Plasma Vorticity and Electromagnetic Angular ...

Utilisation of Electromagnetic Angular Momentum in Studies of Space Bo Thidé Swedish Institute of Space Physics, IRF, Uppsala, Sweden That far-zone OAM from a dipole is generated by near-zone

with contributions from

Fabrizio Tamburini Department of Astronomy, University of Padova, Italy and

LOFAR/LOIS project members Uppsala and elsewhere

Lecture 2, Meudon, France, 22 September, 2010

Very readable paper on photon orbital angular momentum


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Very nice review on photon orbital angular momentum


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EM angular momentum maybe decomposed into spin (SAM) and orbital (OAM) plus a third term


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EM angular momentum maybe decomposed into spin (SAM) and orbital (OAM) plus a third term


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Classical EM linear momentum and angular momentum can be expressed in QM operators EM field total angular momentum (TAM) around the origin 0:

Where A(t,x) is the vector potential and Photon spin angular momentum (SAM) ~ polarisation Photon orbital angular momentum (OAM)

For each (temporal) Fourier component:

, where

Bo Thidé

Linear momentum operator

, where

SAM operator

, where

OAM operator


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Difference between polarisation (SAM) and orbital angular momentum (OAM)


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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


Sjöholm and Palmer, 2007 8

Instantaneous field vectors across an antenna array for a radio beam with circular SAM

Phase 0 deg Bo Thidé & Jan

Phase 45 deg

CSC Colloquium, SETI Institute, Mountain View, Lecture 1, Meudon, France, 21 September, 2010 9 CA, January 2, 2008

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 can carry a lot of extra information! The Jones matrix goes from 2×2 to 2(j+1)×2(j+1), j=s+l .


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Instantaneous field vectors in a cross section of a radio beam carrying both SAM and OAM

Phase 0 deg Bo Thidé & Jan

Phase 45 deg


Orbital angular momentum due to azimuthal phase variation and beam (a)symmetry

Bo Thidé


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The generation of beams carrying OAM proceeds thanks to the insertion in the optical path of a phase modifying device which imprints a certain vorticity on the phase distribution of the incident beam.

Imparting OAM onto a light beam Fork holograms are an example of such devices. If the hologram presents N bifurcations, then at the m-th diffraction order it imposes a OAM value equal to Nmħ (Vaziri et al. 2002).

On-axis

off-axis spectrum of OAM

Spiral Phase Plate

s

l = ∆n λ  s = total thickness Δn = difference of refraction indices.

Fabrizio Tamburini

of

the

plate,


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Conventional radio telescopes not sufficient. Can we do better? The array of fourteen 25 m dishes at Westerboork (NL), sees nearby objects emitting 1420.4 MHz (21 cm λ H hyperfine splitting) lines

M31 (Andromeda, Local group) Bo Thidé


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The Grand Challenge: Observe the first 21 cm radio line emitted after Big Bang!

Bo Thidé

REAL Seminar, BTH, Ronneby, 23 January,2010 2009 Lecture 1, Meudon, France, 21 September,

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Answer: New-generation wide-area radio telescopes with improved sensitivity, resolution and flexibility LOFAR Low Frequency Array (10–240 MHz). Test station at Exloo operational 2004, full-scale deployment of 25 000 antennas in progress. Must be able to handle data streams up to 23 Tbits/s.

LOIS LOFAR In Scandinavia. Pathfinder station near Växjö operational 2004, fast fibre network, supercomputer 2005. Prototype station near Ronneby, 2010. Full-scale station in Poznan, Poland, in the 2011-2013 timeframe.

SKA Square Kilometre Array. Australia or South Africa, ~2020. Very sensitive (5 000 000 antennas!). Bo Thidé


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Radio OAM can be probed with LOFAR-type phased arrays. Best results with vector sensing antennas Thidé et al., Phys. Rev. Lett., 99, 087701, 2007

Bo Thidé


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The OAM radio results agree with theory Theory predicts that a circular polarised radio beam in a pure OAM eigenstate with azimuthal phase dependence exp(ilφ), frequency ω, and energy H, should have a total angular momentum component JzEM = lH/ω along the z (beam) axis.

Bo Thidé


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Controlled antenna-chamber experiments show that radio OAM does indeed work Preliminary results

OAM radio mode l = 1, -1

Bo Thidé

OAM radio mode l = 2, -2


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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


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Field vector sensing means total configurability

Excellent radio coronagraph for the solar corona and exoplanets! Lecture 1, Meudon, France, 21 September, 2010

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First real-world OAM coronagraph example T122 telescope, Asiago, Italy

Sufficient resolution for direct detection of extra-solar planets! Lecture 1, Meudon, France, 21 September, 2010

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LOIS 2nd generation prototype station, 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


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Use large arrays with velectric and magnetic antennas that sample the entire EM field vector

To be first used in Venice, 2010 Bo Thidé


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3D vector antennas allow new types of diagnostics

Bo Thidé


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LOIS has measured the photon spin current V in ionospheric radio signals since 2003

Bo Thidé


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Challenge: Ionospheric and atmospheric turbulence distort low-frequency radio signals from outer space Today it is possible to compensate (‘self-calibrate’) for amplitude and nonsingular phase distortion of signals propagation through the ionosphere. Data from observations at VLA (Very Large Array, NM, USA) at 74 MHz.

