Photonic Spin Hall Effect with Nearly 100% Efficiency

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1 Photonic Spin Hall Effect with Nearly % Efficiency Weijie Luo, Shiyi Xiao, Qiong He, Shulin Sun,* and Lei Zhou* Photonic spin Hall effect (PSHE; i.e., spin-polarized photons can be laterally separated in transportation) gains increasing attention from both science and technology, but available mechanisms either require bulky systems or exhibit very low efficiencies. Here it is demonstrated that a giant PSHE with % efficiency can be realized at certain meta-surfaces with deep-subwavelength thicknesses. Based on rigorous Jones matrix analysis, a general criterion to design meta-surfaces that can realize %-efficiency PSHE is established. The criterion is approachable from two distinct routes at general frequencies. As a demonstration, two microwave meta-surfaces are fabricated and then experimentally characterized, both showing 9% efficiencies for the PSHE. The findings here pave the way for many exciting applications based on high-efficiency manipulations of photon spins, with a polarization detector experimentally demonstrated here as an example.. Introduction The discovery of spin Hall effect (SHE; i.e., moving electrons with opposite spins can be transversely separated) boosted the field of spintronics. [ 4 ] Two mechanisms can generate the SHE, i.e., the intrinsic one [, ] replying on the spin-orbital coup ling (SOC) of electrons and the extrinsic one [,4 ] originating from the spin-dependent scatterings by impurities. Recently, photonic SHE (PSHE) attracted lots of attention. [5 7 ] In direct analogy with its electron counterpart, intrinsic PSHE was first proposed based on semi-classical (geometrical-optics) treatments on wave-packets of light, where SOC naturally occurs when light travels on a curved trajectory. [5,6 ] However, experiments show that PSHE generated by this mechanism, measured by the transverse displacement of spin-polarized photons, is extremely weak since the SOC arises from the first-order correction to the W. Luo, S. Xiao, Q. He, Prof. L. Zhou State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education) Fudan University Shanghai 4, China phzhou@fudan.edu.cn Q. He, Prof. L. Zhou Collaborative Innovation Center of Advanced Microstructures Fudan University Shanghai 4, China Prof. S. Sun Shanghai Engineering Research Center of Ultra-Precision Optical Manufacturing Green Photonics and Department of Optical Science and Engineering Fudan University Shanghai 4, China sls@fudan.edu.cn DOI:./adom.568 geometrical-optics theory. [7 ] Although the intrinsic PSHE was found significantly enhanced by the (spin-independent) phase gradients at carefully designed meta-surfaces (artificial ultra-thin metamaterials composed by planar units with tailored properties exhibiting extraordinary capabilities to control light propagations), [8 7 ] the measured ratio between the transverse displacement of spin-polarized photons and their traveling distance is still very small ( ). [ ] In a parallel line, strong PSHE was discovered at a particular class of meta-surfaces that can scatter spin-polarized lights to different directions, [ 6 ] which is analogous to the extrinsic SHE discovered in electron systems. [ ] The PSHE of this type can be very pronounced because the transverse forces acting on the spin-polarized photons come from the (spindependent) phase gradient (comparable to the wave vector of light in vacuum) on the meta-surface, which is realized at subwavelength scales in a fully controllable manner. [ 6 ] In sharp contrast to the intrinsic PSHE for which a semi-geometrical-optics theory is sufficient, [ ] the extrinsic PSHE can only be understood based on the full-wave Maxwell equations where wave interferences play very important roles. [ 6 ] However, wave interferences can also form unwanted zero-order modes after scatterings by meta-surfaces, so that the devices realized so far all suffer lowefficiency problem: typically only a small portion (theoretical limit 5%) of incident spin-polarized photons can be anomalously deflected by the meta-surfaces yielding the PSHE. [4,5,8,9 ] Here we show that in principle a giant PSHE with nearly % efficiency can be realized at meta-surfaces satisfying certain criterion, which is derived from a general Jones matrix analysis. Such a criterion is approachable from two