Plasma vorticiy and electromagnetic angular momentum

29 Pages·2009·12.49 MB·English

by  Bo Thidé

IPELS 2009, Djurönäset, Stockholm Archipelago, 11 June, 2009
Plasma vorticity and electromagnetic
orbital angular momentum
Bo Thidé
Swedish Institute of Space Physics, IRF, Uppsala, Sweden
LOIS Space Centre, Växjö, Sweden
with contributions from the LOIS OAM/radio topology collaboration
J. Bergman, L. Daldorff, S. Mohammadi, T. Leyser, E. Nordblad. L. Norin (Uppsala),
R. Karlsson (Graz), T. Carozzi (Glasgow), H. Lundstedt (Lund), W. Löwe, W. Baan, M. Milrad (Växjö),
M. Fredriksson, N. Ibragimov, R. Khamitova. C. Svahnberg (BTH, Karlskrona),
H. Then (Oldenburg), T. Mendonca (Lisbon), Ya. N. Istomin (Lebedev Institute, Moscow),
E. Weibust, B. Sjökvist (IBM Sweden), B. Elmegreen, L. Amini, A. Biem, D. Turaga,
and O. Verscheure (IBM Research, NY)
Fundamental question: How much information
is embedded in EM radiation (radio and radar)?
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 IPELS, Djurönäset, Sweden, 8–12 June, 2009 2
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 IPELS, Djurönäset, Sweden, 8–12 June, 2009 3
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 radar.
Bo Thidé IPELS, Djurönäset, Sweden, 8–12 June, 2009 4
Total radiated EM field angular momentum
em
For radiation beams in free space, EM field angular momentum J can
be separated into two parts [Jackson, 1998; Thidé, 2009]:
For each single Fourier mode in real-valued representation [van Enk &
Nienhuis, 1992]:
em
The first part is the EM spin angular momentum (SAM) S , a.k.a.
wave polarisation, and the second part is the EM orbital angular
em
momentum (OAM) L .
em
NB: In general, both EM linear momentum p , and EM angular
em em em
momentum J = L + S are radiated all the way out to the far zone!
Bo Thidé IPELS, Djurönäset, Sweden, 8–12 June, 2009 5
Standard textbooks show that classical
EM angular momentum is indeed
radiated all the way to infinity
Bo Thidé IPELS, Djurönäset, Sweden, 8–12 June, 2009 6
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
Bo Thidé IPELS, Djurönäset, Sweden, 8–12 June, 2009 7
EM beams on the same frequency but with different OAM
would be orthogonal and not interfere with each other
Spiraling Poynting/linear momentum (and OAM) vectors!
l=+1 l=+3
l= -4
Bo Thidé 8
Imparting OAM onto an EM beam (laser, mm wave)
with the help of a spiral plate or hologram
Bo Thidé IPELS, Djurönäset, Sweden, 8–12 June, 2009 9
Observations at 94 GHz radio of angular momentum
induced azimuthal (rotational) Doppler shift
Bo Thidé IPELS, Djurönäset, Sweden, 8–12 June, 2009 10