Abstract

In-plane photonic spin splitting effect is investigated in tunneling terahertz waves through an epsilon-near-zero metamaterial sandwiched between monolayer black phosphorus (BP). The strong in-plane anisotropy of BP layers will induce in-plane asymmetric spin splitting. The asymmetric spin splitting can be flexibly tuned by the angles between the incident plane and the armchair crystalline directions of the top and bottom BP layers, i.e., ϕ1 and ϕ2. Based on this, an angle-resolved barcode-encryption scheme is discussed. For the special case of ϕ1 = ϕ2 = 0 or 90°, the transmitted beam undergoes Goos-Hänchen shift, which varies with the carrier density of BP. We believe these findings can facilitate the development of novel optoelectronic devices in the Terahertz region.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Photonic spin splitting, refer to the spatial separation of two opposite spin components of the reflected/transmitted beam [1–4], has attracted significant attention owing to its application in precise metrology and quantum information [5–7]. The spin splitting can occur in directions both parallel and perpendicular to the plane of incidence, i.e., so-called the in-plane and out-of-plane spin splitting (IPSS and OPSS) [4–6]. Both IPSS and OPSS can be considered as results of spin-orbit coupling [1,3,4,8]. It has been demonstrated by Götte and Dennis in 2012 that the in-plane and out-of-plane spin splitting can be considered as analogous but reverse effects [9]. Different from Goos-Hänchen (GH) shift occurring in total reflection, the IPSS can appear in both cases of partial and total reflections [3,4]. In 2017, the upper limit of IPSS was derived, equal to the incident beam waist [4]. This upper limit can be obtained by optimizing the incident linear polarization state at Brewster angle [4]. Very recently, large IPSS near the critical angle of total reflection was theoretically proposed and experimentally verified [10].

Epsilon-near-zero (ENZ) metamaterial has significant interest due to its novel light-matter interactions [11]. According to the electromagnetic boundary condition, the vanishing epsilon in ENZ material will lead to strong discontinuity in the normal electric field, thus the strong field localization and enhancement [12]. The nonlinear and Purcell effects can therefore be boosted by ENZ metamaterials [13–15]. The vanishing epsilon of ENZ material also results in nearly constant phase advance when an electromagnetic field travels through the whole material [16]. Based on this phenomena, phase-mismatch-free harmonic generation, wavefront reshaping, and ultrafast phase transitions have been developed [17]. It has been demonstrated recently that ENZ metamaterials can enhance the GH shift [18] and the spin splitting [19,20].

To tune the spin splitting, we sandwich the ENZ metamaterial by monolayer black phosphorus. The light-matter interaction in this structure can be tuned by modulating the conductivity of BP, which is proportional to the electron carrier density [21]. BP possesses striking in-plane anisotropy property, enabling novel polarization-dependent and angle-resolved optoelectronic devices [22–26]. The asymmetric spin splitting induced by the in-plane anisotropy of BP was predicted very recently [27]. The reflected beam from a BP layer sitting on a silicon substrate undergoes both in-plane and out-of-plane asymmetric spin splitting near Brewster angle. However, the in-plane displacements of two opposite spin components are always positive, cannot be tuned flexibly [27]. The spin splitting of the transmitted beam from the structure are tiny small. The large asymmetric spin splitting in the transmitted beam is still missing [26,27].

Here, a novel structure combining the ENZ metamaterial and BP layers is proposed to realized large and tunable in-plane asymmetric spin splitting in the transmitted terahertz beam. The ENZ metamaterial acts as an optical cavity, resulting in an enhancement of light-matter interaction in BP layers. The BP layers can tune the asymmetric spin splitting via electron carrier density or angles between the incident plane and the armchair crystalline directions of BP layers.

2. Theory

Figure 1(a) shows the schematic of in-plane asymmetric spin splitting. An ENZ metamaterial is sandwiched by BP layers on both its top and bottom sides. The photonic property of BP layers can be described by surface conductivities. Under the Drude model, the conductivity along the armchair and zigzag crystalline directions are respectively [27,28]

σarm,zig=(iDarm,zig)/[π(ω+iη/)].
Here, Darm,zig = πe2ρ/marm,zig is the Drude weight with marm = ћ2/(2γ2+ ηc), mzig = ћ2/2vc being the electron mass along the armchair or zigzag directions respectively. Parameters η = 10 meV, γ = 4a/π eVm, Δ = 2eV, ηc = ћ2/0.4m0, vc = ћ2/1.4m0. The scale length of BP a = 0.223 nm. The electron carrier density ρ can be changed by electric doping via a bias voltage [21–23].

 

Fig. 1 (a) Schematic of in-plane asymmetric spin splitting. A horizontal incident polarization can be considered as a superposition of two opposite spin, which undergo displacements X ± along x-axis thus separate spatially, after transmitted through the BP-ENZ metamaterial-BP structure. The incident plane makes angles of ϕ1 and ϕ2 to the armchair axes of top and bottom BP layers, respectively. (b) A single BP layer surrounding by two dielectrics with refractive index of nj and nj+1. (c) A stack of N BP layers separated by different dielectrics.

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Owing to the in-plane anisotropy of BP layer, the transmission varies when the incident plane changes with respect to the BP structure. A rotation angle ϕ is introduced, which is the angle between the incident plane and the armchair axis of BP crystal. The rotation angle can be changed practically by rotating the device with fixed incident beams. As shown by [24], the crystalline axes can be determined by analyzing the reflection of normal incident visible light with a polarizer and a CCD. The armchair and zigzag axes of BP are associated with maximum and minimum brightness of R channel, respectively [24].

For a rotation angle of ϕ, the conductance matrix connecting the surface current and electric light field can be given by σ = [σxx, σxy; σyx, σyy], where σxx = σarmcos2ϕ + σzigsin2ϕ, σyy = σarmsin2ϕ + σzigcos2ϕ, and σyx = σxy = (σzig-σarm)sinϕcosϕ [27]. The cross conductivity σyx results from the in-plane anisotropic of BP, which vanishes for isotropic 2D materials such as graphene.

Transfer Matrix method is a powerful tool in the analysis of light propagation through layered media [29,30]. For dielectric media, the propagation of s and p waves are described by two 2 × 2 matrices independently. However, the cross conductivity of BP will induce a coupling between p and s waves. Therefore, a 4 × 4 matrix should be employed to describe the coupling.

Consider the propagation of light across an interface formed by a BP layer that separates two dielectrics with refractive indexes nj and nj+2, as shown by Fig. 1(b). The electric field in media j and j + 1 are respectively

El={[Alklzeikjzz-Blklzeiklzz]/kle^x+[Cleiklzz-Dleiklzz]e^y.l=j,j+1+[-Alklxeiklzz-Blklxeiklzz]/kle^z}eikxz
Al and Cl are the amplitudes of rightward waves, while Bl and Dl are of leftward waves. kx is the x component of wavevector, which is the same in different media. klz=[kl2kx2]1/2 with kl being the wavenumber in is the l medium. The electromagnetic boundary conditions at the interface between media j and j + 1 are
e^z×[EjEj+1]=0,
e^z×[HjHj+1]=σEj+1,
where Hj,j+1 are the magnetic field in media j and j + 1. By substituting Eq. (2) to Eq. (3), we have
[AjBj]kjz/kj=[Aj+1Bj+1]kj+1,z/kj+1,
Cj+Dj=Cj+1+Dj+1,
[CjDj]kjz/ωμ=[Cj+1Dj+1]kj+1,z/ωμ+σyy[Cj+1+Dj+1]+σyx[Aj+1Bj+1]kj+1,z/kj+1,
[Aj+Bj]kj/ωμ=[Aj+1+Bj+1]kj+1/ωμ+σxx[Aj+1Bj+1]kj+1,z/kj+1+σyx[Cj+1+Dj+1],
where ω and μ are circular frequency and permeability, respectively. Therefore, the transmission matrix for a dielectric interface containing BP layer is
Tj,j+1=[kj+1/kj+ηp+ξpσxxkj+1/kjηpξpσxxζpσxyζpσxykj+1/kjηp+ξpσxxkj+1/kj+ηp+ξpσxxζpσxyζpσxyζsσyxζsσyx1+ηs+ξsσyy1ηs+ξsσyyζsσyxζsσyx1ηsξsσyy1+ηsξsσyy],
where ηp=kjkj+1,z/kj+1kjz, ηs=kj+1,z/kjz, ξp=ωμkj+1,z/kj+1kj, ξp=ωμ/kjz,ζp=ωμ/kj,ζs=ωμkj+1,z/kjzkj+1. If the cross conductivities σxy and σyx vanish, the upper-right and lower-left parts of the transmission matrix vanish, thus the 4 × 4 transmission matrix can be rewritten into two 2 × 2 matrices, which connect Aj, Bj with Aj+1, Bj+1 and Cj, Dj with Cj+1, Dj+1, respectively.

