Steering asymmetric spin splitting in photonic spin Hall effect by orbital angular momentum,” Acta Opt. Sin. 33, 1126002 (2013).
[Crossref]

Z. Xiao, H. Luo, and S. Wen, “Goos–Hänchen and Imbert–Fedorov shifts of vortex beams at air left-handed-material interfaces,” Phys. Rev. A 85, 33–35 (2012).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 43806 (2011).
[Crossref]

Woerdman, J. P.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

Woessner, A.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

Xiao, Y. F.

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air–glass interface,” Appl. Phys. Lett. 107, 111105 (2015).
[Crossref]

Xiao, Z.

Z. Xiao, H. Luo, and S. Wen, “Goos–Hänchen and Imbert–Fedorov shifts of vortex beams at air left-handed-material interfaces,” Phys. Rev. A 85, 33–35 (2012).
[Crossref]

Xie, B.

H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015).
[Crossref]

Xie, L.

Xu, J.

X. Liu, Z. Chen, E. P. J. Parrott, B. S.-Y. Ung, J. Xu, and E. Pickwell-MacPherson, “Graphene based terahertz light modulator in total internal reflection geometry,” Adv. Opt. Mater. 3, 1600697 (2016).
[Crossref]

Yu, J.

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, Y. Luo, and Z. Chen, “Large spatial and angular spin splitting in a thin anisotropic ϵ-near-zero metamaterial,” Opt. Express 25, 5196–5205 (2017).
[Crossref]

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass–air interface,” Sci. Rep. 7, 1150 (2017).
[Crossref]

Yu, P.

H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015).
[Crossref]

Yuan, X.

J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Towards nano-optical tweezers with graphene plasmons: Numerical investigation of trapping 10-nm particles with mid-infrared light,” Sci. Rep. 6, 38086 (2016).
[Crossref]

Zhang, J.

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass–air interface,” Sci. Rep. 7, 1150 (2017).
[Crossref]

J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Towards nano-optical tweezers with graphene plasmons: Numerical investigation of trapping 10-nm particles with mid-infrared light,” Sci. Rep. 6, 38086 (2016).
[Crossref]

J. Zhang, Z. Luo, H. Luo, and S. Wen, “Steering asymmetric spin splitting in photonic spin Hall effect by orbital angular momentum,” Acta Opt. Sin. 33, 1126002 (2013).
[Crossref]

Zhang, S.

Y. Chang, C. Liu, C. Liu, S. Zhang, and S. R. Marder, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

Zhang, Z.

Zheng, F.

X. Wang, H. Wang, and F. Zheng, “Properties of group delay for photon tunneling through dispersive metamaterial barriers,” Opt. Commun. 382, 371–376 (2017).
[Crossref]

Zhou, X.

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 43806 (2011).
[Crossref]

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, 682–686 (2015).
[Crossref]

Zhu, W.

Zhu, X.

Zhu, Z.

J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Towards nano-optical tweezers with graphene plasmons: Numerical investigation of trapping 10-nm particles with mid-infrared light,” Sci. Rep. 6, 38086 (2016).
[Crossref]

ACS Photon. (1)

D. Smirnova, S. H. Mousavi, Z. Wang, Y. S. Kivshar, and A. B. Khanikaev, “Trapping and guiding surface plasmons in curved graphene landscapes,” ACS Photon. 3, 875–880 (2016).
[Crossref]

Acta Opt. Sin. (1)

J. Zhang, Z. Luo, H. Luo, and S. Wen, “Steering asymmetric spin splitting in photonic spin Hall effect by orbital angular momentum,” Acta Opt. Sin. 33, 1126002 (2013).
[Crossref]

Adv. Opt. Mater. (2)

X. Liu, Z. Chen, E. P. J. Parrott, B. S.-Y. Ung, J. Xu, and E. Pickwell-MacPherson, “Graphene based terahertz light modulator in total internal reflection geometry,” Adv. Opt. Mater. 3, 1600697 (2016).
[Crossref]

H. Cheng, S. Chen, P. Yu, W. Liu, Z. Li, J. Li, B. Xie, and J. Tian, “Dynamically tunable broadband infrared anomalous refraction based on graphene metasurfaces,” Adv. Opt. Mater. 3, 1744–1749 (2015).
[Crossref]

Appl. Phys. Lett. (1)

J. L. Ren, B. Wang, Y. F. Xiao, Q. Gong, and Y. Li, “Direct observation of a resolvable spin separation in the spin Hall effect of light at an air–glass interface,” Appl. Phys. Lett. 107, 111105 (2015).
[Crossref]

J. Opt. (1)

K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15, 14001 (2013).
[Crossref]

Nano Lett. (1)

F. H. L. Koppens, D. E. Chang, and F. J. García De Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

Nanoscale (1)

X. He, P. Gao, and W. Shi, “A further comparison of graphene and thin metal layers for plasmonics,” Nanoscale 8, 10388–10397 (2016).
[Crossref]

Nat. Commun. (2)

Y. Chang, C. Liu, C. Liu, S. Zhang, and S. R. Marder, “Realization of mid-infrared graphene hyperbolic metamaterials,” Nat. Commun. 7, 10568 (2016).
[Crossref]

