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On-Chip Photonic Spin Hall Lens Luping Du,*,†,‡ Zhenwei Xie,†,‡,§ Guangyuan Si,∥ Aiping Yang,† Congcong Li,† Jiao Lin,†,∥ Guixin Li,⊥ Hong Wang,§ and Xiaocong Yuan*,†

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†

Nanophotonics Research Centre, Shenzhen Key Laboratory of Micro-Scale Optical Information Technology, Institute of Microscale Optoelectronics, Shenzhen University, Shenzhen, 518060, Guangdong, China § School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore ∥ School of Engineering, RMIT University, Melbourne, Victoria 3001, Australia ⊥ Department of Materials Science and Engineering, Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, 1088 Xueyuan Avenue, Shenzhen, 518055, China S Supporting Information *

ABSTRACT: Focusing and Fourier transformation are two key functionalities of optical lenses, which are vital for optical information refining and processing. These unique features persist and are even carried forward on a planar configuration that works on a surface wave, enabling on-chip and ultrafast photonic information processing. Here, we design and demonstrate a type of photonic spin Hall lens (pSHL) that works on surface plasmon polaritons. It could perform spatially separated focusing and photonic Fourier transformation controlled by the handedness of the incident circularly polarized light (CPL). Their splitting distance can easily be adjusted by altering the scaling factor of the phase gradient encoded onto the lens, a manifestation of an optical spin Hall effect. The pSHL is designed to retrieve the phase delay required to compensate for the spatial shift of the lens; this is realized using a plasmonic metasurface that yields the spin-dependent Pancharatnam−Berry phases. Applications with the pSHL for photonic spin routing and OAM-mode demultiplexing are demonstrated. The proposed pSHL is ultrathin, compact, and easy to fabricate. It holds a great promise for the development of ultracompact photonic spin devices. KEYWORDS: surface plasmonic polariton, photonic spin Hall effect, metasurface, angular momentum of light, optical vortices materials. The first PSHE device with a metasurface was demonstrated with V-shaped nanoantennas,22 followed by the emergence of a variety of Pancharatnam−Berry (PB) phase components.23−28 With these PB phase elements, various photonic spin devices were developed, such as the directional polarization coupler,29 spin−optical metamaterial,30 broadband photonic spin resolving,31 metaspiral plasmonic lens,32 Rashbatype plasmonic metasurface,33,34 polarization-controlled surface plasmon polaritons (SPPs),35 and conic-shaped and catenary-shaped photonic spin metasurface.36−38 The spin Hall momentum shift and the radial spin Hall effect of light were also found through the PB phase gradient.39−41 As a fundamental optical element, optical lenses play a vital role in the development of optical technologies for their intrinsic focusing and Fourier transform capabilities, which are crucial for information refining and processing. These unique features persist and are even carried forward on a planar configuration that works on a surface wave,32,42−48 enabling on-chip and ultrafast photonic information processing.49 However, for conventional photonic lenses, the focusing or Fourier transform processes are typically spatially overlapped

T

he spin Hall effect of light, also known as the photonic spin Hall effect (PSHE), was initially revealed from the Imbert−Fedorov effect and the optical Magnus effect, which are optical phenomena relating to transverse beam shifts of the photonic spin when a light beam is reflected or refracted by an inhomogeneous isotropic medium.1−5 Basically, the PSHE results from the coupling between spin angular momentum (SAM) of a photon and its extrinsic orbital angular momentum (OAM) related to the trajectory of light.4−8 As the spin−orbit coupling is a subtle effect of light−matter interaction, PSHE is normally weak and difficult to measure.5,9,10 Nonetheless, to elicit the PSHE, many techniques have been proposed and demonstrated, such as weak measurements, multireflections, and interferometry.8,11−13 In a solid state system, the spin electron accumulation is related to the electric potential gradient.14−16 Accordingly, in a photonic system, the spin-dependent shift is a consequence of the refractive index gradient (phase discontinuity).4,9,10 However, to obtain a large phase discontinuity with traditional materials was difficult. That situation changed after the discovery of metasurfaces:17−20 pixelized phase elements at nanoscale with optical antennas that induce remarkable phase variations within a single wavelength. They opened a new avenue for developing strong PSHE devices, even under normal incidence,21 which is hard to achieve with traditional © XXXX American Chemical Society