As the photonic property of BP layers have been described by surface conductivities, the thicknesses of BP layers are neglected. The propagation matrix in a homogenous medium j with a thickness of dj is [29]

Pj=[eikjzdj0000eikjzdj0000eikjzdj0000eikjzdj].
For the stack of N BP layers shown in Fig. 1(c), the transfer matrix can be obtained by transmission and propagation matrices. Denote the electric field coefficients on left side of the first interface by A1, B1, C1, D1 and those on the right side of the end interface by AN+1, B N+1, CN+1, D N+1. These two sets of field coefficients are then related by a 4 × 4 transfer matrix M, namely,
[A1B1C1D1]=M[AN+1BN+1CN+1DN+1],
with M = T01P1T12P2TN-1,NP NTN,N+1. Equation (7) is the transfer matrix to describe the light propagation through layered media with BP. For a multilayer structure without BP, both the transmission and propagation matrices can be rewritten respectively into two 2 × 2 matrices, the final matrix M can be therefore reduced into two 2 × 2 independent matrices [30].

According to Eq. (7), the Fresnel transmission coefficients can be obtained. By setting C1 = BN + 1 = DN + 1 = 0, we have

tpp=AN+1A1=M33M11M33M13M31,
tsp=CN+1A1=M31M11M33M13M31,
Similarly, by setting A1 = BN + 1 = DN + 1 = 0, we have

tss=CN+1C1=M11M11M33M13M31,
tps=AN+1C1=M13M11M33M13M31,

In our case, two BP layers are considered. The electron carrier densities and rotation angles (Angle between the armchair axis of BP crystal and the xg-axis) of top and bottom BP layers are respectively ρ1, ϕ1 and ρ2, ϕ2, as shown in Fig. 1(a). The carrier densities are set to be the same, i.e., ρ1 = ρ2 = ρ, through the whole paper.

Considering a horizontally (H) polarized Gaussian incident beam tunneling through the BP multi-layer structure. The spectrum of incident beam isE˜i=exp[(kx2+ky2)w02/4]|H where w0 being the beam waist. According to [31,32], the transmitted spectrum can be given by E˜t=QE˜i. The transformation matrix Q can be expressed as

Q=[tpp+κxtpp'κyΙtps+κxtps'+κyΚtsp+κxtsp'+κyΚtss+κxtss'+κyΙ],
for the case with the same material in the first and last media. I = (tsp + tps)cotθ, K = (tpp-tss)cotθ, tij'are the first derivate of tij. κx,y = kx,y/k0 with k0 being the wavenumber in vacuum. In the circular polarization basis, the right- and left-handed circular polarization (RCP and LCP) components of the transmitted beams for H incident polarization are:
E˜t±=[(tpp+κxtpp'κyΙ)i(tsp+κxtsp'+κyΚ)]u˜0|±
The RCP and LCP components are no longer maintaining the Gaussian envelope, and their centroids may shift along x-axis. With respect to the geometric prediction, the centroid displacements can be defined as X±=E˜t±krxE˜t±|dkxdky/|E˜t±|2dkxdky [32]. After some straightforward calculation, we obtain
X±={Im[tpp*tpp'+tsp*tsp']±Re[tpp*tsp*tsp*tpp']}/k0W±,
where the energies of RCP and LCP components are
W±=|tpp|2+|tsp|2±2Im|tpp*tsp|+1k02w02{|tpp'|2+|tsp'|2±2Im|tpp'*tsp'|+|Κ|2+|Ι|22Im[Κ*Ι]}
The first term of Eq. (11) is the GH shift, moving the RCP and LCP components together. The second term is spin-dependent, shifting the two opposite spin components toward opposite directions. This spin dependent term vanishes for a vanishing tsp. Generally, the cooperation effect of the first and second terms will induce an asymmetric spin splitting.

3. Results and discussion

Firstly, we consider the case with the rotation angles of top and bottom BP layers being ϕ1 = ϕ2 = 0. Thus, the cross conductivities are zero, resulting in the vanishing of the spin-dependent term in Eq. (11). Therefore, the transmitted beam undergoes pure GH shift without spin splitting. Figure 2(a) shows the GH shifts changing with the incident angle θ for different carrier density ρ when the refractive index and thickness of ENZ metamaterial are n = 0.1 and d = 0.1 mm, respectively. Here, we focus our attention on the terahertz region by setting the frequency incident beam being 1 THz, since this region is underdeveloped but ripe for exploitation [33]. For each carrier density, the GH shift reaches a peak at θ = 6.12°. The peak GH shift increases with the carrier density, which is clearly shown by the blue line in Fig. 2(c). Thus, the GH shift can be enhanced by the BP layers, since ρ = 0 corresponds to the case without BP. At other incident angle such as θ = 3.5°, the GH shift may decreases with the carrier density.

 

Fig. 2 (a) GH shifts changing with the incident angle for the carrier density ρ = 0, 2.5, and 5 × 1017 m−2, and for (b) the refractive index of ENZ metamaterial n = 0.1, 0.2. 0.4, 0.6, respectively. (c,d) GH shifts changing with the carrier density ρ (c) and the metamaterial thickness d (d). In the calculation, the frequency of the incident beam is 1 THz.

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The GH shift depends on the refractive index n and thickness d of the ENZ metamaterial. As shown by Fig. 2(b), with the increase of n, the peak value of GH shift decreases and the peak position moves, indicating that a larger shift can be obtain by a smaller refractive index of the metamaterial. Figure 2(d) gives the GH shift increases monotonously with thickness d, when ρ = 5 × 1017m−2, θ = 6.12°.

By rotating the BP layer, the transmitted beam undergoes asymmetric spin splitting. The displacements of two opposite spin components of the transmitted beam are given in Fig. 3(a) as function of the incident angle when ϕ1 = ϕ2 = 45°, d = 4.2 μm, n = 0.1. In this special case, the displacements of RCP component X+ are almost vanish for all carrier densities. However, the displacements of LCP component X- can take large values. When the carrier density increases from 2 × 1017 to 5 × 1017m−2, the peak displacement decreases gradually, and change its sign at ρ = 4.7 × 1017m−2. Meanwhile, the peak position moves from 71.5° to 50.5° gradually. At the peak positions, owing to the strong light-interaction in BP layers, the transmission coefficients |tps| are almost identical with coefficients |tpp| (see Fig. 3(b)). And they are with nearly −90° phase difference (φ = arg[tpp/|tps]), as shown by Fig. 3(b). Therefore, the first three terms of W- in Eq. (12) almost vanishes, leading to large displacement in X-. The phenomenon was also found at air-chiral metamaterial interface [34].

 

Fig. 3 Displacements of two opposite spin components of the transmitted beam X+ (solid lines) and X- (dotted lines) (a), transmission coefficients |tpp| and |tps| (b), and phase difference φ = arg[tpp/|tps] (c) changing with the incident angle, respectively. In the calculation, d = 4.2 μm, n = 0.1, ϕ1 = ϕ2 = 45°.

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The refractive index and the thickness of the ENZ metamaterial affect the asymmetric spin splitting in the transmitted beam. Figures 4(a) and 4(b) show the displacements X ± changing with the incident angle θ for the refractive index n = 0.05, 0.1. 0.2 (a), and for n = 0.1, 0.1 + 0.01i, 0.1 + 0.1i(b), respectively. One can find from Fig. 4(a) that, the maximum value of displacements |X ± | as well as the maximum displacement difference |X+-X-| decreases with the increase of the real part of the refractive index Re[n]. Therefore, a near-zero permittivity can enhance the asymmetric spin splitting. The near-zero permittivity can be achieved by both artificial and natural materials. Polar dielectrics like LiF, NaCl, and GaAs are the natural terahertz ENZ materials with the real part of permittivity close to zero near the polaritonic resonance frequency [35]. Effective terahertz ENZ materials have been realized by rectangular waveguide [36], graphene-dielectric composite structure [37], etc.

