orbital angular momentum

Second Colloquium on Scientific and Fundamental Aspects of the GALILEO Programme, Padua, 14–16 October, 2009

Radio Orbital Angular Momentum and Space Physics Bo Thidé Swedish Institute of Space Physics, IRF, and Uppsala University, Uppsala, Sweden LOIS Space Centre, Växjö, Sweden with contributions from the LOIS OAM/radio topology collaboration

J. Bergman, S. Mohammadi, T. Leyser, E. Nordblad (Uppsala), L. Daldorff, (FMI, Helsinki), Second International Colloquium R. Karlsson (Graz), T. Carozzi (Glasgow), H. Lundstedt (Lund), W. Löwe, W. Baan, M. Milrad (Växjö), on Fundamental Aspects and Scientific Applications of Galileo M. Fredriksson, R. Gustavsson, N. Ibragimov, R. Khamitova (BTH, Karlskrona), H. Then (Oldenburg), and GNSS J. T. Mendonça (Lisbon), F. Tamburini (Padova), 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)

Phase singularities (dislocations) are to be expected in radio beams propagating through space

Bo Thidé

2nd Colloquium on the GALILEO Programme, Padua, 14–16 October, 2009

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

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Mechanical effects of EM orbital angular momentum (OAM) predicted 1992

Beth’s experiment, 1936

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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

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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 .


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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

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Sjöholm and Palmer, 2007 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 Bo Thidé

Orbital angular momentum l = 8


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Linear transfer of OAM radio ↔ plasma arXiv; PRL, submiited

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

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Standard textbooks show that electromagnetic angular momentum is indeed radiated all the way to inﬁnity

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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


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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):

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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


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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, 2009]:

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

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Rotational Doppler shift spectrum

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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

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LOFAR Hamburg, 16-19 Sep, 2008 October, 2009 2nd Colloquium on theWorkshop, GALILEO Programme, Padua, 14–16

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Field vector sensing means total configurability

The ultimate radio coronagraph! Bo Thidé


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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., in press, 2009

Distribution of linear momentum (Poynting ) flux and E-field vectors Bo Thidé

Distribution of orbital angular momentum flux


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Use of photon orbital angular momentum (POAM) has come to the fore in astronomy and astrophysics

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Europe is leading the way

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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…

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Spiral (OAM) spectrum imaging results

…and its response

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EM equivalent of fluid vorticity

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Radio photon spin angular momentum (SAM) and orbital angular momentum (OAM) (In press)

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Use three orthogonal electric and magnetic antennas to sample the entire EM field vector

New generation radio sensors, to be first used at LOIS and EISCAT, spring 2010 Bo Thidé


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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)

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

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3D vector antenna allows entirely new radio Better SNR, polarisation in real time, DOA,… Click on pictures for animation! Real data from a real, live outdoor vector receiver at Ångström Lab in Uppsala. On line since 2003. Vector coherency gives superior SNR relative to conventional scalar intensity

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Instantaneous wave polarisation from one single vector antenna


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First OAM/vorticity radio injection experiment in the ionospheric plasma (HAARP, Alaska, 27 Feb, 2008)

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IBM’s latest major data stream software package developed for LOIS radio data

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OAM radio has given rise to many articles in the press

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The OAM topological degree of freedom has revolutionised wireless communications

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Single photons can carry both spin angular momentum S and orbital angular momentum L!

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

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

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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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