1. EISCAT-3D Workshop, Uppsala, 19 – 21 May 2010 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

2. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé2 Phase singularities (dislocations) are to be expected in radio beams propagating through space

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 Thidé3

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 Thidé4 Beth’s experiment, 1936

5. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 EM beam with circular polarisation (SAM) S but no orbital angular momentum (OAM) L Bo Thidé5 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

6. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Different OAM states correspond to different topological charges (vortex winding numbers) Bo Thidé6 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.

7. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Difference between polarisation (SAM) and orbital angular momentum (OAM) 7

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 1–3 μm irradiated by SAM/OAM laser beams

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 Thidé9

10. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé10 Very readable pioneering paper on photon OAM in astrophysics

11. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé11 POAM in light around a Kerr black hole (Sgr A*) Tamburini et al., (Submitted)

12. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé12 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.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?

13. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé13 Polarimetry (SAM) studies of SEE exhibit anomalies Experiments in Vasil’sursk, Russia, 1998

14. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Linear transfer of OAM radio ↔ plasma Bo Thidé14 EPL, in press

15. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Nonlinear transfer of OAM radio ↔ plasma Bo Thidé15 Brillouin = ion line Raman = plasma line

16. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Plasmons (Langmuir waves) can carry OAM but not SAM Bo Thidé16

17. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Fundamental question: What are the complete physical characteristics of EM radiation? Bo Thidé17 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

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. Poynting’s theorem): Homogeneity in space => conservation of system linear momentum (gives rise to translational Doppler shift): Foundation of conventional ‘linear momentum’ radio. Bo Thidé18

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 Thidé19

20. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 EM field angular momentum. Directly from the Maxwell-Lorentz equations Bo Thidé20 EM field angular momentum around the origin:, where where For each (temporal) Fourier component: (SAM operator) (OAM operator)

21. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Radio OAM can be observed by phased arrays Optimal results with vector sensing antennas Bo Thidé21 Thidé et al., Phys. Rev. Lett., 99, 087701, 2007

22. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Field vector sensing means total configurability Bo Thidé22 The ultimate radio coronagraph!

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 Thidé23 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

24. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Observations at 94 GHz of angular momentum induced azimuthal (rotational ) Doppler shift Bo Thidé24

25. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Rotational Doppler shift spectrum Bo Thidé25

26. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 OAM spectrum probing (spiral imaging) – a new scatter radar diagnostic Bo Thidé26 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…

27. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Spiral (OAM) spectrum imaging results Bo Thidé27 …and its response

28. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé28 EM equivalent of fluid vorticity

29. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé29 The OAM topological degree of freedom has revolutionised wireless communications

30. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Hyperentangled SAM and OAM photon states break the linear-optics channel capacity threshold Bo Thidé30

31. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé31 The conventional Shannon dimensionality of 2 can be exceeded by using OAM degrees of freedom

32. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé32 Recent call for funding of practical “on-the-scene” information-rich applications using OAM etc.

33. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Thank you for your attention Bo Thidé33....there may be more things in heaven and earth than even Maxwell had dreamt of …

34. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Conserved quantities in EM fields and matter (1) Bo Thidé34 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):

35. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Conserved quantities in EM fields an matter (2) Bo Thidé35 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.

36. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Total radiated EM field angular momentum Bo Thidé36 For radiation beams in free space, EM field angular momentum J em 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) 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!

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 Thidé37

38. EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010Bo Thidé38 LOIS has measured the photon spin current V in ionospheric radio signals since 2003