 

Fig. 4 Displacements of two opposite spin components X ± changing with the incident angle θ for the refractive index of ENZ metamaterial n = 0.05, 0.1. 0.2 (a), and for n = 0.1, 0.1 + 0.01i, 0.1 + 0.1i (b), respectively. (c) X ± changing with the metamaterial thickness d for different θ. In the calculation, ϕ1 = ϕ2 = 45°.

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The loss of the metamaterial can be described by the image part of the refractive index Im[n] [18]. As shown by Fig. 4(a), Im[n] will reduce the displacements X ± . However, for the Im[n] smaller than 0.01, the displacements X ± are almost unchanged. Figure 4(c) shows the displacements X ± changing with the metamaterial thickness d when n = 0.1. The displacements X ± will approach to asymptotic values when the thickness d increases. For a larger incident angle, both X+ and X- possess a sharper peak.

The asymmetric spin splitting in the transmitted beam depends strongly on the rotation angle of BP layers, as shown in Fig. 5. In Fig. 5, the rotation angles of the top and bottom layers are equal, i.e., ϕ = ϕ1 = ϕ2. The displacements X+ and X- are mirror symmetric about ϕ = 90°. The displacements of the RCP component X+ takes large values ϕ>90°, while X- for ϕ<90° . When θ = 44°, X+ has a positive peak, and become two positive peaks for θ = 47°. When θ>50°, a positive and a negative peaks can be found in the pattern of X+. And distance between this two peaks enlarges with the increase of the incident angle θ.

 

Fig. 5 Displacements X ± as functions of the rotation angle ϕ, where ϕ = ϕ1 = ϕ2·. The other parameters are the same as Fig. 3.

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In the above case, one spin component has large displacement while the other almost vanishes. Figure 6(a) gives the displacements X ± changing with the incident angle for the thickness d = 0.15 mm the carrier density ρ = 0 and 5 × 1017m−2, respectively. Without BP layers (ρ = 0), X+ and X- coincide each other. When ρ = 5 × 1017m−2, however, X+ and X- are different excepting for ϕ = 0, 90°, or 180°. At these three angles, the two opposite spin components of the transmitted beam do not split. However, the two spin components may split if the incident beam is elliptically polarized [4]. At θ = 6.21°, both X+ and X- are positive. However, X+ and X- are opposite in sign at θ = 11.5°. Figures 6(b) and 6(c) show the displacements X ± changing with the rotation angle for θ = 6.21° and 11.5°, respectively. The displacements vary with rotation angle flexibly.

 

Fig. 6 Displacements X ± as functions of the incident angle θ for ρ = 0 and 5 × 1017m−2, when d = 0.15 mm, ϕ1 = ϕ2 = 45° (a). X ± changing with the rotation angle ϕ (ϕ = ϕ1 = ϕ2) for θ = 6.21° (b) and 11.50° (c), respectively. The inset in (b) shows the rotation of BP-metamaterial structure. Schematics of barcode encryption based on the asymmetric spin splitting are also shown by choosing the threshold as 0 (b) and 1.8 mm (c), respectively.

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The asymmetric displacements for LCP and RCP components of the transmitted beam along x-axis can be regarded as two independent channels for information processing [27]. The centroid displacements larger than a certain threshold value can be considered as “1”, while smaller than that value as “0”. The encoding rule varies with the choice of the threshold values. For the case of θ = 11.5°, three different codes: “11”, “10”, “01” can be obtained by tuning the rotation angle with a threshold of 0. All four different codes: “11”, “10”, “01”, “00” are found for the case of θ = 6.21° with a threshold of 1.8 mm. This is comparing to best three different codes in [27] and [38].

Twisted bilayer graphene have attracted much attention recently owing to its unconventional superconductivity at the magic-angle [39]. When the rotation angles of the top and bottom BP layers are different, the transmitted beam shows interesting spin splitting phenomena. Figure 7 shows the displacements X ± as functions of ϕ1 and ϕ2 when θ = 14.14° and d = 0.15 mm. X+ and X- are almost symmetric about the centroid point of (ϕ1,ϕ2) = (90°,90°). Both X+ and X- will change sign when ϕ2 crosses 90°. With the change of ϕ1, only the magnitude of X ± will change.

 

Fig. 7 Displacements X+ (a) and X- (b) as functions the rotation angles ϕ1 and ϕ2 when θ = 14.14°, d = 0.15 mm, ρ = 5 × 1017m−2.

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Figure 8 shows Displacements X ± changing with the rotation angle ϕ2 for different ϕ1 when θ = 10° (a), 20° (b),30° (c), respectively. When θ = 10°, there is one peaks for X ± in the ϕ2 region of 0-90°. When θ = 20° and 30°, the X- become two peaks in the same region, while the X+ are nearly flat.

 

Fig. 8 Displacements X+ (solid lines) and X- (dotted lines) changing with the rotation angle ϕ2 for different ϕ1 and θ, when d = 0.05 mm, ρ = 5 × 1017m−2.

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The ENZ metamaterials sandwiched with BP layers show unique photonic spin splitting effect. Although the CVD growth of 2D black phosphorus film has been demonstrated in 2016, the large-scale of monolayer BP is still challenge [40]. Hopeful methods have been proposed recently to address this challenge [41]. The unique photonic spin splitting effect based on BP can be readily extended to other anisotropic 2D materials such as ReSe2 and ReS2, for which high quality large-scale atomic films are well reachable [42].

4. Conclusions

In conclusion, we have extended the transformation matrix to describe the propagation in a multi-layer dielectric stack containing BP layers. A novel air-BP-metamaterial-BP-air structure is proposed to enhance the in-plane photonic spin splitting effect. The transmitted beam through the structure undergoes asymmetric spin splitting due to the strong in-plane anisotropy of BP layers. The asymmetric splitting depends strongly on the rotation angles of BP layers, namely, ϕ1 and ϕ2. However, only the GH shift occurs without spin splitting for ϕ1 = ϕ2 = 0 or 90°. Based on the tunable asymmetric spin splitting, a two-channel angle-resolved barcode encoding is achieved. The photonic spin splitting effect in BP layers promises novel angle-resolved optoelectronic devices in the Terahertz region.

Funding

National Natural Science Foundation of China (61705086, 61675092, 61475066); Natural Science Foundation of Guangdong Province (2017A030313375, 2016TQ03X962, 2017A010102006, 2016A030311019, 2016A030313079, 2017A030313359); Science & Technology Project of Guangzhou (201803020023, 201707010396, 201704030105, 201605030002, 201604040005).

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23. B. Deng, R. Frisenda, C. Li, X. Chen, A. Castellanos-Gomez, and F. Xia, “Progress on Black Phosphorus Photonics,” Adv. Opt. Mater. 6(19), 1800365 (2018). [CrossRef]  

24. N. Mao, J. Tang, L. Xie, J. Wu, B. Han, J. Lin, S. Deng, W. Ji, H. Xu, K. Liu, L. Tong, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016). [CrossRef]   [PubMed]  

25. Y. Wang, F. Zhang, X. Tang, X. Chen, Y. Chen, W. Huang, Z. Liang, L. Wu, Y. Ge, Y. Song, J. Liu, D. Zhang, J. Li, and H. Zhang, “All-Optical Phosphorene Phase Modulator with Enhanced Stability Under Ambient Conditions,” Laser Photonics Rev. 12(6), 1800016 (2018). [CrossRef]  

26. W. Shu, J. Zhang, H. Luo, S. Chen, W. Zhang, W. Wu, S. Wen, and X. Ling, “Photonic spin Hall effect on the surface of anisotropic two-dimensional atomic crystals,” Photon. Res. 6(6), 511 (2018). [CrossRef]  

27. 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]  

28. T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014). [CrossRef]   [PubMed]  

29. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. New York, (Oxford University, 2007).

