orbital angular momentum and other newly recongnised em degrees of freedom
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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. - PowerPoint PPT PresentationTRANSCRIPT
EISCAT-3D Workshop, Uppsala, 19 – 21 May 2010
Orbital Angular Momentum and other newly recongnised EM degrees of freedom
Bo ThidéSwedish Institute of Space Physics, IRF, Uppsala, Sweden
With contributions from the LOIS OAM/radio topology collaboration
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé 2
Phase singularities (dislocations) are to be expectedin radio beams propagating through space
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 Thidé 3
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Mechanical effects of photon spin angular momentum (1936)and of photon orbital angular momentum (1992)
Bo Thidé 4
Beth’s experiment, 1936
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
EM beam with circular polarisation (SAM) S butno orbital angular momentum (OAM) L
Bo Thidé 5
M. J. Padgett, J. Leach et al., U. Glasgow, UK; Royal Society
Phase fronts (loci of constant phase)
Sjöholm and Palmer, 2007
Optics (LG)
Radio
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Different OAM states correspond to different topological charges (vortex winding numbers)
Bo Thidé 6
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 2×2 to 2(j+1)×2(j+1), j=s+l .
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Difference between polarisation (SAM) and orbital angular momentum (OAM)
7
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 1–3 μm irradiated by SAM/OAM laser beams
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 Thidé 9
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé 10
Very readable pioneering paper on photon OAM in astrophysics
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé 11
POAM in light around a Kerr black hole (Sgr A*)Tamburini et al., (Submitted)
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé 12
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.
O mode SEE
X mode SEE
Circular, (nearly) O-mode pumping
1983 experiment: polarisation (SAM) of the secondary radio emissions exhibit polarimetry anomalies – OAM?
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé 13
Polarimetry (SAM) studies of SEE exhibit anomaliesExperiments in Vasil’sursk, Russia, 1998
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Linear transfer of OAM radio ↔ plasma
Bo Thidé 14
EPL, in press
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Nonlinear transfer of OAM radio ↔ plasma
Bo Thidé 15
Brillouin = ion lineRaman = plasma line
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Plasmons (Langmuir waves) can carry OAM but not SAM
Bo Thidé 16
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Fundamental question: What are the completephysical characteristics of EM radiation?
Bo Thidé 17
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].
Start from the beginning: the microscopic Maxwell-Lorentz equations
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. 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 18
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 Jmech . The second part is the EM angular momentum Jfield . Foundation of ‘angular momentum’ radio or ‘dual radio’.
Bo Thidé 19
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
EM field angular momentum. Directlyfrom the Maxwell-Lorentz equations
Bo Thidé 20
EM field angular momentum around the origin:
, where
, where
where
For each (temporal) Fourier component:
(SAM operator)
(OAM operator)
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Radio OAM can be observed by phased arrays Optimal results with vector sensing antennas
Bo Thidé 21
Thidé et al., Phys. Rev. Lett., 99, 087701, 2007
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Field vector sensing means total configurability
Bo Thidé 22
The ultimate radio coronagraph!
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Radio beam carrying both SAM and OAMLinear momentum (Poynting) flux and E(t,x) vs. OAM flux
Bo Thidé 23
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
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Observations at 94 GHz of angular momentum induced azimuthal (rotational ) Doppler shift
Bo Thidé 24
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Rotational Doppler shift spectrum
Bo Thidé 25
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
OAM spectrum probing (spiral imaging) – a new scatter radar diagnostic
Bo Thidé 26
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…
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Spiral (OAM) spectrum imaging results
Bo Thidé 27
…and its response
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé 28
EM equivalent of fluid vorticity
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé 29
The OAM topological degree of freedom has revolutionised wireless communications
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Hyperentangled SAM and OAM photon states break the linear-optics channel capacity threshold
Bo Thidé 30
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé 31
The conventional Shannon dimensionality of 2 can be exceeded by using OAM degrees of freedom
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé 32
Recent call for funding of practical “on-the-scene” information-rich applications using OAM etc.
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Thank you for your attention
Bo Thidé 33
....there may be more things in heaven and earth than even Maxwell had dreamt of …
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Conserved quantities in EM fields and matter (1)
Bo Thidé 34
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):
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Conserved quantities in EM fields an matter (2)
Bo Thidé 35
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 vorticityprobing radio and radar methods.
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
Total radiated EM field angular momentum
Bo Thidé 36
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!
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010
LOIS prototype station under construction in RonnebyTo 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 37
EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé 38
LOIS has measured the photon spin current Vin ionospheric radio signals since 2003