Received: April 11, 2019 Published: July 23, 2019 A

DOI: 10.1021/acsphotonics.9b00551 ACS Photonics XXXX, XXX, XXX−XXX

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Figure 1. Design and working principle of the photonic spin Hall lens. (a) Schematic illustrating the functioning of the pSHL. Incident beams of the two circularly polarized light produce a split focusing path and enable the spatially separated Fourier transform of the emitted SPP field from the lens. (b) Design principle of the pSHL, considered as two virtual plasmonic lenses (dashed circles) with a spin dependence. Spin splitting is achieved by coding the phase delay caused by shifting the virtual lenses from its central position (solid circle) to the targeted pSHL, with the phase modulated by plasmonic PB phase elements (paired perpendicular nanogrooves of varying orientation). (c) Phase modulation on SPPs with the paired nanogrooves, obtained by varying their orientation angles, under the illumination with LCP (red line) and RCP (blue line) beam. (d) Demonstration of the wavefront modulation with a vertical array of paired nanogrooves with linearly increasing orientation angles. The tilted SPP wavefront clearly indicates the linear phase modulation on the SPPs by linearly varying the orientation of the nanogrooves. The red circular arrows indicate the spin state of the incident beam. The white arrow indicates the propagating direction of the coupled SPPs.

retrieving the phase delay arising from the shift by the lens, expressible as (see Supporting Information for a derivation)

when illuminated with the two different circular polarizations of light. This impairs greatly the usefulness of these lenses for processing optical spin information. Recently, Zhou et al. demonstrated an optical spin Hall meta-lens that works on a free space wave by attaching the PB phase lens with a traditional lens.50 Nevertheless, the planar scheme that aims for a surface wave has not been reported. Although state-of-the-art methods have been proposed to achieve the spin-controlled focusing of surface waves,47,51,52 they are generally at the expense of the Fourier-transform capability of the lens, a great loss for optical information processing. Here, we propose and demonstrate a photonic spin Hall lens (pSHL) that works using surface plasmon polaritons (SPPs). This pSHL contains a specific azimuthal geometric phase gradient in real space that creates a spin-splitting in momentum space while maintaining its Fourier transform capabilities.53 The spin-splitting in momentum space will result in a focal shift regarding the spin state of the incident beam. The splitting distance between the two focal spots can be easily adjusted by altering the scaling factor of the phase gradient. With all these unique features, the pSHL may in the future provide benefits for the on-chip spin Hall device, quantum computation, and spin detection. The pSHL (Figure 1a) is designed based on the plasmonic PB phase elements, which are gold nanofilms with rectangularshaped nanogrooves. Our aim is to achieve a plasmonic lens with spin Hall splitting (see Figure 1b). The pSHL designed comprises two virtual plasmonic lenses (marked by dashed circles) with a position shift of ±Δs with respect to the target position of the lens (solid circle). One lens responds to lefthanded circular polarized (LCP) light, the other to righthanded circular polarized (RCP) light. In using plasmonic PB phase elements, these two spin-dependent plasmonic lenses act as a single pSHL. The phase profile of this lens is obtained by

eiΦ = ei2πγ

cos(φ − φ0)

(1)

where γ = Δs/λspp is the scaling factor of the plasmonic lens, which determines the degree of the lateral shift of the lens in units of wavelength λspp, φ is the azimuthal angle, and φ0 is the shift direction with respect to the x-axis. This specially designed phase profile enables the Fourier transform functionality of the plasmonic lens to be retained by only adjusting the focusing shift. This may be understood by expressing the electromagnetic field of the SPP emitted from the pSHL in the angular spectrum representation. Knowing that the coupled SPP from an unmodulated plasmonic lens is a Bessel function,49,54 after modulation with the phase of eq 1, the SPP field becomes (see Supporting Information for a derivation) Ez =

1 2π

∫0

2π

ei2πγ

cos(φ − φ0) −ik sp(x cos φ + y sin φ) dφ ·e

= J0 (ksp (x − Δx)2 + (y − Δy)2 )

