Geometric Spin Hall Effect of Light

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Geometric Spin Hall Effect of Light
Andrea Aiello, Norbert Lindlein, Christoph
Marquardt, Gerd Leuchs

• MPL Olomouc, June 24, 2009

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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) http//www.physics.gla.ac.uk/Optics/play/ph
otonOAM/
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Spin Hall effect of light
This effect is also known as Imbert-Fedorov shift
Onur Hosten and Paul Kwiat, Science 319, 787-790
(2008)
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Geometrodynamics of spinning light
K. Y. Bliokh et al. Nature Photon. 2, 748753
(2008).
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Geometric spin Hall effect of light
z
y
y
z
x
x
A. Aiello, N. Lindlein, C. Marquardt, G. Leuchs,
arXiv0902.4639v1quant-ph (2009).
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Questions

1. What is the physical origin of such a shift?
2. Is this shift measurable?

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Reminder Helicity of light
helicity
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Linear and angular momentum of light
Total linear and angular momenta
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Linear and angular momentum of light per unit
length
Transverse linear momentum
Transverse angular momentum
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Centroid (barycenter) of the intensity
distribution
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Angular momentum-vs-transverse shift
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Geometric Spin Hall Effect of Light
at z 0
helicity
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Questions

1. What is the physical origin of such a shift?
2. Is this shift measurable?

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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

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• 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
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Conclusions

1. 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