Slide 1

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