different routes, leading to two types of meta-surfaces with distinct symmetry properties. While the idea is realizable at general frequencies, as a proof of concept, here we design and fabricate two realistic microwave samples and perform experiments to demonstrate that both can realize PSHE with 9% efficiency within a broad frequency bandwidth ( 4 GHz). Finally, we experimentally demonstrate that our meta-surfaces can work as efficient and broadband polarization detectors as one illustration of many potential applications of our findings.. Results and Discussion.. Criterion to Realize PSHE with % Efficiency We start from analyzing the electromagnetic (EM) properties of the building block (meta-atom) of our meta-surfaces. As shown in Figure a, consider a generic slab, representing a D array Adv. Optical Mater. 5, DOI:./adom WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com

2 Figure. Extrinsic PSHE realized by meta-surface consisting of spatially rotated meta-atoms. a) Jones matrices of a slab consisting of a periodical array of meta-atoms with local axes rotated by an angle φ. b) The Pancharatnam Berry phase gained by the last two terms in Equation ( ), which is equal to the area ( φ ) surrounded by two curves on the Poincaré sphere with blue iφσˆ iφσˆ and red dashed lines representing the operations of ˆσ and e σˆ e, respectively. c) A meta-surface formed by meta-atoms with local coordinates rotated successively (, φ, φ, φ, ). d) Schematics of the %-effi ciency PSHE realized at our reflective meta-surface: a linearly polarized incident beam is split into two spin-polarized reflection beams traveling to two offnormal directions while the specular reflection mode disappears completely. of identical subwavelength planar meta-atoms, illuminated by a normally incident light. Let { uv ˆ, ˆ} be the reference coordinates of the system, which are usually attached to the principle axes (if existing) of the meta-atoms for the convenience of discussions. Assume that the transmission/reflection properties of the slab tuu tuv are characterized by two Jones matrices, T( )= tvu tvv ruu ruv and R ( )= rvu rvv. Consider the reflection matrix first and choose circularly polarized (CP) modes with unit vectors defined as eˆ ± () = ( uˆ ± ivˆ)/ as our new bases, we get the reflection matrix R ( ) in the new frame. R ( ), like any other matrix, can be formally expanded to linear combinations of three Pauli matrices { σˆ, σˆ, σˆ } and the identity matrix Î. Specifically, we have () ˆ i R = ( ruu + rvv ) I+ ( ruv rvu ) σˆ + ( ruu rvv ) σˆ + ( ruv + rvu ) σˆ Now consider the case that the slab is rotated by an angle φ with respect to the z axis (see Figure a). In the CP bases defined in the original (laboratory) frame, the reflection matrix is given by R( φ)= M ( φ) R () M ( φ), where the rotation operator is written as ˆ M( φ ) = e iφσ. Utilizing the commutation relations among Pauli s matrixes, we get (see the Supporting Information for derivation details) ˆ i R ( φ) = ( ruu + rvv ) I+ ( ruv rvu ) σˆ iφ iφ + ( ruu rvv )( e σˆ+ + e σˆ ) i iφ iφ + ( ruv + rvu )( e σˆ+ + e σˆ ) () () spin-up (i.e., ê + ) and spin-down (i.e., ê ) states, respectively. [] The transmission Jones matrix T ( φ) for the rotated slab has a similar form with R ( φ) but with { ruu, ruv, rvu, rvv } changed to { tuu, tuv, tvu, tvv }. Now the advantages of adopting the Pauli matrix representation are clear: we can understand each term in Equation () physically. The first two terms, which all conserve the spin index, take their original forms as in the unrotated frame (see Equation (), simply ˆ because the rotation operator e iφσ commutes with operators Î and σ ˆ. Meanwhile, the last two terms, which all tend to flip the spin, gain additional phase factors e ± i φ caused by ˆ the noncommutations between e iφσ and ˆσ ±. Such phases are often interpreted as the Pancharatnam Berry (PB) s phases, [,] which can be easily understood based on our notations. Consider as an example the operation ˆσ which tends to flip the spin from + to iφσˆ ˆ iφσ ˆ e σ e. In the rotated frame, the same term becomes which now contains three successive operations. The states iφσˆ ˆ iφσ obtained by operating ˆσ and ˆ e σ e on +, although both representing the same state, exhibit a phase difference φ, which is equal to the area surrounded by the closed loop created by two operations on the Poincare