(2)

where Δx = Δs·cos(φ0) and Δy = Δs·sin(φ0). We find that the coupled SPP field remains a Bessel function with merely a shift in position of (Δx, Δy). This imposed phase is realized using the plasmonic PB phase elements, paired perpendicular nanogrooves (Figure 1b). Before determining the orientation of the nanogrooves that promotes the functionality of the pSHL, we investigate initially the phase modulation of these paired nanoantennas. The length and width of each groove are denoted L and W, their separation is P, and the orientation angle of the right-side groove is θ. These plasmonic nanoantennas couple the light to the propagating surface plasmon polaritons approximating a B

DOI: 10.1021/acsphotonics.9b00551 ACS Photonics XXXX, XXX, XXX−XXX

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Figure 2. Numerical simulations for the pSHLs with scaling factors of γ = 0, 2, and 4. (a) Amplitude and phase of the emitted SPP field (Ez) from the pSHL for an incident Gaussian beam with different polarizations (left panels: linear polarized (LP), middle panels: left-handed circular polarized (LCP), right panels: right-handed circular polarized (RCP). The focal spot shift is linearly proportional to the scaling factor of the pSHL and is strongly spin-dependent. (b) Similarly for an incident optical vortex beam carrying orbital angular momentum (OAM). The topological charge of each beam is m = 1. The scale bars in (a) and (b) represent 1 μm.

2D dipolar emission.29,31,51 Under the stationary phase approximation, the coupled SPPs from a vertical array of paired nanogrooves with the same orientation produce an electric field31 Ez(x , y) = ηE0

λspp r

which clearly indicates that the phase induced by the nanogroove pair is linearly proportional to its orientation angle (i.e., the plasmonic version of the Pancharatnam−Berry phase), and more importantly, is spin reversed. This is validated numerically in simulations using the finite-difference time-domain method (Figure 1c). Subsequently, we demonstrated the phase modulation of a vertical array of the paired nanogrooves but with a linear variation of their orientation angles (Figure 1d, LCP illumination only). The chain of antennae with linearly varying orientations results in a tilted propagating wavefront of a SPP, verifying the linearity of the phase gradient from the nanogrooves. The designed pSHL is composed of a ring of pairs of nanogrooves, with their orientation angles determined by the phase required to achieve spin-Hall splitting from the lens, that is,

eiφc·eiπ /4 ·eiksppx ·eiσs·θ

× [cos(θ) ·e−iksppP /2 − σs·i sin(θ) ·eiksppP /2]

(3)

where η is the coupling efficiency from light to SPPs, E0 is the amplitude of the incident light, λspp is the wavelength of the SPP, r is the distance apart from the geometric center of the antenna, φc is the coupling phase, kspp is the wave vector of the SPPs, and σs is the spin state of the incident beam (1 for LCP and −1 for RCP). When the distance between the two nanogrooves is half the SPP wavelength (P = λspp/2), the phase is Φ = arg[Ez(x , y)] ∝ σs·2θ

ΦPSHL = σs·2πγ cos(φ − φ0)

(4) C

(5) DOI: 10.1021/acsphotonics.9b00551 ACS Photonics XXXX, XXX, XXX−XXX

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which yields an orientation angle θ=

ΦPSHL = πγ cos(φ − φ0) 2σs

(6)