30. T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013). [CrossRef]   [PubMed]  

31. M. Liu, L. Cai, S. Chen, Y. Liu, H. Luo, and S. Wen, “Strong spin-orbit interaction of light on the surface of atomically thin crystals,” Phys. Rev. A (Coll. Park) 95(6), 063827 (2017). [CrossRef]  

32. K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013). [CrossRef]  

33. X. Zhang, A. Shkurinov, and Y. Zhang, “Extreme terahertz science,” Nat. Photonics 11(1), 16–18 (2017). [CrossRef]  

34. M. Jiang, H. Lin, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, and Z. Chen, “Chirality induced asymmetric spin splitting of light beams reflected from an air-chiral interface,” Opt. Express 26(6), 6593–6601 (2018). [CrossRef]   [PubMed]  

35. M. Kafesaki, A. A. Basharin, E. N. Economou, and C. M. Soukoulis, “THz metamaterials made of phonon-polariton materials,” Photon. Nanostructures 12(4), 376–386 (2014). [CrossRef]  

36. V. Pacheco-Peña, N. Engheta, S. Kuznetsov, A. Gentselev, and M. Beruete, “Experimental Realization of an Epsilon-Near-Zero Graded-Index Metalens at Terahertz Frequencies,” Phys. Rev. Appl. 8(3), 034036 (2017). [CrossRef]  

37. M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-Dielectric Composite Metamaterials: Evolution from Elliptic to Hyperbolic Wavevector Dispersion and The Transverse Epsilon-Near-Zero Condition,” Nanophotonics 7(1), 073089 (2013). [CrossRef]  

38. 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), 201701212 (2018). [CrossRef]  

39. Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, “Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices,” Nature 556(7699), 80–84 (2018). [CrossRef]   [PubMed]  

40. J. B. Smith, D. Hagaman, and H. F. Ji, “Growth of 2D black phosphorus film from chemical vapor deposition,” Nanotechnology 27(21), 215602 (2016). [CrossRef]   [PubMed]  

41. T. Niu, “New properties with old materials: Layered black phosphorous,” Nano Today 12, 7–9 (2017). [CrossRef]  

42. A. Dathbun, Y. Kim, S. Kim, Y. Yoo, M. S. Kang, C. Lee, and J. H. Cho, “Large-Area CVD-Grown Sub-2 V ReS2 Transistors and Logic Gates,” Nano Lett. 17(5), 2999–3005 (2017). [CrossRef]   [PubMed]  

References

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  1. O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
    [Crossref] [PubMed]
  2. K. Y. Bliokh, C. T. Samlan, C. Prajapati, G. Puentes, N. K. Viswanathan, and F. Nori, “Spin - Hall effect and circular birefringence of a uniaxial crystal plate,” optia 3, 1039 (2016).
    [Crossref]
  3. 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(6), 1018–1021 (2015).
    [Crossref] [PubMed]
  4. 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(1), 1150 (2017).
    [Crossref] [PubMed]
  5. X. Zhou, L. Sheng, and X. Ling, “Photonic spin Hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
    [Crossref] [PubMed]
  6. X. Zhou, Z. Xiao, H. Luo, S. Wen, Z. Xiao, Z. H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012).
    [Crossref]
  7. X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
    [Crossref]
  8. 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] [PubMed]
  9. J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
    [Crossref]
  10. X. Zhou, L. Xie, X. Ling, S. Cheng, Z. Zhang, H. Luo, and H. Sun, “Large in-plane asymmetric spin angular shifts of a light beam near the critical angle,” Opt. Lett. 44(2), 207–210 (2019).
    [Crossref] [PubMed]
  11. A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and lectromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B Condens. Matter Mater. Phys. 75(15), 155410 (2007).
    [Crossref]
  12. I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
    [Crossref]
  13. L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017).
    [Crossref]
  14. M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
    [Crossref] [PubMed]
  15. A. V. Chebykin, A. A. Orlov, A. S. Shalin, A. N. Poddubny, and P. A. Belov, “Strong Purcell effect in anisotropic ε-near-zero metamaterials,” Phys. Rev. B Condens. Matter Mater. Phys. 91(20), 205126 (2015).
    [Crossref]
  16. I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
    [Crossref] [PubMed]
  17. X. Niu, X. Hu, S. Chu, and Q. Gong, “Epsilon-Near-Zero Photonics: A New Platform for Integrated Devices,” Adv. Opt. Mater. 6(10), 1701292 (2018).
    [Crossref]
  18. Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5(1), 8681 (2015).
    [Crossref] [PubMed]
  19. W. Zhu and W. She, “Enhanced spin Hall effect of transmitted light through a thin epsilon-near-zero slab,” Opt. Lett. 40(13), 2961–2964 (2015).
    [Crossref] [PubMed]
  20. M. Jiang, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Giant spin splitting induced by orbital angular momentum in an epsilon-near-zero metamaterial slab,” Opt. Lett. 42(17), 3259–3262 (2017).
    [Crossref] [PubMed]
  21. X. Wang and S. Lan, “Optical properties of black phosphorus,” Adv. Opt. Photonics 8(4), 618 (2016).
    [Crossref]
  22. R. Peng, K. Khaliji, N. Youngblood, R. Grassi, T. Low, and M. Li, “Midinfrared Electro-optic Modulation in Few-Layer Black Phosphorus,” Nano Lett. 17(10), 6315–6320 (2017).
    [Crossref] [PubMed]
  23. B. Deng, R. Frisenda, C. Li, X. Chen, A. Castellanos-Gomez, and F. Xia, “Progress on Black Phosphorus Photonics,” Adv. Opt. Mater. 6(19), 1800365 (2018).
    [Crossref]
  24. N. Mao, J. Tang, L. Xie, J. Wu, B. Han, J. Lin, S. Deng, W. Ji, H. Xu, K. Liu, L. Tong, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016).
    [Crossref] [PubMed]
  25. Y. Wang, F. Zhang, X. Tang, X. Chen, Y. Chen, W. Huang, Z. Liang, L. Wu, Y. Ge, Y. Song, J. Liu, D. Zhang, J. Li, and H. Zhang, “All-Optical Phosphorene Phase Modulator with Enhanced Stability Under Ambient Conditions,” Laser Photonics Rev. 12(6), 1800016 (2018).
    [Crossref]
  26. W. Shu, J. Zhang, H. Luo, S. Chen, W. Zhang, W. Wu, S. Wen, and X. Ling, “Photonic spin Hall effect on the surface of anisotropic two-dimensional atomic crystals,” Photon. Res. 6(6), 511 (2018).
    [Crossref]
  27. 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]
  28. T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
    [Crossref] [PubMed]
  29. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. New York, (Oxford University, 2007).
  30. T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
    [Crossref] [PubMed]
  31. M. Liu, L. Cai, S. Chen, Y. Liu, H. Luo, and S. Wen, “Strong spin-orbit interaction of light on the surface of atomically thin crystals,” Phys. Rev. A (Coll. Park) 95(6), 063827 (2017).
    [Crossref]
  32. K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
    [Crossref]
  33. X. Zhang, A. Shkurinov, and Y. Zhang, “Extreme terahertz science,” Nat. Photonics 11(1), 16–18 (2017).
    [Crossref]
  34. M. Jiang, H. Lin, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, and Z. Chen, “Chirality induced asymmetric spin splitting of light beams reflected from an air-chiral interface,” Opt. Express 26(6), 6593–6601 (2018).
    [Crossref] [PubMed]
  35. M. Kafesaki, A. A. Basharin, E. N. Economou, and C. M. Soukoulis, “THz metamaterials made of phonon-polariton materials,” Photon. Nanostructures 12(4), 376–386 (2014).
    [Crossref]
  36. V. Pacheco-Peña, N. Engheta, S. Kuznetsov, A. Gentselev, and M. Beruete, “Experimental Realization of an Epsilon-Near-Zero Graded-Index Metalens at Terahertz Frequencies,” Phys. Rev. Appl. 8(3), 034036 (2017).
    [Crossref]
  37. M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-Dielectric Composite Metamaterials: Evolution from Elliptic to Hyperbolic Wavevector Dispersion and The Transverse Epsilon-Near-Zero Condition,” Nanophotonics 7(1), 073089 (2013).
    [Crossref]
  38. 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), 201701212 (2018).
    [Crossref]
  39. Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, “Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices,” Nature 556(7699), 80–84 (2018).
    [Crossref] [PubMed]
  40. J. B. Smith, D. Hagaman, and H. F. Ji, “Growth of 2D black phosphorus film from chemical vapor deposition,” Nanotechnology 27(21), 215602 (2016).
    [Crossref] [PubMed]
  41. T. Niu, “New properties with old materials: Layered black phosphorous,” Nano Today 12, 7–9 (2017).
    [Crossref]
  42. A. Dathbun, Y. Kim, S. Kim, Y. Yoo, M. S. Kang, C. Lee, and J. H. Cho, “Large-Area CVD-Grown Sub-2 V ReS2 Transistors and Logic Gates,” Nano Lett. 17(5), 2999–3005 (2017).
    [Crossref] [PubMed]