s sphere (see Figure b), according to PB s theory. [,] Having obtained a general expression for the Jones matrix, we can then derive a rigorous criterion for achieving the %-efficiency PSHE. We first note that a meta-surface can be formed via combining meta-atoms (lateral size l << λ ) with local orientation angles rotated successively (, φ, φ, φ,.), as illustrated in Figure c. When we shine this meta-surface by a normally incident linear polarized (LP) light, the scattered waves generated by different meta-atoms on the meta-surface will interfere with each other, forming reflected/transmitted beams traveling along different directions. To get the %-efficiency PSHE, the metasurface should avoid multimode operation so that the building block must be either perfectly transparent or perfectly reflective. Let us assume T () at the moment and study the condition satisfied by R (). The last two terms in Equation ( ) contribute to spin-dependent lateral phase gradients, ξ± =± φ/l, so that according to the generalized Snell s law, [8,9] the reflected beams contributed by these two terms must travel to two off-normal directions depending on the input spin. Such spin-dependent scattering is the origin of the extrinsic PSHE discovered recently. [ 6] On the contrary, the first two terms in Equation ( ) do not supply any PB phases, so that their contributions are only to generate normally reflected (zero-order) modes. Presence of these spin-independent scatterings inevitably decreases the efficiency of the PSHE, which is a key problem of previous studies. [ 6] To get the %-efficiency PSHE (see Figure d), we need to eliminate all those normal modes, which means that ruu + rvv = ruv rvu = () where we have defined two spin-flip operators σˆ ± = ( σˆ ± iσˆ )/ satisfying σ ˆ ± ± = and ˆσ ± = ±, with ± denoting the Equation ( ) is the desired criterion to realize the %-efficiency PSHE at reflective meta-surfaces. For transmissive wileyonlinelibrary.com 5 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Adv. Optical Mater. 5, DOI:./adom.568

3 meta-surfaces, similar arguments show that the criterion is just R () plus an equation similar to Equation ( ) but with { ruu, ruv, rvu, rvv } changed to { tuu, tuv, tvu, tvv }... Practical Designs and Experimental Demonstrations We found two practical routes to reach the criterion (Equation ( ) ). First, we restrict our attention on meta-atoms exhibiting mirror symmetry (thus ruv = rvu ) so that Equation ( ) reduces to ruu = rvv. Neglecting material losses, we must have ruu = rvv = due to the energy conservation. Thus, the criterion becomes Φvv Φ uu = 8 with Φ ij denoting the phase of r ij, indicating that the desired system is a perfect λ / wave-plate working in reflection mode. Such a device has been successfully realized using anisotropic magnetic meta-surfaces in different frequency domains, [,4] so here we follow ref. [ ] to design our meta-atom. The inset in Figure a shows a practical design, which is a sandwich structure consisting of a metallic Jerusalem cross and a ground metallic plane, separated by a.9 mm-thick FR4 dielectric spacer ( ε = 4.). The ground metallic plane blocks all transmissions through the system (i.e., T () ), and more importantly, couples with the metallic crosses to create magnetic resonances at frequencies dictated by the geometrical parameters. [5,6] Such structures, sometimes called high-impedance surfaces, can strongly modulate the phase of reflected wave to undergo a 8 to 8 variation as frequency passes through the magnetic resonance. [5,6] Therefore, we can fully control the phase difference Φvv Φuu via tuning the positions and quality (Q) factors of two magnetic resonances for two polarizations. Through careful structural optimizations assisted by finite difference time domain () simulations, we obtain a final design and then fabricate a sample consisting of a periodic array of the designed meta-atoms (see the picture in Figure a). Both microwave experiments and simulations show that Φ vv Φ uu of this sample can indeed keep at 8 (Figure b) and thus the desired spin-dependent term can approach (Figure c) within a broad frequency band ( 4 GHz). Such broadband functionality comes from the engineered dispersion cancellation between two low-q magnetic resonances. The computed scattering patterns of a single meta-atom (see the Supporting Information) reinforced our