J.-M. Poumirol, P. Q. Liu, T. M. Slipchenko, A. Y. Nikitin, L. Martin-Moreno, J. Faist, and A. B. Kuzmenko, “Electrically controlled terahertz magneto-optical phenomena in continuous and patterned graphene,” Nat. Commun. 8, 14626 (2017).
[Crossref]

Nat. Mater. (1)

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2014).
[Crossref]

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, 682–686 (2015).
[Crossref]

New J. Phys. (1)

A. Aiello, “Goos–Hänchen and Imbert–Fedorov shifts: a novel perspective,” New J. Phys. 14, 013058 (2012).
[Crossref]

Opt. Commun. (1)

X. Wang, H. Wang, and F. Zheng, “Properties of group delay for photon tunneling through dispersive metamaterial barriers,” Opt. Commun. 382, 371–376 (2017).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (3)

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84, 43806 (2011).
[Crossref]

Z. Xiao, H. Luo, and S. Wen, “Goos–Hänchen and Imbert–Fedorov shifts of vortex beams at air left-handed-material interfaces,” Phys. Rev. A 85, 33–35 (2012).
[Crossref]

Phys. Rev. Lett. (2)

C. Paterson, “Atmospheric turbulence and orbital angular momentum of single photons for optical communication,” Phys. Rev. Lett. 94, 153901 (2005).
[Crossref]

J. B. Götte, W. Löffler, and M. R. Dennis, “Eigenpolarizations for giant transverse optical beam shifts,” Phys. Rev. Lett. 112, 233901 (2014).
[Crossref]

Phys. Rev. X (1)

N. Mohammadi Estakhri and A. Alù, “Wave-front transformation with gradient metasurfaces,” Phys. Rev. X 6, 41008 (2016).
[Crossref]

Sci. Rep. (4)

T. Q. Tran, S. Lee, H. Heo, and S. Kim, “Tunable wide-angle tunneling in graphene-assisted frustrated total internal reflection,” Sci. Rep. 6, 19975 (2016).
[Crossref]

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

W. Zhu, J. Yu, H. Guan, H. Lu, J. Tang, J. Zhang, Y. Luo, and Z. Chen, “The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass–air interface,” Sci. Rep. 7, 1150 (2017).
[Crossref]

J. Zhang, W. Liu, Z. Zhu, X. Yuan, and S. Qin, “Towards nano-optical tweezers with graphene plasmons: Numerical investigation of trapping 10-nm particles with mid-infrared light,” Sci. Rep. 6, 38086 (2016).
[Crossref]

Science (1)

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

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic of the OAM-dependent spin splitting. A vertically polarized LG beam is coupled into a graphene metamaterial slab through a CaF2 prism. The two opposite spin components of the transmitted beam will separate along the xt axis. (b) The intensity distributions of the RCP and LCP components of the incident and transmitted beams along the xi and xt axes, respectively. (c) The graphene metamaterial composed of alternating graphene sheets and Al2O3 layers.
Fig. 2.
Fig. 2. (a) Changes of the normalized OAM-dependent spin splitting Δ/Δup with the incident angle θi and thickness of metamaterial d when w0=180μm. (b) The dependences of Δ/Δup on θi for w0=90μm (red color), 225 μm (blue color), and 450 μm (green color). In our calculations, =1, EF=0.335eV, d=7.5μm, and λ=4.509μm.
Fig. 3.
Fig. 3. (a) Changes of the spin splitting Δ (red dots) and its upper bounds Δup (blue dots) with the incident OAM for θi=33° and d=7.5μm. (b) The normalized spin splitting Δ/Δup changing with the incident angle θi for OAM =±10 (red color), ±5 (blue color), ±1 (green color), and 0 (black color).
Fig. 4.
Fig. 4. (a) Dependences of the normalized spin splitting Δ/Δup on the Fermi energy EF for =3 and d=7.2μm (red color), 8.3 μm (blue color), and 9.0 μm (green color). (b) The normalized intensities of the RCP (solid lines) and LCP (dotted lines) components of the transmitted beams along the xt axis for d=8.3μm and EF=0.275eV (red color), 0.299 eV (blue color), 0.318 eV (green color), 0.356 eV (pink color), and 0.4 eV (black color).
Fig. 5.
Fig. 5. Spin splitting Δ changing with the wavelength λ when EF=0.3eV (red color), 0.335 eV (blue color), 0.38 eV (green color), and 0.45 eV (black color). The inset shows the real part of in-plane permittivity of the graphene metamaterial Re[ϵeff,//] changing with λ for different values of EF.

Equations (7)

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ϵeff,//=ϵd+iσZ0λ2πd,
ϵeff,=ϵd,
σ=2e2kBTπ2iw+iτ1ln(2coshEF2kBT)+e24(12+1πtan1wEF2kBT)i2πln(w+2EF)2(w2EF)2+(2kBT)2.
E˜t=Atsk[w0(iηktx+skty)2]||exp[(η2ktx2+kty2)w024][δskty|H+(kiηXsktx)|V],
Et±=its2πw02||!exp[(xt2/η2+yt2)w02]{[1+Xsxt/η±δsytkw02/2][(xt/η+isyt)w0]||||[Xs±isδs]kw0[(xt/η+isyt)w0]|1|}|±.
Δ±=η[Re(Xs)±Im(δs)]k[1+(||+1)(|Xs|2+|δs|2)/k2w02].
Δup=ηw0||||+1.

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