2019 (1)

2018 (9)

X. Niu, X. Hu, S. Chu, and Q. Gong, “Epsilon-Near-Zero Photonics: A New Platform for Integrated Devices,” Adv. Opt. Mater. 6(10), 1701292 (2018).
[Crossref]

X. Zhou, L. Sheng, and X. Ling, “Photonic spin Hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
[Crossref] [PubMed]

Y. Wang, F. Zhang, X. Tang, X. Chen, Y. Chen, W. Huang, Z. Liang, L. Wu, Y. Ge, Y. Song, J. Liu, D. Zhang, J. Li, and H. Zhang, “All-Optical Phosphorene Phase Modulator with Enhanced Stability Under Ambient Conditions,” Laser Photonics Rev. 12(6), 1800016 (2018).
[Crossref]

W. Shu, J. Zhang, H. Luo, S. Chen, W. Zhang, W. Wu, S. Wen, and X. Ling, “Photonic spin Hall effect on the surface of anisotropic two-dimensional atomic crystals,” Photon. Res. 6(6), 511 (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]

B. Deng, R. Frisenda, C. Li, X. Chen, A. Castellanos-Gomez, and F. Xia, “Progress on Black Phosphorus Photonics,” Adv. Opt. Mater. 6(19), 1800365 (2018).
[Crossref]

M. Jiang, H. Lin, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, and Z. Chen, “Chirality induced asymmetric spin splitting of light beams reflected from an air-chiral interface,” Opt. Express 26(6), 6593–6601 (2018).
[Crossref] [PubMed]

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), 201701212 (2018).
[Crossref]

Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, “Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices,” Nature 556(7699), 80–84 (2018).
[Crossref] [PubMed]

2017 (11)

T. Niu, “New properties with old materials: Layered black phosphorous,” Nano Today 12, 7–9 (2017).
[Crossref]

A. Dathbun, Y. Kim, S. Kim, Y. Yoo, M. S. Kang, C. Lee, and J. H. Cho, “Large-Area CVD-Grown Sub-2 V ReS2 Transistors and Logic Gates,” Nano Lett. 17(5), 2999–3005 (2017).
[Crossref] [PubMed]

X. Zhang, A. Shkurinov, and Y. Zhang, “Extreme terahertz science,” Nat. Photonics 11(1), 16–18 (2017).
[Crossref]

V. Pacheco-Peña, N. Engheta, S. Kuznetsov, A. Gentselev, and M. Beruete, “Experimental Realization of an Epsilon-Near-Zero Graded-Index Metalens at Terahertz Frequencies,” Phys. Rev. Appl. 8(3), 034036 (2017).
[Crossref]

M. Liu, L. Cai, S. Chen, Y. Liu, H. Luo, and S. Wen, “Strong spin-orbit interaction of light on the surface of atomically thin crystals,” Phys. Rev. A (Coll. Park) 95(6), 063827 (2017).
[Crossref]

M. Jiang, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Giant spin splitting induced by orbital angular momentum in an epsilon-near-zero metamaterial slab,” Opt. Lett. 42(17), 3259–3262 (2017).
[Crossref] [PubMed]

I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
[Crossref] [PubMed]

R. Peng, K. Khaliji, N. Youngblood, R. Grassi, T. Low, and M. Li, “Midinfrared Electro-optic Modulation in Few-Layer Black Phosphorus,” Nano Lett. 17(10), 6315–6320 (2017).
[Crossref] [PubMed]

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(1), 1150 (2017).
[Crossref] [PubMed]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017).
[Crossref]

2016 (4)

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

X. Wang and S. Lan, “Optical properties of black phosphorus,” Adv. Opt. Photonics 8(4), 618 (2016).
[Crossref]

N. Mao, J. Tang, L. Xie, J. Wu, B. Han, J. Lin, S. Deng, W. Ji, H. Xu, K. Liu, L. Tong, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016).
[Crossref] [PubMed]

J. B. Smith, D. Hagaman, and H. F. Ji, “Growth of 2D black phosphorus film from chemical vapor deposition,” Nanotechnology 27(21), 215602 (2016).
[Crossref] [PubMed]

2015 (4)

A. V. Chebykin, A. A. Orlov, A. S. Shalin, A. N. Poddubny, and P. A. Belov, “Strong Purcell effect in anisotropic ε-near-zero metamaterials,” Phys. Rev. B Condens. Matter Mater. Phys. 91(20), 205126 (2015).
[Crossref]

Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5(1), 8681 (2015).
[Crossref] [PubMed]

W. Zhu and W. She, “Enhanced spin Hall effect of transmitted light through a thin epsilon-near-zero slab,” Opt. Lett. 40(13), 2961–2964 (2015).
[Crossref] [PubMed]

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(6), 1018–1021 (2015).
[Crossref] [PubMed]

2014 (2)

M. Kafesaki, A. A. Basharin, E. N. Economou, and C. M. Soukoulis, “THz metamaterials made of phonon-polariton materials,” Photon. Nanostructures 12(4), 376–386 (2014).
[Crossref]

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

2013 (3)

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-Dielectric Composite Metamaterials: Evolution from Elliptic to Hyperbolic Wavevector Dispersion and The Transverse Epsilon-Near-Zero Condition,” Nanophotonics 7(1), 073089 (2013).
[Crossref]

K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

2012 (3)

J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, S. Wen, Z. Xiao, Z. H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012).
[Crossref]

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

2008 (1)

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

2007 (1)

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and lectromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B Condens. Matter Mater. Phys. 75(15), 155410 (2007).
[Crossref]

2006 (1)

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] [PubMed]

Aiello, A.

K. Y. Bliokh and A. Aiello, “Goos–Hänchen and Imbert–Fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

Alam, M. Z.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

Alù, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and lectromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B Condens. Matter Mater. Phys. 75(15), 155410 (2007).
[Crossref]

Ashoori, R. C.

Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, “Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices,” Nature 556(7699), 80–84 (2018).
[Crossref] [PubMed]

Avouris, P.

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

Basharin, A. A.

M. Kafesaki, A. A. Basharin, E. N. Economou, and C. M. Soukoulis, “THz metamaterials made of phonon-polariton materials,” Photon. Nanostructures 12(4), 376–386 (2014).
[Crossref]

Belov, P. A.

A. V. Chebykin, A. A. Orlov, A. S. Shalin, A. N. Poddubny, and P. A. Belov, “Strong Purcell effect in anisotropic ε-near-zero metamaterials,” Phys. Rev. B Condens. Matter Mater. Phys. 91(20), 205126 (2015).
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V. Pacheco-Peña, N. Engheta, S. Kuznetsov, A. Gentselev, and M. Beruete, “Experimental Realization of an Epsilon-Near-Zero Graded-Index Metalens at Terahertz Frequencies,” Phys. Rev. Appl. 8(3), 034036 (2017).
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M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
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Cai, L.

M. Liu, L. Cai, S. Chen, Y. Liu, H. Luo, and S. Wen, “Strong spin-orbit interaction of light on the surface of atomically thin crystals,” Phys. Rev. A (Coll. Park) 95(6), 063827 (2017).
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Cao, Y.

Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, “Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices,” Nature 556(7699), 80–84 (2018).
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Capolino, F.

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-Dielectric Composite Metamaterials: Evolution from Elliptic to Hyperbolic Wavevector Dispersion and The Transverse Epsilon-Near-Zero Condition,” Nanophotonics 7(1), 073089 (2013).
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Castellanos-Gomez, A.