notation that our meta-atoms predominantly support spin-dependent anomalous scatterings, which is the basis to achieve the %-efficiency PSHE. There is, however, another possible route to reach the criterion Equation ( ), which does not require the meta-atom to exhibit any mirror symmetry. The idea is to use the strong offaxis responses of asymmetrical meta-atoms [7,8] (see the inset in Figure a) to manipulate both diagonal and off-diagonal elements of R ( ), and in turn, to make Equation ( ) satisfied. The design can greatly benefit from symmetry arguments, which are summarized in the Supporting Information. In lossless systems, time-reversal symmetry dictates that ruv = rvu, so that our aim is to find a system, even without any mirror symmetry, that can still yield ruu + rvv =. An extreme solution among many possibilities is ruu = rvv =. Indeed, when the structure is excited by an EM wave polarized along ˆv, one can engineer the asymmetry of the pattern to let the induced current only flow along Φuu ( ) (c) (ruu rvv)/ /R û in average (see the insets in Figure c). Again aided by simulations, we successfully obtain a design for such asymmetric meta-atom and then fabricate out a sample consisting of a periodic array of such meta-atoms (see Figure a for the sample picture). The measured and simulated spectra of the sample (Figure b) confirm that Equation ( ) can indeed be approximately satisfied within a broad frequency band ( 4 GHz). We emphasize that ruu = rvv = is not a necessary condition and many other possible asymmetrical metatoms can be designed to satisfy the criterion (Equation ( ) ). We find the working mechanism of such an asymmetrical meta-atom is quite intriguing. Now R ( ) generally contains offdiagonal elements in the { uv ˆ, ˆ} frame (which we choose only for convenience and definiteness), we can diagonalize the matrix R ( )to retrieve two effective principle axes { uˆ, vˆ } of our metaatom. Figure c shows that the effective principle axes { uˆ, vˆ } are not fixed but rather rotate as frequency varies. In particular, Φvv ( ) 8 Figure. Design of the symmetrical meta-atom. a) Picture of a sample formed by an array of symmetrical meta-atoms (sized 7 7 mm ) with a = 4 mm, b = 5 mm, c =. mm, d =. mm (see the inset). The thickness and width of metallic wires are.5 and.5 mm, respectively. Spectra of b) reflection phases (Φ uu and Φ vv ) and c) normalized reflectance ( ruu rvv )/ / R for the sample shown in, obtained by experiments (symbols) and simulations (line). Here, R = ( ruu + rvv + ruv + rvu )/ represents the total reflected energy summing up contributions from all four terms in Equation ( ), and the gray region in and (c) indicates the working band of our sample which is determined by the condition of ( ruu + rvv )/ + ( ruv rvu )/ / R <.. Adv. Optical Mater. 5, DOI:./adom WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com

4 r uu /R r vv /R (c) θ ( ) (d) Φu u ( ) v u v u 8 v u 8 Φv v ( ) Figure. Design of the asymmetrical meta-atom. a) Picture of a sample formed by an array of asymmetrical meta-atoms (sized 7 7 mm ) with a =. mm, b =. mm, c =.4 mm, d =.5 mm (see the inset). The thickness and width of metallic wires are.5 and.5 mm, respectively. b) Measured and simulated spectra of ruu / R and r vv / R for the sample shown in. c) Orientation angle θ of the effective principle axes {ˆ u,ˆ v } for our asymmetrical meta-atom with respect to its original coordinate {ˆ,ˆ} uv, retrieved by diagonalizing the experimentally measured and -simulated reflection matrices. Insets show the current distributions on the metallic wires in our meta-atom, excited by normally incident electromagnetic waves polarized E v ˆ at frequencies 9,, and 5 GHz, respectively. d) Measured and -simulated spectra of reflection phases ( Φ uu, Φ vv ) for the sample shown in. Here, R = ( ruu + rvv + ruv + rvu )/ represents the total reflected energy summing up contributions from all four terms in Equation ( ), and the gray region in (b d) indicates the working frequency band of our system which is determined by the condition of ( r + r )/ + ( r r )/ / R <.. uu vv uv vu the angle between û and û just equals 45 at GHz within the working band. Meanwhile, the phase difference between two reflection coefficients along two effective principle axes is also equal to 8 at GHz (Figure d). All these features suggest that the symmetrical and asymmetrical