As proof of the concept, we analyze pSHLs with scaling factors of γ = 0, 2, and 4. Here, φ0 is set to 0, and hence, the two spin-dependent lenses are horizontally split. Numerical simulation results (Figure 2) were obtained for Gaussian incident beams (top panel) and optical vortex beams (bottom panel) carrying orbital angular momentum (OAM). For the γ = 0 pSHL, no splitting of the lens is expected. Therefore, there is only one single focal spot of the SPP emitted from the pSHL regardless of the spin state of the incident beam (Figure 2a, first row). The second row shows an instance with γ = 2. Under the illumination with CP light, the focal spot of the SPP is shifted accordingly by 2λspp (to the left/right with an LCP/ RCP beam). More importantly, the shifting of the focal spot does not induce a change in the global intensity profile of the SPP. The linearly polarized incident light, as expected, generates two separated focal spots of the SPP with a separation of 4λspp. For the γ = 4 pSHL, the splitting distance becomes 8λspp (third row). To further demonstrate this unique feature of the pSHL, we performed similar simulations with incident vortex beams with a topological charge of m = 1 (Figure 2b). We find that the coupled SPPs become a hollowshaped plasmonic vortex with a topological charge of 1 for both LCP and RCP incident beams. On increasing the scaling factor of the pSHL, the initial OAM of the coupled SPPs is retained after the shift in position. We subsequently performed experiments to validate the above theory. The designed pSHL structure (Figure 3a) is an 8 μm radius ring of two 50 nm deep tracks of grooves, milled onto a 200 nm thick gold film. The length and width of each groove are 240 and 60 nm. At the focal positions of the pSHL, through-holes of radius 50 nm are added and employed to couple the focused SPPs to the far field for convenience in measurement. The corresponding SEM images for the fabricated pSHL (γ = 0, 2, 4) are presented in Figure 3b−d, respectively; the measured results are shown in Figure 4 (see Experimental methods in the Supporting Information for experimental details). When the γ = 0 pSHL is illuminated with LP, LCP, and RCP Gaussian beams, only one bright spot is observed at the geometric center (Figure 4a−c). For pSHLs with γ = 2 and 4, there are two separated bright spots under the LP illumination (Figure 4d,g), whereas with LCP/RCP incident beams, the bright spot only shows up at the left/right side (Figure 4e,h and Figure 4f,i). These results demonstrate the capabilities of the pSHL to detect and sort photonic spin. Aside from spin detection, the pSHL may be used for OAMmode sorting and demultiplexing. This functionality is enabled by the two key pSHL features: (1) the capability to split the beams with different incident spins spatially and (2) the capability to perform a Fourier transform accompanying the spin-splitting. Here, because the size of the plasmonic OAM mode is related to its topological charge,55 nanoring slits are used as plasmonic out-couplers of the OAM modes. By altering the inner and outer radii of the nanoring slit, the order l of the plasmonic OAM mode that is coupled out is changed accordingly.56 To out-couple the plasmonic OAM mode with topological charge of l = ±1 at a wavelength of 632.8 nm, the inner and outer radii of the nanoring slit are set to 75 and 125 nm, whereas for the l = ±3 OAM modes, they are 200 and 250

Figure 3. Design and fabrication of nanostructures to verify the spinsplitting of the pSHL. (a) Schematic diagram of the designed structure, where two circular holes are fabricated at the designed focal spots to out-couple the emitted SPP field from the pSHL for detection. (b−d) SEM images of the fabricated structures with scaling factors γ = 0, 2, and 4, respectively. The top panels give a top-side view, and the bottom panels are the corresponding area that indicated by the dashed squares in the top panels.

nm, respectively. A spiral phase profile is generated for the pSHL to convert the incident OAM beam into a preset plasmonic vortex. By combining two pSHLs with spin-splitting directions of φ0 = 0 and φ0 = −π/2, we achieve an eight OAMmode sorter (Figure 5a). The pSHL acts as an OAM-mode spatial router that shifts the coupled SPPs vortex to locations where the nanoring slits are fabricated to out-couple the targeted OAM mode. The orientation angles of the PB phase antennae are specifically l o πγ1 cos(φ) + m1φ/2 for φ0 = 0 o o θ=m o o o πγ2 cos(φ + π /2) + m2φ/2 for φ0 = − π /2 n

(7)

where γ1 and γ2 are the scaling factors for the horizontal and vertical phase shifts, and m1 and m2 are the topological charges of the spiral phases encoded onto the pSHL. Here, the orientation angle for each pairs of the antennae is selected from the two values shown in eq 7 by turns, which means that the two pSHLs are merged into a single pSHL (Supporting Information, Figure S4). Assuming that the topological charge of the incident beam is m, the total angular momentum of the coupled SPPs is l = m + σsmj, where j = 1 and 2 for φ0 = 0 and −π/2, respectively. Once the AM mode of the coupled SPPs is given, the topological charge of the incident beam can be calculated accordingly. For the eight OAM modes structure, D

