Spin–orbit interactions of light

NATURE PHOTONICS | VOL 9 | DECEMBER 2015 | www.nature.com/naturephotonics Light consists of electromagnetic waves that oscillate in time and propagate in space. Scalar waves are described by their intensity and phase distributions. These are the spatial (orbital) degrees of freedom common to all types of waves, both classical and quantum. In particular, a localized intensity distribution determines the position of a wave beam or packet, whereas the phase gradient describes the propagation of a wave (that is, its wavevector or momentum). Importantly, electromagnetic waves are described by vector fields1. Light therefore also possesses intrinsic polarization degrees of freedom, which are associated with the directions of the electric and magnetic fields oscillating in time. In the quantum picture, the rightand left-hand circular polarizations, with the electric and magnetic fields rotating about the wavevector direction, correspond to two spin states of photons2. Recently, there has been enormous interest in the spin–orbit interactions (SOI) of light3–6. These are striking optical phenomena in which the spin (circular polarization) affects and controls the spatial degrees of freedom of light; that is, its intensity distributions and propagation paths. The intrinsic SOI of light originate from the fundamental spin properties of Maxwell’s equations7,8 and, therefore, are analogous to the SOI of relativistic quantum particles2,9,10 and electrons in solids11,12. As such, intrinsic SOI phenomena appear in all basic optical processes but, akin to the Planck-constant smallness of the electron SOI, they have a spatial scale of the order of the wavelength of light, which is small compared with macroscopic length scales. Traditional ‘macroscopic’ geometrical optics can safely neglect the wavelength-scale SOI phenomena by treating the spatial and polarization properties of light separately. In particular, these degrees of freedom can be independently manipulated: by lenses or prisms, on the one hand, and polarizers or anisotropic waveplates, on the other. SOI phenomena come into play at the subwavelength scales of nano-optics, photonics and plasmonics. These areas of modern optics essentially deal with nonparaxial, structured light fields characterized by wavelength-scale inhomogeneities. The usual intuition of geometrical optics (based on the properties of scalar waves) does not work in such fields and should be substituted by the full-vector analysis of Maxwell waves. The SOI of light represent a new paradigm that provides physical insight and describes the behaviour of polarized light at subwavelength scales. In the new reality of nano-optics, SOI phenomena have a two-fold importance. First, the coupling between the spatial and polarization Spin–orbit interactions of light