geometric spin hall effect of light
DESCRIPTION
Geometric Spin Hall Effect of Light. Andrea Aiello , Norbert Lindlein, Christoph Marquardt, Gerd Leuchs. MPL Olomouc, June 24, 2009. OAM. SAM. Optical angular momentum and spin-orbit coupling. - PowerPoint PPT PresentationTRANSCRIPT
Geometric Spin Hall Effect of Light
Andrea Aiello, Norbert Lindlein,
Christoph Marquardt, Gerd Leuchs
MPL Olomouc, June 24, 2009
Olomouc, 24/6/2009 2
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/photonOAM/
SAM OAM
Olomouc, 24/6/2009 3
Spin Hall effect of light
Onur Hosten and Paul Kwiat, Science 319, 787-790 (2008)
This effect is also known as
Imbert-Fedorov shift
Olomouc, 24/6/2009 4
Geometrodynamics of spinning light
K. Y. Bliokh et al. Nature Photon. 2, 748–753 (2008).
Olomouc, 24/6/2009 5
Geometric spin Hall effect of light
x
yz
z’x’
y’
L
R
tan
2
x
A. Aiello, N. Lindlein, C. Marquardt, G. Leuchs, arXiv:0902.4639v1[quant-ph] (2009).
Olomouc, 24/6/2009 6
1. What is the physical origin of such a shift?
2. Is this shift measurable?
Questions
Olomouc, 24/6/2009 7
Reminder: Helicity of light
x
yz
E
ˆ ˆ
ˆ ˆ
x y
R R L L
E x y
e e
1ˆ ˆ ˆ
21
ˆ ˆ ˆ2
R
L
i
i
e x y
e x y
22**RLyxyxi helicity
122 RL
Olomouc, 24/6/2009 8
Linear and angular momentum of light
* 30 Re ( ) ( )2
d rJ r E r B r
r3d)(rP p Total linear and angular momenta
)()(
)()(Re2
)( *0
rrr
rBrEr
pj
p
Time-averaged linear and
angular momentum densities(per unit of volume) = Poynting vector = energy density flux
)(2 rpc
Olomouc, 24/6/2009 9
Transverse angular momentum
zyxr ˆˆˆdd)( zyx PPPyx pP
zyxr ˆˆˆdd)( zyx JJJyx jJ
yx ˆˆ yx JJ J
Linear and angular momentum of light per unit length
Transverse linear momentumyx ˆˆ yx PP P
Olomouc, 24/6/2009 10
Centroid (barycenter) of the intensity distribution
z
z
P
yxpyx
yxI
yxI
dd)(ˆˆ
dd)(
dd)(
ryx
r
rrr
),,()(2 zyxIpc z r
intensity integrated 2 zPc
Olomouc, 24/6/2009 11
Angular momentum-vs-transverse shift
zxy
yzx
PxPzJ
PzPyJ
yxP
yxpy
P
yxpx
z
z
z
zyx
ry
rxr ˆˆ
dd)(ˆ
dd)(ˆ
)()()(
)()()(
)()()(
rrr
rrr
rrr
xyz
zxy
yzx
pypxj
pxpzj
pzpyj
zyxr ˆˆˆdd)( zyx JJJyx jJ
zyxr ˆˆˆdd)( zyx PPPyx pP
Olomouc, 24/6/2009 12
Geometric Spin Hall Effect of Light
xPJ
yPJ
zy
zx
at z = 0
x
z j
y
z
x̂xjj
y
z’L
1helicity
Olomouc, 24/6/2009 13
1. What is the physical origin of such a shift?
2. Is this shift measurable?
Questions
Olomouc, 24/6/2009 14
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:
2222)()()()( rrrrE zyx EEE
22)()(fluxintensity rr yx EE
Olomouc, 24/6/2009 15
• 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:
( )xE r ( )zE r
Observation plane
Olomouc, 24/6/2009 16
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
Conclusions