Orbital Angular Momentum and other newly
recongnised EM degrees of freedom
Bo Thidé
Swedish Institute of Space Physics, IRF, Uppsala, Sweden
With contributions from the LOIS OAM/radio topology collaboration
EISCAT-3D Workshop, Uppsala, 19 – 21 May 2010
Phase singularities (dislocations) are to be expected
in radio beams propagating through space
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
2
EM angular momentum is a conserved
physical observable. Just like the linear
momentum (Poytning vector), it that can
carry information over huge distances
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
3
Mechanical effects of photon spin angular momentum (1936)
and of photon orbital angular momentum (1992)
Beth’s experiment, 1936
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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EM beam with circular polarisation (SAM) S but
no orbital angular momentum (OAM) L
Phase fronts (loci of constant phase)
Optics (LG)
Radio
M. J. Padgett, J. Leach et al., U. Glasgow, UK; Royal Society
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Sjöholm and Palmer, 2007
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Different OAM states correspond to different
topological charges (vortex winding numbers)
M. J. Padgett, J. Leach et al., U. Glasgow, UK; Royal Society
l=+3
l=+1
l= -4
Bo Thidé
Spiraling Poynting/OAM
vectors carry a lot of
information! The Jones
matrix goes from 2×2 to
2(j+1)×2(j+1), j=s+l .
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Difference between polarisation (SAM) and orbital
angular momentum (OAM)
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Micromechanical action of laser light carrying
SAM and OAM
Particles of sizes 1–3 μm irradiated by SAM/OAM laser beams
Spin angular momentum s = 1
Orbital angular momentum l = 8
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
8
Imparting vorticity/OAM onto an EM beam (laser,
mm wave) with the help of a spiral plate or hologram
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Very readable pioneering paper on photon OAM in
astrophysics
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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POAM in light around a Kerr black hole (Sgr A*)
Tamburini et al., (Submitted)
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
11
1983 experiment: polarisation (SAM) of the secondary radio
emissions exhibit polarimetry anomalies – OAM?
Bo Thidé. Stimulated Electromagnetic Emission and nonlinear wave-wave interactions in
ionospheric heating experiments. In M. Q. Tran and M. L. Sawley, editors, Proceedings,
Contributed Papers, International Conference on Plasma Physics, volume I, page 131,
Lausanne, Switzerland, 27 June-3 July 1984. Centre de Recherche en Physique des
Plasmas, Ecole Polytechnique Federal de Lausanne, CRPP-EPFL.
Circular, (nearly) O-mode pumping
O mode SEE
X mode SEE
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Polarimetry (SAM) studies of SEE exhibit anomalies
Experiments in Vasil’sursk, Russia, 1998
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Linear transfer of OAM radio ↔ plasma
EPL, in press
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Nonlinear transfer of OAM radio ↔ plasma
Brillouin = ion line
Raman = plasma line
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Plasmons (Langmuir waves) can carry OAM but not SAM
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Fundamental question: What are the complete
physical characteristics of EM radiation?
Start from the beginning: the microscopic Maxwell-Lorentz equations
Symmetric under inhomogeneous Lorentz transformations. The
concomitant Lie group is the 10-dimensional Poincaré group P(10).
According to Noether’s theorem there therefore exist 10 conserved
EM quantities. In fact there exist 23 exact continuous
symmetries/conserved quantities (in vacuo), plus an as yet unknown
number of approximate, conservation laws [Ibragimov, 2008].
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Conserved quantities in a closed electromechanical
system (matter + EM fields) [Boyer, 2005] (1)
Homogeneity in time => conservation of system energy
(cf. Poynting’s theorem):
Homogeneity in space => conservation of system linear
momentum (gives rise to translational Doppler shift):
Foundation of conventional ‘linear momentum’ radio.
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Conserved quantities in a closed electromechanical
system (matter + EM fields) [Boyer, 2005] (2)
Invariance under proper Lorentz transformations =>
conservation of system centre of energy:
Isotropy in space => conservation of system angular
momentum (gives rise to azimuthal Doppler shift):
The first part is the mechanical angular momentum Jmech .
The second part is the EM angular momentum Jfield .
Foundation of ‘angular momentum’ radio or ‘dual radio’.
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
19
EM field angular momentum. Directly
from the Maxwell-Lorentz equations
EM field angular momentum around the origin:
where
For each (temporal) Fourier component:
Bo Thidé
, where
(SAM operator)
, where
(OAM operator)
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Radio OAM can be observed by phased arrays
Optimal results with vector sensing antennas
Thidé et al., Phys. Rev. Lett., 99, 087701, 2007
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Field vector sensing means total configurability
The ultimate radio coronagraph!
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Radio beam carrying both SAM and OAM
Linear momentum (Poynting) flux and E(t,x) vs. OAM flux
Mohammadi et al., IEEE Trans. Ant. Propag., Vol. 58 ,2009
Distribution of linear momentum
(Poynting ) flux and E-field vectors
Bo Thidé
Distribution of orbital angular
momentum flux
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Observations at 94 GHz of angular momentum
induced azimuthal (rotational ) Doppler shift
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Rotational Doppler shift spectrum
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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OAM spectrum probing (spiral imaging) – a
new scatter radar diagnostic
Recent digital spiral imaging experiments (Ll. Torner et al., Opt. Express, 13, 873–881, 2005;
Molina-Terriza et al., J. Eur. Opt. Soc., Rapid Publ., 2, 07014, 2007) have demonstrated that
probing with OAM gives a wealth of new information about the object under study.
The stimulus…
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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Spiral (OAM) spectrum imaging results
…and its response
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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EM equivalent of fluid vorticity
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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The OAM topological degree of freedom has
revolutionised wireless communications
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
29
Hyperentangled SAM and OAM photon states break
the linear-optics channel capacity threshold
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
30
The conventional Shannon dimensionality of 2 can be
exceeded by using OAM degrees of freedom
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
31
Recent call for funding of practical “on-the-scene”
information-rich applications using OAM etc.
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
32
Thank you for your attention
....there may be more things in heaven and earth than even Maxwell had dreamt of …
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
33
Conserved quantities in EM fields and matter (1)
Homogeneity in time => conservation of system energy
(Poynting’s theorem):
Homogeneity in space => conservation of system linear
momentum (gives, e.g., rise to EM Doppler shift):
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
34
Conserved quantities in EM fields an matter (2)
Invariance under proper Lorentz transformations =>
conservation of system centre of energy:
Isotropy in space => conservation of system angular
momentum (gives rise to azimuthal Doppler shift):
Foundation of ‘angular momentum radio’ and vorticity
probing radio and radar methods.
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
35
Total radiated EM field angular momentum
For radiation beams in free space, EM field angular momentum Jem can
be separated into two parts [Jackson, 1998; Thidé, 2010]:
For each single Fourier mode in real-valued representation [van Enk &
Nienhuis, 1992]:
The first part is the EM spin angular momentum (SAM) Sem , a.k.a.
wave polarisation, and the second part is the EM orbital angular
momentum (OAM) Lem .
NB: In general, both EM linear momentum pem, and EM angular
momentum Jem = Lem + Sem are radiated all the way out to the far zone!
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
36
LOIS prototype station under construction in Ronneby
To be augmented by two outer, concentric rings, with 16 and 24 radio units,
respectively, for a total of 48 units with three dipoles each (funding permitting)
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
37
LOIS has measured the photon spin current V
in ionospheric radio signals since 2003
Bo Thidé
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
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