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The spin Hall effect is a basic phenomenon arising from the spin-orbit coupling of electrons.¹ The optical spin Hall effect (OSHE) – beam displacement and momentum shift due to the optical spin (polarization helicity) – was recently presented in propagating polarized light,² in a plasmonic topological defect,³ and in a thermal antenna lattice.⁴ The effect was attributed to the optical spin-orbit interaction occurring when the light passes through an anisotropic and inhomogeneous medium.

Here, we present the optical spin Hall effects in coupled localized plasmonic chains manifested by a spin-dependent momentum redirection.⁵ A straight chain of anisotropic nanoantennas whose local orientation varies along the chain axis was fabricated. Due to the collective interaction of the localized mode within the periodic plasmonic chain a spin-dependent beam deflection, with an opposite spin state relative to the incident beam (spin-flip), was observed in the momentum space. This effect is regarded as the locally anisotropic optical spin Hall effect (OSHE-LA) and it arises due to the interaction between the optical spin and the rotating anisotropic nanoantennas.

In light of these results one can address the question: Is it possible to observe the OSHE with isotropic nanoantennas? We demonstrated a similar spin Hall momentum deviation with isotropic antennas. This effect is regarded as the locally isotropic optical spin Hall effect (OSHE-LI) and it results from the interaction between the optical spin and the plasmonic chain curvature.

When the structure symmetry, or more explicitly the chain path, is circular, the corresponding conservation rule is for the angular momentum (AM). The AM of an optical beam can have two components: an intrinsic component associated with the handedness of the optical spin, and an extrinsic (orbital) component associated with its spatial structure. The OSHE-LI and OSHE-LA were observed in circular chains with isotropic nanoantennas and rotating anisotropic nanoantennas with an integer-fold rotation, respectively. The scattered spin-flip components were measured and a characteristic singular beam is clearly seen in the images which is a signature of orbital AM. The observed orbital AM in circular symmetry is a manifestation of a spiral phase front which is directly linked to the azymuthal spin Hall momentum deviation.^3,5 Using the twin vortex sources interference method, we experimentally demonstrated that the orbital AM of the spin-flip component equals to twice of the incident spin for the OSHE-LI, and an integer-fold magnification is obtained for the OSHE-LA.

In summary, we observed the optical spin Hall effect in plasmonic coupled localized mode chains. Compared to the OSHE-LI in circular symmetry, the OSHE-LA provides an additional degree of freedom for optical AM generation, which may be utilized for spin-dependent plasmonic vortex driven nanomotors. The spin of photons may provide an additional degree of freedom in nanoscale photonics leading to a new branch in optics – spinoptics.

(a) The scanning electron microscope (SEM) image of a chain in which the orientation of the nanorods (anisotropic nanoantennas) varies linearly along the chain axis with a period of , and the measured spin-dependent momentum deviation for the OSHE-LA. The red and blue lines stand for incident right-handed (spin up) and left-handed (spin down) circularly polarized light, respectively. Bottom, the SEM image of a curved chain consisting of coaxial apertures (isotropic nanoantennas); the designed local orientation of the curved chain results in a similar spin Hall momentum deviation. (b) The OSHE-LI and OSHE-LA for circular chains. The measured far-field intensity distribution of the spin-flip component scattered from a circular chain of coaxial apertures (left) and rotating nanorods with a double rotation rate (right); bottom, SEM images of the chains. The spin Hall momentum deviation is accompanied by a spiral phase-front with an orbital AM per photon of and , for the OSHE-LI and OSHE-LA, respectively

1. M. I. Dyakonov and V. I. Perel, "Current-induced spin orientation of electrons in semiconductors", Phys. Lett. A 35, 459 (1971).

2. K. Y. Bliokh, A. Niv, V. Kleiner and E. Hasman, "Geometrodynamics of spinning light", Nature Photon. 2, 748 (2008).

3. Y. Gorodetski, S. Nechayev, V. Kleiner and E. Hasman, "Plasmonic Aharonov-Bohm effect: optical spin as the magnetic flux parameter", Phys. Rev. B 82, 125433 (2010).

4. N. Dahan, Y. Gorodetski, K. Frischwasser, V. Kleiner and E. Hasman, "Geometric Doppler effect: spin-split dispersion of thermal radiation", Phys. Rev. Lett. 105, 136402 (2010).

5. N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner and E. Hasman, "Optical spin Hall effects in plasmonic chains", Nano Lett. 11, 2038 (2011)