DOI: 10.1021/acsphotonics.9b00551 ACS Photonics XXXX, XXX, XXX−XXX

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the horizontally routed AM modes (φ0 = 0) are thus (σs = 1, m = l − m1) and (σs = −1, m = l + m1); the vertically routed AM modes (φ0 = −π/2) are (σs = 1, m = l − m2) and (σs = −1, m = l + m2) (see Supporting Information for detailed derivation). In principle, the parameters of the nanoring slits and m1, m2 can be altered as required, and therefore, the topological charges of the sorted OAM modes can be varied accordingly. As an example, let the scaling factors be γ1 = γ2 = 2, and m1 = 0, m2 = 6; the eight OAM modes to be sorted are then (φ0 = 0, l = 3, σs = 1, m = 3), (φ0 = 0, l = 1, σs = 1, m = 1), (φ0 = 0, l = −1, σs = −1, m = −1), (φ0 = 0, l = −3, σs = −1, m = −3), (φ0 = −π/2, l = −3, σs = 1, m = −9), (φ0 = −π/2, l = −1, σs = 1, m = −7), (φ0 = −π/2, l = 1, σs = −1, m = 7), (φ0 = −π/2, l = 3, σs = −1, m = 9); see Figure 5b for the simulation results (the parameter details are shown in Supporting Information, Table S1). To verify the pSHL flexibility, we demonstrated angular sorting of incident OAM modes (Figure 6a). The final pSHL is composed of a mixture of three pSHLs with φ0 = 0, −π/3, and −2π/3. Nanorings corresponding to AM modes of l = ±1 were fabricated at the desired locations to out-couple the plasmonic OAM mode. This pSHL enables the six OAM modes to be routed spatially at angular intervals of 60°. The orientation angles of the paired nanogrooves are determined from

Figure 4. Experimental measurements of the pSHLs for the different scaling factors. Results for (a−c) the γ = 0 pSHL, (d−f) the γ = 2 pSHL, and (g−i) the γ = 4 pSHL illuminated with LP, LCP, and RCP Gaussian beams, respectively. Dashed circles indicate the pSHL positions.

Figure 5. Demonstration of an on-chip, 8-OAM-mode sorting structure making use of the pSHL. (a) Schematic illustrating the design of the sorting structure. The outer pSHL is employed to focus and Fourier-transform the emitted SPP fields with different incident optical vortex beams to different focal spots. The inner nanoring slits are designed at the focal spots to out-couple the excited plasmonic OAM modes to the far field for detection. (b) The sorting results for eight incident OAM beams, including: four OAM beams of topological charge 3, 1, −9, and −7 with LCP, and four OAM beams of topological charge −1, −3, 7, and 9 with RCP. The white cross in (b) marks the geometric center of the pSHL. E

DOI: 10.1021/acsphotonics.9b00551 ACS Photonics XXXX, XXX, XXX−XXX

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Figure 6. Demonstration of a 6-OAM-mode angular sorting structure, making use of the pSHL. (a) Schematic of the sorting structure and the angular distribution of the six sorted OAM modes. (b) Sorting results for the six incident OAM beams, including the three OAM beams of topological charges of 1, −3, and 2 with LCP and three OAM beams of topological charges of −1, 3, and −2 with RCP. l o πγ1 cos(φ) + m1φ/2 for φ0 = 0 o o o o o o πγ2 cos(φ + π /3) + m2φ/2 for φ0 = − π /3 θ=m o o o o o o πγ cos(φ + 2π /3) + m3φ/2 for φ0 = − 2π /3 o n 3

both in theory and by experimental demonstration. Enabled by the unique features of the pSHL and the intrinsic mode coupling nature of the nanoring slit, we demonstrated spindemultiplexing, omnidirectional OAM modes coupling and sorting, and angular-distributed OAM-mode sorting. Considering that this lens is ultracompact and ultrathin, it provides a new platform for on-chip manipulation of SAM and OAM of light. Its integration into chip-scale applications may benefit optical communications, quantum computing and information, and biosensing in the future.