meta-atoms share the same working mechanism right at the center working frequency, although the routes on which they approach the criterion (Equation ( ) ) are different. Such new structures add many new possibilities [9 ] and freedoms to the family of meta-atoms that can realize the %-efficiency PSHE, which are very helpful for researchers to flexibly design their own systems and realize certain effects unique to asymmetrical structures. Having obtained two practical designs for meta-atoms, we now fabricate the corresponding meta-surfaces ( Figure 4 a,e) according to the scheme described in Figure c and then verify their abilities to achieve the PSHE with nearly % efficiency. In our experiments, we shine the meta-surfaces with normally incident LP beams, and then, respectively, use a left circular polarization (LCP) antenna and a right circular polarization (RCP) antenna to measure the normalized angular distributions for scattered-wave intensities with + (Figure 4 c,g) and (Figure 4 b,f) polarizations. Here the reference is taken as the signal measured by the same receiver but with the metasurface replaced by a metallic plate of the same size, which is essentially half of the input power. Within a quite broad frequency band, we find both meta-surfaces can split the incident LP beam into spin-up and spin-down beams traveling along two distinct directions: a finger-print feature of the giant PSHE. Most importantly, the diminishment of specular (normal) refection modes within the working frequency band implies the high efficiency of the observed PSEH, which is further reinforced by the observation that the maximum normalized scattered power (see Figure 4 ) can approach %. Quantitative estimations on the PSHE efficiency are obtained by integrating the power over the angle regions spanned by the reflection modes, which has also been adopted in previous study. [ ] The obtained PSHE efficiencies are shown as functions of frequency in Figure 4 d,h for two meta-surfaces, respectively. At a typical frequency GHz, the absolute efficiencies of PSHE for both meta-surfaces are found within the range of 8% 9% based on our experiments, and 9% 95% based on our simulations (see the Supporting Information). If we only care about the relative PSHE efficiency, defined as the ratio between the anomalous-mode signal and the total reflected signal, the experimentally measured efficiency can reach the level of 9% 95%. The deviations of these efficiencies from the theoretical prediction are mostly caused by materials losses, sample imperfections, as well as the nonideal performances of our antennas. Outside the working band, significant specular reflections appear which lowers the PSHE efficiencies, similar to previously discovered PSHE. [ 4,5 ] We note that criterion Equation ( ) is so general that it can also help us design optical meta-surfaces supporting PSHE with very high efficiencies. Full-wave simulations (with dispersions/losses of realistic materials fully considered) on a designed optical meta-surface show that the absolute PSHE efficiency can approach to 88% while the relative PSHE efficiency can be even higher (9%) at the working wavelength µm (see the Supporting Information). Although fabrication/characterization challenges might decrease these predicted values, experimental demonstration of the idea in the optical domain is still highly interesting. Our high-efficiency PSHE, being extrinsic in nature, can be fully controlled by the engineered meta-surfaces upon design. 4 wileyonlinelibrary.com 5 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Adv. Optical Mater. 5, DOI:./adom.568

5 (e) 6 4 Theory Symmetrical (f) Asymmetrical (c) 6 (g) 4 Symmetrical Asymmetrical (d) θ r ( ) 6 4 (h) θ r ( ) PSHE Efficiency PSHE Efficiency Figure 4. Experimental verifi cation of high-effi ciency and broadband PSHE. Pictures of fabricated meta-surfaces (both sized mm ) formed by a) symmetrical and e) asymmetrical meta-atoms. Measured normalized scattered-fi eld intensities (color map) versus frequency and detecting angle for two meta-surfaces illuminated by normally incident linearly polarized beams, with receivers chosen as a circularly polarized antenna with polarization b, f) + and c, g), respectively. d,h) PSHE effi ciencies versus frequency for two meta-surfaces, obtained by analyzing the experimental data in (b,c,f,g). Here dotted lines