B. Deng, R. Frisenda, C. Li, X. Chen, A. Castellanos-Gomez, and F. Xia, “Progress on Black Phosphorus Photonics,” Adv. Opt. Mater. 6(19), 1800365 (2018).
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Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5(1), 8681 (2015).
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A. V. Chebykin, A. A. Orlov, A. S. Shalin, A. N. Poddubny, and P. A. Belov, “Strong Purcell effect in anisotropic ε-near-zero metamaterials,” Phys. Rev. B Condens. Matter Mater. Phys. 91(20), 205126 (2015).
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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).
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Y. Xu, C. T. Chan, and H. Chen, “Goos-Hänchen effect in epsilon-near-zero metamaterials,” Sci. Rep. 5(1), 8681 (2015).
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W. Shu, J. Zhang, H. Luo, S. Chen, W. Zhang, W. Wu, S. Wen, and X. Ling, “Photonic spin Hall effect on the surface of anisotropic two-dimensional atomic crystals,” Photon. Res. 6(6), 511 (2018).
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M. Liu, L. Cai, S. Chen, Y. Liu, H. Luo, and S. Wen, “Strong spin-orbit interaction of light on the surface of atomically thin crystals,” Phys. Rev. A (Coll. Park) 95(6), 063827 (2017).
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Y. Wang, F. Zhang, X. Tang, X. Chen, Y. Chen, W. Huang, Z. Liang, L. Wu, Y. Ge, Y. Song, J. Liu, D. Zhang, J. Li, and H. Zhang, “All-Optical Phosphorene Phase Modulator with Enhanced Stability Under Ambient Conditions,” Laser Photonics Rev. 12(6), 1800016 (2018).
[Crossref]

B. Deng, R. Frisenda, C. Li, X. Chen, A. Castellanos-Gomez, and F. Xia, “Progress on Black Phosphorus Photonics,” Adv. Opt. Mater. 6(19), 1800365 (2018).
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Chen, Y.

Y. Wang, F. Zhang, X. Tang, X. Chen, Y. Chen, W. Huang, Z. Liang, L. Wu, Y. Ge, Y. Song, J. Liu, D. Zhang, J. Li, and H. Zhang, “All-Optical Phosphorene Phase Modulator with Enhanced Stability Under Ambient Conditions,” Laser Photonics Rev. 12(6), 1800016 (2018).
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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).
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M. Jiang, H. Lin, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, and Z. Chen, “Chirality induced asymmetric spin splitting of light beams reflected from an air-chiral interface,” Opt. Express 26(6), 6593–6601 (2018).
[Crossref] [PubMed]

M. Jiang, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Giant spin splitting induced by orbital angular momentum in an epsilon-near-zero metamaterial slab,” Opt. Lett. 42(17), 3259–3262 (2017).
[Crossref] [PubMed]

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(1), 1150 (2017).
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Cheng, S.

Cho, J. H.

A. Dathbun, Y. Kim, S. Kim, Y. Yoo, M. S. Kang, C. Lee, and J. H. Cho, “Large-Area CVD-Grown Sub-2 V ReS2 Transistors and Logic Gates,” Nano Lett. 17(5), 2999–3005 (2017).
[Crossref] [PubMed]

Chu, S.

X. Niu, X. Hu, S. Chu, and Q. Gong, “Epsilon-Near-Zero Photonics: A New Platform for Integrated Devices,” Adv. Opt. Mater. 6(10), 1701292 (2018).
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Córdova-Castro, R. M.

L. H. Nicholls, F. J. Rodríguez-Fortuño, M. E. Nasir, R. M. Córdova-Castro, N. Olivier, G. A. Wurtz, and A. V. Zayats, “Ultrafast synthesis and switching of light polarization in nonlinear anisotropic metamaterials,” Nat. Photonics 11(10), 628–633 (2017).
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Dai, Y.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
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Dathbun, A.

A. Dathbun, Y. Kim, S. Kim, Y. Yoo, M. S. Kang, C. Lee, and J. H. Cho, “Large-Area CVD-Grown Sub-2 V ReS2 Transistors and Logic Gates,” Nano Lett. 17(5), 2999–3005 (2017).
[Crossref] [PubMed]

De Leon, I.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

Demir, A.

Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, “Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices,” Nature 556(7699), 80–84 (2018).
[Crossref] [PubMed]

Deng, B.

B. Deng, R. Frisenda, C. Li, X. Chen, A. Castellanos-Gomez, and F. Xia, “Progress on Black Phosphorus Photonics,” Adv. Opt. Mater. 6(19), 1800365 (2018).
[Crossref]

Deng, S.

N. Mao, J. Tang, L. Xie, J. Wu, B. Han, J. Lin, S. Deng, W. Ji, H. Xu, K. Liu, L. Tong, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016).
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J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
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Du, J.

Economou, E. N.

M. Kafesaki, A. A. Basharin, E. N. Economou, and C. M. Soukoulis, “THz metamaterials made of phonon-polariton materials,” Photon. Nanostructures 12(4), 376–386 (2014).
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I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
[Crossref] [PubMed]

Engheta, N.

I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
[Crossref] [PubMed]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

V. Pacheco-Peña, N. Engheta, S. Kuznetsov, A. Gentselev, and M. Beruete, “Experimental Realization of an Epsilon-Near-Zero Graded-Index Metalens at Terahertz Frequencies,” Phys. Rev. Appl. 8(3), 034036 (2017).
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A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and lectromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B Condens. Matter Mater. Phys. 75(15), 155410 (2007).
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Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, “Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices,” Nature 556(7699), 80–84 (2018).
[Crossref] [PubMed]

Fatemi, V.

Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, “Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices,” Nature 556(7699), 80–84 (2018).
[Crossref] [PubMed]

Frisenda, R.

B. Deng, R. Frisenda, C. Li, X. Chen, A. Castellanos-Gomez, and F. Xia, “Progress on Black Phosphorus Photonics,” Adv. Opt. Mater. 6(19), 1800365 (2018).
[Crossref]

Gao, F.

Ge, Y.

Y. Wang, F. Zhang, X. Tang, X. Chen, Y. Chen, W. Huang, Z. Liang, L. Wu, Y. Ge, Y. Song, J. Liu, D. Zhang, J. Li, and H. Zhang, “All-Optical Phosphorene Phase Modulator with Enhanced Stability Under Ambient Conditions,” Laser Photonics Rev. 12(6), 1800016 (2018).
[Crossref]

Gentselev, A.

V. Pacheco-Peña, N. Engheta, S. Kuznetsov, A. Gentselev, and M. Beruete, “Experimental Realization of an Epsilon-Near-Zero Graded-Index Metalens at Terahertz Frequencies,” Phys. Rev. Appl. 8(3), 034036 (2017).
[Crossref]

Gong, Q.

X. Niu, X. Hu, S. Chu, and Q. Gong, “Epsilon-Near-Zero Photonics: A New Platform for Integrated Devices,” Adv. Opt. Mater. 6(10), 1701292 (2018).
[Crossref]

Götte, J. B.

J. B. Götte and M. R. Dennis, “Generalized shifts and weak values for polarization components of reflected light beams,” New J. Phys. 14(7), 073016 (2012).
[Crossref]

Grassi, R.

R. Peng, K. Khaliji, N. Youngblood, R. Grassi, T. Low, and M. Li, “Midinfrared Electro-optic Modulation in Few-Layer Black Phosphorus,” Nano Lett. 17(10), 6315–6320 (2017).
[Crossref] [PubMed]

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]

M. Jiang, H. Lin, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, and Z. Chen, “Chirality induced asymmetric spin splitting of light beams reflected from an air-chiral interface,” Opt. Express 26(6), 6593–6601 (2018).
[Crossref] [PubMed]

M. Jiang, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Giant spin splitting induced by orbital angular momentum in an epsilon-near-zero metamaterial slab,” Opt. Lett. 42(17), 3259–3262 (2017).
[Crossref] [PubMed]

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(1), 1150 (2017).
[Crossref] [PubMed]

Guclu, C.

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-Dielectric Composite Metamaterials: Evolution from Elliptic to Hyperbolic Wavevector Dispersion and The Transverse Epsilon-Near-Zero Condition,” Nanophotonics 7(1), 073089 (2013).
[Crossref]

Guinea, F.

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
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Hagaman, D.

J. B. Smith, D. Hagaman, and H. F. Ji, “Growth of 2D black phosphorus film from chemical vapor deposition,” Nanotechnology 27(21), 215602 (2016).
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Han, B.

N. Mao, J. Tang, L. Xie, J. Wu, B. Han, J. Lin, S. Deng, W. Ji, H. Xu, K. Liu, L. Tong, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016).
[Crossref] [PubMed]

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] [PubMed]

Hu, X.