(8)

Similarly, the orientation angle for each pair of the antennas is selected from the three values given by eq 8 in sequence, which means that the three pSHLs are merged into a single pSHL (Supporting Information, Figure S6). Knowing the orders of the spiral phases (m1, m2, m3) encoded onto the lens, the topological charges of the incident OAM beams are m = l − σs· mj, j = 1, 2, and 3. In our situation, the scaling factors are set to γ1 = γ2 = γ3 = 2, and m1 = 0, m2 = 2, m3 = −1. In consequence, the angular-sorted six OAM modes are (φ0 = 0, l = 1, σs = 1, m = 1), (φ0 = 0, l = −1, σs = 1, m = −1), (φ0 = −π/3, l = −1, σs = 1, m = −3), (φ0 = −π/3, l = 1, σs = −1, m = 3), (φ0 = −2π/3, l = 1, σs = 1, m = 2), and (φ0 = −2π/3, l = −1, σs = −1, m = −2); see Figure 6 for the simulation results (details for sorting schematic are shown in Supporting Information, Table S2). To sum up, we designed and demonstrated a pSHL that achieves spin-dependent shifts of the plasmonic lenses and, more importantly, retain Fourier-transform functionality of the lens. We revealed the relationship between the spin-dependent splitting of the focal spot and the phase profile of the pSHL

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.9b00551. Phase profiles of the pSHL and experimental setup. Figure S1: Schematic of the pSHL; Figure S2: Experiment setup; Figure S3: Sketch for the eight OAM mode demultiplexer; Figure S4: Schematic diagram illustrating the merging strategy for the eight OAM mode demultiplexer; Figure S5: Sketch for the annular distributed six OAM mode demultiplexer; F

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(6) Liberman, V. S.; Zel’dovich, B. Y. Spin-orbit interaction of a photon in an inhomogeneous medium. Phys. Rev. A: At., Mol., Opt. Phys. 1992, 46, 5199−5207. (7) Marrucci, L.; Manzo, C.; Paparo, D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett. 2006, 96, 163905. (8) Bliokh, K. Y.; Niv, A.; Kleiner, V.; Hasman, E. Geometrodynamics of spinning light. Nat. Photonics 2008, 2, 748−753. (9) Bliokh, K. Y.; Rodríguez-Fortuño, F. J.; Nori, F.; Zayats, A. V. Spin-orbit interactions of light. Nat. Photonics 2015, 9, 796−808. (10) Cardano, F.; Marrucci, L. Spin-orbit photonics. Nat. Photonics 2015, 9, 776−778. (11) Hosten, O.; Kwiat, P. Observation of the spin hall effect of light via weak measurements. Science 2008, 319, 787−90. (12) Gorodetski, Y.; Bliokh, K. Y.; Stein, B.; Genet, C.; Shitrit, N.; Kleiner, V.; Hasman, E.; Ebbesen, T. W. Weak measurements of light chirality with a plasmonic slit. Phys. Rev. Lett. 2012, 109, No. 013901. (13) Prajapati, C.; Ranganathan, D.; Joseph, J. Spin Hall effect of light measured by interferometry. Opt. Lett. 2013, 38, 2459. (14) Sinova, J.; Culcer, D.; Niu, Q.; Sinitsyn, N. A.; Jungwirth, T.; MacDonald, A. H. Universal Intrinsic Spin Hall Effect. Phys. Rev. Lett. 2004, 92, 126603. (15) Wunderlich, J.; Park, B. G.; Irvine, A. C.; Zarbo, L. P.; Rozkotova, E.; Nemec, P.; Novak, V.; Sinova, J.; Jungwirth, T. Spin Hall effect transistor. Science 2010, 330, 1801−4. (16) Kato, Y. K.; Myers, R. C.; Gossard, A. C.; Awschalom, D. D. Observation of the spin hall effect in semiconductors. Science 2004, 306, 1910−1913. (17) Kildishev, A. V.; Boltasseva, A.; Shalaev, V. M. Planar photonics with metasurfaces. Science 2013, 339, 1232009. (18) Zhang, L.; Mei, S.; Huang, K.; Qiu, C. W. Advances in Full Control of Electromagnetic Waves with Metasurfaces. Adv. Opt. Mater. 2016, 4, 818−833. (19) Yu, N.; Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 2014, 13, 139−150. (20) Meinzer, N.; Barnes, W. L.; Hooper, I. R. Plasmonic metaatoms and metasurfaces. Nat. Photonics 2014, 8, 889−898. (21) Yin, X.; Ye, Z.; Rho, J.; Wang, Y.; Zhang, X. Photonic spin Hall effect at metasurfaces. Science 2013, 339, 1405−1407. (22) Yu, N.; Genevet, P.; Kats, M. A.; Aieta, F.; Tetienne, J. P.; Capasso, F.; Gaburro, Z. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 2011, 334, 333− 7. (23) Chiao, R. Y.; Wu, Y. S. Manifestations of Berry’s topological phase for the photon. Phys. Rev. Lett. 1986, 57, 933−936. (24) Berry, M. V. The adiabatic phase and Pancharatnam’s phase for polarized light. J. Mod. Opt. 1987, 34, 1401−1407. (25) Bomzon, Z.; Kleiner, V.; Hasman, E. Pancharatnam-Berry phase in space-variant polarization-state manipulations with subwavelength gratings. Opt. Lett. 2001, 26, 1424−1426. (26) Bomzon, Z.; Biener, G.; Kleiner, V.; Hasman, E. Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings. Opt. Lett. 2002, 27, 1141−1143. (27) Hasman, E.; Kleiner, V.; Biener, G.; Niv, A. Polarization dependent focusing lens by use of quantized Pancharatnam-Berry phase diffractive optics. Appl. Phys. Lett. 2003, 82, 328−330. (28) Huang, L.; Chen, X.; Mühlenbernd, H.; Li, G.; Bai, B.; Tan, Q.; Jin, G.; Zentgraf, T.; Zhang, S. Dispersionless Phase Discontinuities for Controlling Light Propagation. Nano Lett. 2012, 12, 5750−5755. (29) Lin, J.; Mueller, J. P.; Wang, Q.; Yuan, G.; Antoniou, N.; Yuan, X.-C. C.; Capasso, F. Polarization-controlled tunable directional coupling of surface plasmon polaritons. Science 2013, 340, 331−334. (30) Shitrit, N.; Yulevich, I.; Maguid, E.; Ozeri, D.; Veksler, D.; Kleiner, V.; Hasman, E. Spin-optical metamaterial route to spincontrolled photonics. Science 2013, 340, 724−726. (31) Du, L.; Kou, S. S.; Balaur, E.; Cadusch, J. J.; Roberts, A.; Abbey, B.; Yuan, X.-C. C.; Tang, D.; Lin, J. Broadband chirality-coded metaaperture for photon-spin resolving. Nat. Commun. 2015, 6, 10051.

