Orbital Angular Momentum and other newly recongnised EM degrees of freedom

1. 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. Phase singularities (dislocations) are to be expectedin radio beams propagating through space

3. EM angular momentum is a conserved physical observable. Just like the linear momentum (Poytningvector), it that can carry information over huge distances

4. Mechanical effects of photon spin angular momentum (1936)and of photon orbital angular momentum (1992) Beth’s experiment, 1936

5. EM beam with circular polarisation (SAM) S butno 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 Sjöholm and Palmer, 2007

6. 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 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 . l= -4

7. Differencebetween polarisation (SAM) and orbitalangularmomentum (OAM)

8. Micromechanical action of laser light carrying SAM and OAM Particles of sizes 1–3 μm irradiated by SAM/OAM laser beams Orbital angular momentum l = 8 Spin angular momentum s = 1

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

10. Very readable pioneering paper on photon OAM in astrophysics

11. POAM in light around a Kerr black hole (Sgr A*) Tamburiniet al., (Submitted)

12. 1983 experiment: polarisation (SAM) of the secondary radio emissions exhibit polarimetry anomalies – OAM? 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, EcolePolytechnique Federal de Lausanne, CRPP-EPFL. Circular, (nearly) O-mode pumping O mode SEE X mode SEE

13. Polarimetry (SAM) studies of SEE exhibit anomalies Experiments in Vasil’sursk, Russia, 1998

14. Linear transfer of OAM radio ↔ plasma EPL, in press

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

16. Plasmons (Langmuir waves) can carry OAM but not SAM

17. Fundamental question: What are the completephysical 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].

18. 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.

19. 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 momentumJfield . Foundation of ‘angular momentum’ radio or ‘dual radio’.

20. EM field angular momentum. Directlyfrom the Maxwell-Lorentz equations EM field angular momentum around the origin: where For each (temporal) Fourier component: , where (SAM operator) , where (OAM operator)

21. Radio OAM can be observed by phased arrays Optimal results with vector sensing antennas Thidé et al., Phys. Rev. Lett., 99, 087701, 2007

22. Field vector sensing means total configurability The ultimate radio coronagraph!

23. Radio beam carrying both SAM and OAMLinear 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 Distribution of orbital angular momentum flux

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

25. Rotational Doppler shift spectrum

26. 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…

27. Spiral (OAM) spectrum imaging results …and its response

28. EM equivalent of fluid vorticity

29. The OAM topological degree of freedom has revolutionised wireless communications

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

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

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

33. Thank you for your attention ....there may be more things in heaven and earth than even Maxwell had dreamt of …

34. 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):

35. 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.

36. 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+ Semare radiated all the way out to the far zone!

37. 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)

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