in (b,c,f,g) are calculated by Equation ( 4) under normal-incidence condition. Regions surrounded by black dashed lines in (a,e) represent the supercells of two samples. Specifically, the deflection angle θ ± r of the spin-polarized wave is determined by ± ± θ = sin (sin θ + ξ / ) r i k according to the generalized Snell s law, [8,9] where θ i is the incident angle and k = ω/ c is the vacuum wave-vector. Equation ( 4) shows that the spin-dependent deflection is controlled by the phase gradient ξ ±, which can be tuned by adjusting the orientation angle step φ or the dimension l of the metaatom. In addition, given a meta-surface with fixed ξ ±, Equation (4) shows that θ ± r depends also on frequency (through k ) (4) and θ i. Dotted lines in Figure 4 b,c,f,g are calculated based on Equation (4) with ξ ± =± π/ mm (experimental values for both meta-surfaces) and with θ i = fixed, which can well describe the experimentally observed frequency dependences of θ ± r. Meanwhile, we also measured the θ ± r ~ θ i relations for two spin-polarized reflection modes with frequency fixed at GHz, and depict the obtained results in Figure 5. The measured θ ± r ~ θ i relations are again in perfect agreement with the simulations and theoretical prediction (Equation (4)). simulations are performed to well reproduce all experimental results in Figure 4, with details presented in the Supporting Information. Adv. Optical Mater. 5, DOI:./adom WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 5

6 θ r ( ) θ r ( ) Our findings can stimulate many interesting applications based on spin-dependent light manipulations. Here as one example, we show that our systems can work as efficient and broadband polarization detectors. As shown in Figure 6 a, when a beam with unknown polarization is illuminated onto our meta-surfaces, two spin components will be reflected to two different directions. Detecting the amplitudes and phases of these two modes simultaneously can help retrieve the polarization state of the original beam. To test the functionality of our device, we design and fabricate a meta-material wave-plate (see the Supporting Information for its characteristics) to help generate a beam with particular elliptical polarization, which is then incident onto our meta-surface with symmetrical meta-atom as an input beam with polarization to be detected. Figure 6 b shows that the polarization states retrieved from our measurements, characterized by two parameters (the orientation angle χ and the ellipticity angle ψ ; see the inset in Figure 6 a), are in excellent agreement with the polarizations of the input beam. Slight discrepancies for χ at.5 GHz are caused by the ambiguities in determining this value for a pure circular polarization (note here ψ = 45 ). Compared to standard polarization detectors, our scheme is more efficient and stable.. Conclusion Theory θ ( ) i Figure 5. Angle of the anomalously reflected beam θ r versus incident angle θ i for meta-surfaces with a) symmetrical and b) asymmetrical metaatoms under illuminations of spin-polarized waves, obtained from experiments (solid symbols), simulations (open symbols), and theory (Equation ( 4) ), lines) at frequency GHz. In summary, we show that in principle PSHE with nearly % efficiency can be realized at meta-surfaces satisfying a certain χ ( ) criterion. Two realistic microwave samples with distinct symmetry properties, which approach the criterion from two different routes, are experimentally characterized, both showing very high efficiencies for PSHE within a broad frequency band. An efficient and broadband polarization detector is demonstrated as a simple application of our discovery. Our findings can lead to many exciting applications based on high-performance photonic spin manipulations (such as high-efficiency spin-controlled surface plasmon couplers and spin-dependent holographic imaging), and provide a powerful platform for further fundamental research along this direction. In particular, considering the dramatic progresses that have been made on optical meta-surfaces, such as low-loss dielectric meta-surfaces [, ] and gap plasmon-based gradient meta-surfaces, [ 4 ] it is quite promising to finally realize these ideas in the optical regime and in transmission geometry. 