Bo Thidé

Asiago, 24October, Lecture 1, Meudon, France, 21 2008 September, 2010

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Close collaboration with IBM Research, NY, on the analysis of streaming data from digital radio sensors

Bo Thidé


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SEE as an on-demand space plasma EM turbulence diagnostics Complements – and supplements – optics, radars, satellites,etc.

BoThidé


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Secondary HF radio emission dependence HF pump frequency swept continuously up and down across 4f at Sura, Russia on primary HF radio frequency ce

BUM hysteresis

HF excited secondary radiation (SEE) as recorded at the radio facility SURA near Nizhniy Novgorod, Russia, 1999. The HF pump frequency is swept across the ionospheric 4th electron gyroharmonic. 

60 kHz

Pump

5340 kHz

 (Click for animation)

4fce

BoThidé

5540 kHz


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2D polarimetric signatures of EM radiation from space plasma turbulence induced by radio pumping

Essentially 2D Stokes parameters Concomitant symmetry group: SU(2) Expansion to 3D [SU(3)] straightforward Bo Thidé


Anderson-Higgs mechanism affected by POAM

Bo Thidé


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EM equivalent of fluid/plasma vorticity

Bo Thidé


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Plasmons (Langmuir waves) can carry OAM but not SAM

Bo Thidé


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Nonlinear transfer of OAM radio ↔ plasma Brillouin = ion line Raman = plasma line

Bo Thidé


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Europe is leading the way

Bo Thidé


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POAM in light around a Kerr black hole (Sgr A*)

Bo Thidé


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Bo Thidé


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Bo Thidé


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Bo Thidé


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Bo Thidé


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Sardinia Radio Telescope first to use radio OAM

Bo Thidé


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Observations at 94 GHz of angular momentum induced azimuthal (rotational) Doppler shift

Bo Thidé


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Rotational Doppler shift spectrum

Bo Thidé


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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


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Spiral (OAM) spectrum imaging results

…and its response

Bo Thidé


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OAM detection of inhomogeneities (in transmission)

Bo Thidé & Jan


Conventional radio multipath diversity utilises three extra electromagnetic degrees of freedom The first multipath diversity paper

The physics behind multipath diversity

Reflection, i.e. space inversion x → x´ = -x is represented physically by the transformations

implying the threefold EM symmetry/three extra degrees of freedom:

Bo Thidé


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Radiation generation by utilising the rotational degrees of freedom of the EM field

Bo Thidé


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Recent call for funding of practical “on-the-scene” information-rich applications using OAM etc.

Bo Thidé


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Five radio channels on the one and the same frequency but in different (orthogonal) OAM states Sum of l = -2, -1, 0, +1, +2

l = -2

Spiral frequency axis (phase rotation in space)

l = -1 Ordinary frequency axis (amplitude oscillation in time)

l=0 l = +1 l = +2

Bo Thidé


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The OAM topological degree of freedom has revolutionised wireless communications

Bo Thidé


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Hyperentangled SAM and OAM photon states break the linear-optics channel capacity threshold

Bo Thidé


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The conventional Shannon dimensionality of 2 can be exceeded by using OAM degrees of freedom

Bo Thidé


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Thank you for your attention

....there may be more things in heaven and earth than even Maxwell had dreamt of … Bo Thidé


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Thank you

....there may be more things in heaven and earth than even Maxwell had dreamt of … Bo Thidé


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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


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Conserved quantities in EM fields an matter (2) 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. Invariance under proper Lorentz transformations => conservation of system centre of energy:

Bo Thidé


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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


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Imparting vorticity/OAM onto an EM beam (laser, microwave) with the help of a spiral plate or hologram

Bo Thidé


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POAM can improve the (Rayleigh) resolving power of a telescope by one order of magnitude

The James Webb Space Telescope Super Resolution with OVs in diffraction-limited telescopes and other optical instruments

Fabrizio Tamburini


Credit: ESA (C. Carreau)

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Optical Vortices and Stellar Coronagraphy

OVC Lyot stop

ordinary Lyot stop

We place the spiral phase plate (SPP) in the focal plane of the telescope to generate an ℓ = 2 OV for the on-axis star, then followed by a ring-shaped Lyot stop to block that vortex. The off-axis secondary star light, instead, will pass through the Lyot mask without being affected. Sub-Rayleigh by a factor 10. Fabrizio Tamburini et al.


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Plasma Vorticity and Electromagnetic Angular ...

Plasma Vorticity and Electromagnetic Angular ...

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