EISCAT-3D Workshop, Uppsala, 19 21 May 2010 Orbital Angular
Momentum and other newly recongnised EM degrees of freedom Bo Thid
Swedish Institute of Space Physics, IRF, Uppsala, Sweden With
contributions from the LOIS OAM/radio topology collaboration
Slide 2
EISCAT_3D Workshop, Uppsala, 19 21 May 2010Bo Thid2 Phase
singularities (dislocations) are to be expected in radio beams
propagating through space
Slide 3
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 EM angular momentum
is a conserved physical observable. Just like the linear momentum
(Poytning vector), it that can carry information over huge
distances Bo Thid3
Slide 4
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Mechanical effects
of photon spin angular momentum (1936) and of photon orbital
angular momentum (1992) Bo Thid4 Beths experiment, 1936
Slide 5
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 EM beam with
circular polarisation (SAM) S but no orbital angular momentum (OAM)
L Bo Thid5 M. J. Padgett, J. Leach et al., U. Glasgow, UK; Royal
Society Phase fronts (loci of constant phase) Sjholm and Palmer,
2007 Optics (LG) Radio
Slide 6
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Different OAM
states correspond to different topological charges (vortex winding
numbers) Bo Thid6 M. J. Padgett, J. Leach et al., U. Glasgow, UK;
Royal Society l=+1 l=+3 l= -4 Spiraling Poynting/OAM vectors carry
a lot of information! The Jones matrix goes from 22 to
2(j+1)2(j+1), j=s+l.
Slide 7
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Difference between
polarisation (SAM) and orbital angular momentum (OAM) 7
Slide 8
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Micromechanical
action of laser light carrying SAM and OAM 8 Spin angular momentum
s = 1 Orbital angular momentum l = 8 Particles of sizes 13 m
irradiated by SAM/OAM laser beams
Slide 9
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Imparting
vorticity/OAM onto an EM beam (laser, mm wave) with the help of a
spiral plate or hologram Bo Thid9
Slide 10
EISCAT_3D Workshop, Uppsala, 19 21 May 2010Bo Thid10 Very
readable pioneering paper on photon OAM in astrophysics
Slide 11
EISCAT_3D Workshop, Uppsala, 19 21 May 2010Bo Thid11 POAM in
light around a Kerr black hole (Sgr A*) Tamburini et al.,
(Submitted)
Slide 12
EISCAT_3D Workshop, Uppsala, 19 21 May 2010Bo Thid12 Bo Thid.
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.Stimulated Electromagnetic Emission and nonlinear
wave-wave interactions in ionospheric heating experiments O mode
SEE X mode SEE Circular, (nearly) O-mode pumping 1983 experiment:
polarisation (SAM) of the secondary radio emissions exhibit
polarimetry anomalies OAM?
Slide 13
EISCAT_3D Workshop, Uppsala, 19 21 May 2010Bo Thid13
Polarimetry (SAM) studies of SEE exhibit anomalies Experiments in
Vasilsursk, Russia, 1998
Slide 14
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Linear transfer of
OAM radio plasma Bo Thid14 EPL, in press
Slide 15
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Nonlinear transfer
of OAM radio plasma Bo Thid15 Brillouin = ion line Raman = plasma
line
Slide 16
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Plasmons (Langmuir
waves) can carry OAM but not SAM Bo Thid16
Slide 17
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Fundamental
question: What are the complete physical characteristics of EM
radiation? Bo Thid17 Symmetric under inhomogeneous Lorentz
transformations. The concomitant Lie group is the 10-dimensional
Poincar group P(10). According to Noethers 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]. Start from the beginning: the microscopic Maxwell-Lorentz
equations
Slide 18
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Conserved
quantities in a closed electromechanical system (matter + EM
fields) [Boyer, 2005] (1) Homogeneity in time => conservation of
system energy (cf. Poyntings theorem): Homogeneity in space =>
conservation of system linear momentum (gives rise to translational
Doppler shift): Foundation of conventional linear momentum radio.
Bo Thid18
Slide 19
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 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 J mech. The second part is the EM
angular momentum J field. Foundation of angular momentum radio or
dual radio. Bo Thid19
Slide 20
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 EM field angular
momentum. Directly from the Maxwell-Lorentz equations Bo Thid20 EM
field angular momentum around the origin:, where where For each
(temporal) Fourier component: (SAM operator) (OAM operator)
Slide 21
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Radio OAM can be
observed by phased arrays Optimal results with vector sensing
antennas Bo Thid21 Thid et al., Phys. Rev. Lett., 99, 087701,
2007
Slide 22
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Field vector
sensing means total configurability Bo Thid22 The ultimate radio
coronagraph!
Slide 23
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Radio beam carrying
both SAM and OAM Linear momentum (Poynting) flux and E(t,x) vs. OAM
flux Bo Thid23 Mohammadi et al., IEEE Trans. Ant. Propag., Vol.
58,2009 Distribution of linear momentum (Poynting ) flux and
E-field vectors Distribution of orbital angular momentum flux
Slide 24
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Observations at 94
GHz of angular momentum induced azimuthal (rotational ) Doppler
shift Bo Thid24
Slide 25
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Rotational Doppler
shift spectrum Bo Thid25
Slide 26
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 OAM spectrum
probing (spiral imaging) a new scatter radar diagnostic Bo Thid26
Recent digital spiral imaging experiments (Ll. Torner et al., Opt.
Express, 13, 873881, 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
Slide 27
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Spiral (OAM)
spectrum imaging results Bo Thid27 and its response
Slide 28
EISCAT_3D Workshop, Uppsala, 19 21 May 2010Bo Thid28 EM
equivalent of fluid vorticity
Slide 29
EISCAT_3D Workshop, Uppsala, 19 21 May 2010Bo Thid29 The OAM
topological degree of freedom has revolutionised wireless
communications
Slide 30
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Hyperentangled SAM
and OAM photon states break the linear-optics channel capacity
threshold Bo Thid30
Slide 31
EISCAT_3D Workshop, Uppsala, 19 21 May 2010Bo Thid31 The
conventional Shannon dimensionality of 2 can be exceeded by using
OAM degrees of freedom
Slide 32
EISCAT_3D Workshop, Uppsala, 19 21 May 2010Bo Thid32 Recent
call for funding of practical on-the-scene information-rich
applications using OAM etc.
Slide 33
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Thank you for your
attention Bo Thid33....there may be more things in heaven and earth
than even Maxwell had dreamt of
Slide 34
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Conserved
quantities in EM fields and matter (1) Bo Thid34 Homogeneity in
time => conservation of system energy (Poyntings theorem):
Homogeneity in space => conservation of system linear momentum
(gives, e.g., rise to EM Doppler shift):
Slide 35
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Conserved
quantities in EM fields an matter (2) Bo Thid35 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.
Slide 36
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 Total radiated EM
field angular momentum Bo Thid36 For radiation beams in free space,
EM field angular momentum J em can be separated into two parts
[Jackson, 1998; Thid, 2010]: For each single Fourier mode in
real-valued representation [van Enk & Nienhuis, 1992]: The
first part is the EM spin angular momentum (SAM) S em, a.k.a. wave
polarisation, and the second part is the EM orbital angular
momentum (OAM) L em. NB: In general, both EM linear momentum p em,
and EM angular momentum J em = L em + S em are radiated all the way
out to the far zone!
Slide 37
EISCAT_3D Workshop, Uppsala, 19 21 May 2010 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
Thid37
Slide 38
EISCAT_3D Workshop, Uppsala, 19 21 May 2010Bo Thid38 LOIS has
measured the photon spin current V in ionospheric radio signals
since 2003