4. Experimental Section Meas. Input ψ ( ) Figure 6. PSHE-based polarization detector. a) Schematics of our polarization-detecting experiments. The inset depicts a general elliptic polarization state defi ned by the orientation angle χ and the degree of ellipticity ψ. b) Polarization states (described by χ and ψ ) of the input beam measured by our experiments (symbols), compared with the input values (lines) calculated from the wave-plate characteristics. All microwave samples were fabricated using.9 mm-thick FR4-printed circuit boards with one side covered by a 5 µm-thick continuous copper film and another side covered with the copper patterns etched based on the theoretical designs. We measure the reflection coefficients and scatteredwave powers based on a homemade D angle-resolved system connecting two horn antennas (source and receiver) with a vector network analyzer (Agilent E86C PNA). Typically, we fix the position of the source antenna and freely rotate the receiver antenna on a circular track at a distance.5 m away from the sample to measure the scattered-wave power wileyonlinelibrary.com 5 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Adv. Optical Mater. 5, DOI:./adom.568

7 Supporting Information Supporting Information is available from the Wiley Online Library or from the author. Acknowledgements This work was supported by National Natural Science Foundation China (Grant Nos , 7455, 44, and 446), MOE of China (Grant No. B6), and Shanghai Science and Technology Committee (Grant No. 4PJ4). Received: January, 5 Revised: March 6, 5 Published online: [] S. Murakami, N. Nagaosa, S.-C. Zhang, Science,, 48. [] J. Sinova, D. Culcer, Q. Niu, N. Sinitsyn, T. Jungwirth, A. H. MacDonald, Phys. Rev. Lett. 4, 9, 66. [] J. Hirsch, Phys. Rev. Lett. 999, 8, 84. [4] S. Zhang, Phys. Rev. Lett., 85, 9. [5] M. Onoda, S. Murakami, N. Nagaosa, Phys. Rev. Lett. 4, 9, 89. [6] K. Y. Bliokh, Y. P. Bliokh, Phys. Rev. Lett. 6, 96, 79. [7] O. Hosten, P. Kwiat, Science 8, 9, 787. [8] N. Yu, P. Genevet, M. a Kats, F. Aieta, J.-P. Tetienne, F. Capasso, Z. Gaburro, Science, 4,. [9] S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, L. Zhou, Nat. Mater.,, 46. [] S. Sun, K. Yang, C. Wang, T. Juan, W. T. Chen, C. Y. Liao, Q. He, S. Xiao, W. Kung, G. Guo, L. Zhou, D. P. Tsai, Nano Lett.,, 6. [] W. T. Chen, K. Yang, C. Wang, Y. Huang, G. Sun, C. Y. Liao, W. Hsu, H. T. Lin, S. Sun, L. Zhou, A. Q. Liu, D. P. Tsai, Nano Lett. 4, 4, 5. [] X. Yin, Z. Ye, J. Rho, Y. Wang, X. Zhang, Science, 9, 45. [] N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, E. Hasman, Nano Lett.,, 8. [4] L. Huang, X. Chen, B. Bai, Q. Tan, G. Jin, T. Zentgraf, S. Zhang, Light Sci. Appl.,, e7. [5] J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, F. Capasso, Science, 4,. [6] N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, E. Hasman, Science, 4, 74. [7] Y. Zhao, X.-X. Liu, A. Alù, J. Opt. 4, 6,. [8] F. Monticone, N. M. Estakhri, A. Alù, Phys. Rev. Lett.,, 9. [9] X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. de Lustrac, Q. Wu, C.-W. Qiu, A. Alù, Adv. Mater. 5, 7, 95. [] We note that and actually should be interpreted as the spin-down and spin-up states in the local frame for the reflected modes since the direction of is reversed here. [] B. Y. S. Pancharatnam, Proc. Indian Acad. Sci. Sect. A 956, 44, 47. [] M. V. Berry, Proc. R. Soc. A Math. Phys. Eng. Sci. 984, 9, 45. [] J. Hao, Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, L. Zhou, Phys. Rev. Lett. 7, 99, 698. [4] J. Hao, Q. Ren, Z. An, X. Huang, Z. Chen, M. Qiu, L. Zhou, Phys. Rev. A 9, 8, 87. [5] D. Sievenpiper, R. F. J. Broas, N. G. Alexopolous, E. Yablonovitch, IEEE Trans. Microwave Theory Tech. 999, 47, 59. [6] J. Hao, L. Zhou, C. T. Chan, Appl. Phys. A 7, 87, 8. [7] a. Papakostas, a. Potts, D. Bagnall, S. Prosvirnin, H. Coles, N. Zheludev, Phys. Rev. Lett., 9, 744. [8] M. Decker, M. W. Klein, M. Wegener, S. Linden, Opt. Lett. 7,, 856. [9] Y. Li, J. Zhang, S. Qu, J. Wang, H. Chen, L. Zheng, Z. Xu, A. Zhang, J. Phys. D: Appl. Phys. 4, 47, 45. [] D. Lin, P. Fan, E. Hasman, M. L. Brongersma, Science 4, 45, 98. [] M. Khorasaninejad, K. B. Crozier, Nat. Commun. 4, 5, 586. [] A. Pors, M. G. Nielsen, S. I. Bozhevolnyi, Opt. Lett., 8, 5. [] A. Pors, O. Albrektsen, I. P. Radko, S. I. Bozhevolnyi, Sci. Rep.,, 55. [4] A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, S. I. Bozhevolnyi, Light Sci. Appl. 4,, e97. Adv. Optical Mater. 5, DOI:./adom WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com 7