X. Niu, X. Hu, S. Chu, and Q. Gong, “Epsilon-Near-Zero Photonics: A New Platform for Integrated Devices,” Adv. Opt. Mater. 6(10), 1701292 (2018).
[Crossref]

Huang, W.

Y. Wang, F. Zhang, X. Tang, X. Chen, Y. Chen, W. Huang, Z. Liang, L. Wu, Y. Ge, Y. Song, J. Liu, D. Zhang, J. Li, and H. Zhang, “All-Optical Phosphorene Phase Modulator with Enhanced Stability Under Ambient Conditions,” Laser Photonics Rev. 12(6), 1800016 (2018).
[Crossref]

Jarillo-Herrero, P.

Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, “Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices,” Nature 556(7699), 80–84 (2018).
[Crossref] [PubMed]

Ji, H. F.

J. B. Smith, D. Hagaman, and H. F. Ji, “Growth of 2D black phosphorus film from chemical vapor deposition,” Nanotechnology 27(21), 215602 (2016).
[Crossref] [PubMed]

Ji, W.

N. Mao, J. Tang, L. Xie, J. Wu, B. Han, J. Lin, S. Deng, W. Ji, H. Xu, K. Liu, L. Tong, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016).
[Crossref] [PubMed]

Jiang, M.

Kafesaki, M.

M. Kafesaki, A. A. Basharin, E. N. Economou, and C. M. Soukoulis, “THz metamaterials made of phonon-polariton materials,” Photon. Nanostructures 12(4), 376–386 (2014).
[Crossref]

Kang, M. S.

A. Dathbun, Y. Kim, S. Kim, Y. Yoo, M. S. Kang, C. Lee, and J. H. Cho, “Large-Area CVD-Grown Sub-2 V ReS2 Transistors and Logic Gates,” Nano Lett. 17(5), 2999–3005 (2017).
[Crossref] [PubMed]

Kaxiras, E.

Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, “Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices,” Nature 556(7699), 80–84 (2018).
[Crossref] [PubMed]

Khaliji, K.

R. Peng, K. Khaliji, N. Youngblood, R. Grassi, T. Low, and M. Li, “Midinfrared Electro-optic Modulation in Few-Layer Black Phosphorus,” Nano Lett. 17(10), 6315–6320 (2017).
[Crossref] [PubMed]

Kim, S.

A. Dathbun, Y. Kim, S. Kim, Y. Yoo, M. S. Kang, C. Lee, and J. H. Cho, “Large-Area CVD-Grown Sub-2 V ReS2 Transistors and Logic Gates,” Nano Lett. 17(5), 2999–3005 (2017).
[Crossref] [PubMed]

Kim, Y.

A. Dathbun, Y. Kim, S. Kim, Y. Yoo, M. S. Kang, C. Lee, and J. H. Cho, “Large-Area CVD-Grown Sub-2 V ReS2 Transistors and Logic Gates,” Nano Lett. 17(5), 2999–3005 (2017).
[Crossref] [PubMed]

Kuznetsov, S.

V. Pacheco-Peña, N. Engheta, S. Kuznetsov, A. Gentselev, and M. Beruete, “Experimental Realization of an Epsilon-Near-Zero Graded-Index Metalens at Terahertz Frequencies,” Phys. Rev. Appl. 8(3), 034036 (2017).
[Crossref]

Kwiat, P.

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

Lan, S.

X. Wang and S. Lan, “Optical properties of black phosphorus,” Adv. Opt. Photonics 8(4), 618 (2016).
[Crossref]

Lee, C.

A. Dathbun, Y. Kim, S. Kim, Y. Yoo, M. S. Kang, C. Lee, and J. H. Cho, “Large-Area CVD-Grown Sub-2 V ReS2 Transistors and Logic Gates,” Nano Lett. 17(5), 2999–3005 (2017).
[Crossref] [PubMed]

Li, C.

B. Deng, R. Frisenda, C. Li, X. Chen, A. Castellanos-Gomez, and F. Xia, “Progress on Black Phosphorus Photonics,” Adv. Opt. Mater. 6(19), 1800365 (2018).
[Crossref]

Li, J.

Y. Wang, F. Zhang, X. Tang, X. Chen, Y. Chen, W. Huang, Z. Liang, L. Wu, Y. Ge, Y. Song, J. Liu, D. Zhang, J. Li, and H. Zhang, “All-Optical Phosphorene Phase Modulator with Enhanced Stability Under Ambient Conditions,” Laser Photonics Rev. 12(6), 1800016 (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), 201701212 (2018).
[Crossref]

Li, M.

R. Peng, K. Khaliji, N. Youngblood, R. Grassi, T. Low, and M. Li, “Midinfrared Electro-optic Modulation in Few-Layer Black Phosphorus,” Nano Lett. 17(10), 6315–6320 (2017).
[Crossref] [PubMed]

Li, Y.

I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
[Crossref] [PubMed]

Liang, Z.

Y. Wang, F. Zhang, X. Tang, X. Chen, Y. Chen, W. Huang, Z. Liang, L. Wu, Y. Ge, Y. Song, J. Liu, D. Zhang, J. Li, and H. Zhang, “All-Optical Phosphorene Phase Modulator with Enhanced Stability Under Ambient Conditions,” Laser Photonics Rev. 12(6), 1800016 (2018).
[Crossref]

Liberal, I.

I. Liberal, A. M. Mahmoud, Y. Li, B. Edwards, and N. Engheta, “Photonic doping of epsilon-near-zero media,” Science 355(6329), 1058–1062 (2017).
[Crossref] [PubMed]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

Lin, 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]

M. Jiang, H. Lin, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, and Z. Chen, “Chirality induced asymmetric spin splitting of light beams reflected from an air-chiral interface,” Opt. Express 26(6), 6593–6601 (2018).
[Crossref] [PubMed]

Lin, J.

N. Mao, J. Tang, L. Xie, J. Wu, B. Han, J. Lin, S. Deng, W. Ji, H. Xu, K. Liu, L. Tong, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016).
[Crossref] [PubMed]

Ling, X.

Liu, J.

Y. Wang, F. Zhang, X. Tang, X. Chen, Y. Chen, W. Huang, Z. Liang, L. Wu, Y. Ge, Y. Song, J. Liu, D. Zhang, J. Li, and H. Zhang, “All-Optical Phosphorene Phase Modulator with Enhanced Stability Under Ambient Conditions,” Laser Photonics Rev. 12(6), 1800016 (2018).
[Crossref]

Liu, K.

N. Mao, J. Tang, L. Xie, J. Wu, B. Han, J. Lin, S. Deng, W. Ji, H. Xu, K. Liu, L. Tong, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016).
[Crossref] [PubMed]

Liu, M.

M. Liu, L. Cai, S. Chen, Y. Liu, H. Luo, and S. Wen, “Strong spin-orbit interaction of light on the surface of atomically thin crystals,” Phys. Rev. A (Coll. Park) 95(6), 063827 (2017).
[Crossref]

Liu, X.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
[Crossref] [PubMed]

Liu, Y.

M. Liu, L. Cai, S. Chen, Y. Liu, H. Luo, and S. Wen, “Strong spin-orbit interaction of light on the surface of atomically thin crystals,” Phys. Rev. A (Coll. Park) 95(6), 063827 (2017).
[Crossref]

Low, T.

R. Peng, K. Khaliji, N. Youngblood, R. Grassi, T. Low, and M. Li, “Midinfrared Electro-optic Modulation in Few-Layer Black Phosphorus,” Nano Lett. 17(10), 6315–6320 (2017).
[Crossref] [PubMed]

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

Lu, 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]

M. Jiang, H. Lin, L. Zhuo, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, and Z. Chen, “Chirality induced asymmetric spin splitting of light beams reflected from an air-chiral interface,” Opt. Express 26(6), 6593–6601 (2018).
[Crossref] [PubMed]

M. Jiang, W. Zhu, H. Guan, J. Yu, H. Lu, J. Tan, J. Zhang, and Z. Chen, “Giant spin splitting induced by orbital angular momentum in an epsilon-near-zero metamaterial slab,” Opt. Lett. 42(17), 3259–3262 (2017).
[Crossref] [PubMed]

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(1), 1150 (2017).
[Crossref] [PubMed]

Luo, H.

