Geometric Spin Hall Effect of Light Andrea Aiello, Norbert Lindlein, Christoph Marquardt, Gerd Leuchs MPL Olomouc, June 24, 2009

Olomouc, 24/6/20092 Optical angular momentum and spin-orbit coupling A suitably prepared beam of light may have both a spin and an orbital angular momentum (SAM and OAM). SAM  circular polarization OAM  spiraling phase-front SAM and OAM may be coupled! L. Allen, M. W. Beijersbergen, R. J. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185, (1992) SAM OAM

Olomouc, 24/6/20093 Spin Hall effect of light Onur Hosten and Paul Kwiat, Science 319, (2008) This effect is also known as Imbert-Fedorov shift

Olomouc, 24/6/20094 Geometrodynamics of spinning light K. Y. Bliokh et al. Nature Photon. 2, 748–753 (2008).

Olomouc, 24/6/20095 Geometric spin Hall effect of light x y z z’ x’ y’ A. Aiello, N. Lindlein, C. Marquardt, G. Leuchs, arXiv: v1[quant-ph] (2009).

Olomouc, 24/6/ What is the physical origin of such a shift? 2.Is this shift measurable? Questions

Olomouc, 24/6/20097 Reminder: Helicity of light x y z helicity

Olomouc, 24/6/20098 Linear and angular momentum of light Total linear and angular momenta Time-averaged linear and angular momentum densities (per unit of volume) = Poynting vector = energy density flux

Olomouc, 24/6/20099 Transverse angular momentum Linear and angular momentum of light per unit length Transverse linear momentum

Olomouc, 24/6/ Centroid (barycenter) of the intensity distribution

Olomouc, 24/6/ Angular momentum-vs-transverse shift

Olomouc, 24/6/ Geometric Spin Hall Effect of Light at z = 0 x y z z’ helicity

Olomouc, 24/6/ What is the physical origin of such a shift? 2.Is this shift measurable? Questions

Olomouc, 24/6/ The answer is: YES, but…. Many detectors are sensitive to the electric field energy density rather than Poynting vector flux, Such energy density contains the contributions given by the three components (x,y,z) of the electric field: The flux of the Poynting vector across the observation plane contains the contributions given by the two transverse components ( x,y ) of the electric field only:

Olomouc, 24/6/ In practice, it will be sufficient to use a polarizer (non tilted!) in front of the detector to attenuate either or in order to measure a non-zero shift. The difference between energy density and linear momentum distributions is also relevant, e.g., in atomic beam deflection experiments: Observation plane

Olomouc, 24/6/ When a circularly polarized beam of light is observed from a reference frame tilted with respect to the direction of propagation of the beam, the barycenter of the latter undergoes a shift comparable with the wavelength of the light 2.Extensive numerical simulations performed with the program POLFOCUS agree very well with analytical predictions for well collimated beams not too close to grazing incidence Conclusions