Figure S6: Schematic diagram illustrating the merging strategy for the six OAM mode demultiplexer; Figure S7: Measured far-filed scattering with AM mode of l = 1; Table S1: Parameters of the pSHL for eight OAM modes sorting; Table S2: Parameters of the pSHL for six OAM modes sorting (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Zhenwei Xie: 0000-0002-4526-9746 Jiao Lin: 0000-0002-3943-5947 Guixin Li: 0000-0001-9689-8705 Xiaocong Yuan: 0000-0003-2605-9003 Author Contributions

L.D. developed the concept presented in this paper. Z.X. and L.D. performed the analytical and numerical modeling, designed the device, and wrote the manuscript. G.S. and J.L. fabricated the device. Z.X., A.Y., and C.L. conducted the measurements. L.D. and X.Y. supervised the entire project. All authors discussed the results and commented on the article. Author Contributions ‡

These authors contributed equally to this work.

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61490712, U1701661, 61622504, 61427819, 11604218); the Leading Talents of Guangdong Province Program No. 00201505; the Natural Science Foundation of Guangdong Province (Grant No. 2016A030312010); the Science and Technology Innovation Commission of Shenzhen (Grant Nos. KQTD2015071016560101, ZDSYS201703031605029, KQTD2017033011044403, KQJSCX20170727100838364, JCYJ20180507182035270); and the Start-up Funding of SZU (2019075). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was performed in part at the Melbourne Centre for Nanofabrication in the Victorian Node of the Australian National Fabrication Facility. L. Du acknowledges the support given by Guangdong Special Support Program.

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DOI: 10.1021/acsphotonics.9b00551 ACS Photonics XXXX, XXX, XXX−XXX