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X. Zhou, Z. Xiao, H. Luo, S. Wen, Z. Xiao, Z. H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012).
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X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
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N. Mao, J. Tang, L. Xie, J. Wu, B. Han, J. Lin, S. Deng, W. Ji, H. Xu, K. Liu, L. Tong, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016).
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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), 201701212 (2018).
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T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
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W. Shu, J. Zhang, H. Luo, S. Chen, W. Zhang, W. Wu, S. Wen, and X. Ling, “Photonic spin Hall effect on the surface of anisotropic two-dimensional atomic crystals,” Photon. Res. 6(6), 511 (2018).
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X. Zhang, A. Shkurinov, and Y. Zhang, “Extreme terahertz science,” Nat. Photonics 11(1), 16–18 (2017).
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Zhou, X.

X. Zhou, L. Xie, X. Ling, S. Cheng, Z. Zhang, H. Luo, and H. Sun, “Large in-plane asymmetric spin angular shifts of a light beam near the critical angle,” Opt. Lett. 44(2), 207–210 (2019).
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Zhuo, L.

Zi, J.

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter 25(21), 215301 (2013).
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Adv. Opt. Mater. (3)

X. Niu, X. Hu, S. Chu, and Q. Gong, “Epsilon-Near-Zero Photonics: A New Platform for Integrated Devices,” Adv. Opt. Mater. 6(10), 1701292 (2018).
[Crossref]

B. Deng, R. Frisenda, C. Li, X. Chen, A. Castellanos-Gomez, and F. Xia, “Progress on Black Phosphorus Photonics,” Adv. Opt. Mater. 6(19), 1800365 (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), 201701212 (2018).
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Adv. Opt. Photonics (1)

X. Wang and S. Lan, “Optical properties of black phosphorus,” Adv. Opt. Photonics 8(4), 618 (2016).
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Appl. Phys. Lett. (1)

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
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J. Am. Chem. Soc. (1)

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J. Opt. (1)

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Laser Photonics Rev. (1)

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Figures (8)

Fig. 1
Fig. 1 (a) Schematic of in-plane asymmetric spin splitting. A horizontal incident polarization can be considered as a superposition of two opposite spin, which undergo displacements X ± along x-axis thus separate spatially, after transmitted through the BP-ENZ metamaterial-BP structure. The incident plane makes angles of ϕ1 and ϕ2 to the armchair axes of top and bottom BP layers, respectively. (b) A single BP layer surrounding by two dielectrics with refractive index of nj and nj+1. (c) A stack of N BP layers separated by different dielectrics.
Fig. 2
Fig. 2 (a) GH shifts changing with the incident angle for the carrier density ρ = 0, 2.5, and 5 × 1017 m−2, and for (b) the refractive index of ENZ metamaterial n = 0.1, 0.2. 0.4, 0.6, respectively. (c,d) GH shifts changing with the carrier density ρ (c) and the metamaterial thickness d (d). In the calculation, the frequency of the incident beam is 1 THz.
Fig. 3
Fig. 3 Displacements of two opposite spin components of the transmitted beam X+ (solid lines) and X- (dotted lines) (a), transmission coefficients |tpp| and |tps| (b), and phase difference φ = arg[tpp/|tps] (c) changing with the incident angle, respectively. In the calculation, d = 4.2 μm, n = 0.1, ϕ1 = ϕ2 = 45°.
Fig. 4
Fig. 4 Displacements of two opposite spin components X ± changing with the incident angle θ for the refractive index of ENZ metamaterial n = 0.05, 0.1. 0.2 (a), and for n = 0.1, 0.1 + 0.01i, 0.1 + 0.1i (b), respectively. (c) X ± changing with the metamaterial thickness d for different θ. In the calculation, ϕ1 = ϕ2 = 45°.
Fig. 5
Fig. 5 Displacements X ± as functions of the rotation angle ϕ, where ϕ = ϕ1 = ϕ2·. The other parameters are the same as Fig. 3.
Fig. 6
Fig. 6 Displacements X ± as functions of the incident angle θ for ρ = 0 and 5 × 1017m−2, when d = 0.15 mm, ϕ1 = ϕ2 = 45° (a). X ± changing with the rotation angle ϕ (ϕ = ϕ1 = ϕ2) for θ = 6.21° (b) and 11.50° (c), respectively. The inset in (b) shows the rotation of BP-metamaterial structure. Schematics of barcode encryption based on the asymmetric spin splitting are also shown by choosing the threshold as 0 (b) and 1.8 mm (c), respectively.
Fig. 7
Fig. 7 Displacements X+ (a) and X- (b) as functions the rotation angles ϕ1 and ϕ2 when θ = 14.14°, d = 0.15 mm, ρ = 5 × 1017m−2.
Fig. 8
Fig. 8 Displacements X+ (solid lines) and X- (dotted lines) changing with the rotation angle ϕ2 for different ϕ1 and θ, when d = 0.05 mm, ρ = 5 × 1017m−2.

Equations (19)

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σ a r m , z i g = ( i D a r m , z i g ) / [ π ( ω + i η / ) ] .
E l = { [ A l k l z e i k j z z -B l k l z e i k l z z ] / k l e ^ x + [ C l e i k l z z -D l e i k l z z ] e ^ y . l = j , j + 1 + [ - A l k lx e i k l z z -B l k l x e i k l z z ] / k l e ^ z } e i k x z
e ^ z × [ E j E j + 1 ] = 0 ,
e ^ z × [ H j H j + 1 ] = σ E j + 1 ,
[ A j B j ] k j z / k j = [ A j + 1 B j + 1 ] k j + 1 , z / k j + 1 ,
C j + D j = C j + 1 + D j + 1 ,
[ C j D j ] k j z / ω μ = [ C j + 1 D j + 1 ] k j + 1 , z / ω μ + σ y y [ C j + 1 + D j + 1 ] + σ y x [ A j + 1 B j + 1 ] k j + 1 , z / k j + 1 ,
[ A j + B j ] k j / ω μ = [ A j + 1 + B j + 1 ] k j + 1 / ω μ + σ x x [ A j + 1 B j + 1 ] k j + 1 , z / k j + 1 + σ y x [ C j + 1 + D j + 1 ] ,
T j , j + 1 = [ k j + 1 / k j + η p + ξ p σ x x k j + 1 / k j η p ξ p σ x x ζ p σ x y ζ p σ x y k j + 1 / k j η p + ξ p σ x x k j + 1 / k j + η p + ξ p σ x x ζ p σ x y ζ p σ x y ζ s σ y x ζ s σ y x 1 + η s + ξ s σ y y 1 η s + ξ s σ y y ζ s σ y x ζ s σ y x 1 η s ξ s σ y y 1 + η s ξ s σ y y ] ,
P j = [ e i k j z d j 0 0 0 0 e i k j z d j 0 0 0 0 e i k j z d j 0 0 0 0 e i k j z d j ] .
[ A 1 B 1 C 1 D 1 ] = M [ A N + 1 B N + 1 C N + 1 D N + 1 ] ,
t p p = A N + 1 A 1 = M 33 M 11 M 33 M 13 M 31 ,
t s p = C N + 1 A 1 = M 31 M 11 M 33 M 13 M 31 ,
t s s = C N + 1 C 1 = M 11 M 11 M 33 M 13 M 31 ,
t p s = A N + 1 C 1 = M 13 M 11 M 33 M 13 M 31 ,
Q = [ t p p + κ x t p p ' κ y Ι t p s + κ x t p s ' + κ y Κ t s p + κ x t s p ' + κ y Κ t s s + κ x t s s ' + κ y Ι ] ,
E ˜ t ± = [ ( t p p + κ x t p p ' κ y Ι ) i ( t s p + κ x t s p ' + κ y Κ ) ] u ˜ 0 | ±
X ± = { Im [ t p p * t p p ' + t s p * t s p ' ] ± Re [ t p p * t s p * t s p * t p p ' ] } / k 0 W ± ,
W ± = | t p p | 2 + | t s p | 2 ± 2 Im | t p p * t s p | + 1 k 0 2 w 0 2 { | t p p ' | 2 + | t s p ' | 2 ± 2 Im | t p p ' * t s p ' | + | Κ | 2 + | Ι | 2 2 Im [ Κ * Ι ] }

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