#### Transcript orbital angular momentum

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 EISCAT-3D Workshop, Uppsala, 19 – 21 May 2010 Phase singularities (dislocations) are to be expected in radio beams propagating through space Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 2 EM angular momentum is a conserved physical observable. Just like the linear momentum (Poytning vector), it that can carry information over huge distances Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 3 Mechanical effects of photon spin angular momentum (1936) and of photon orbital angular momentum (1992) Beth’s experiment, 1936 Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 4 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 EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 Sjöholm and Palmer, 2007 5 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 carry a lot of information! The Jones matrix goes from 2×2 to 2(j+1)×2(j+1), j=s+l . EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 6 Difference between polarisation (SAM) and orbital angular momentum (OAM) EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 7 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 Orbital angular momentum l = 8 EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 8 Imparting vorticity/OAM onto an EM beam (laser, mm wave) with the help of a spiral plate or hologram Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 9 Very readable pioneering paper on photon OAM in astrophysics Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 10 POAM in light around a Kerr black hole (Sgr A*) Tamburini et al., (Submitted) Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 11 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, Ecole Polytechnique Federal de Lausanne, CRPP-EPFL. Circular, (nearly) O-mode pumping O mode SEE X mode SEE Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 12 Polarimetry (SAM) studies of SEE exhibit anomalies Experiments in Vasil’sursk, Russia, 1998 Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 13 Linear transfer of OAM radio ↔ plasma EPL, in press Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 14 Nonlinear transfer of OAM radio ↔ plasma Brillouin = ion line Raman = plasma line Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 15 Plasmons (Langmuir waves) can carry OAM but not SAM Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 16 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 EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 17 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 Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 18 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 momentum Jfield . Foundation of ‘angular momentum’ radio or ‘dual radio’. Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 19 EM field angular momentum. Directly from the Maxwell-Lorentz equations EM field angular momentum around the origin: where For each (temporal) Fourier component: Bo Thidé , where (SAM operator) , where (OAM operator) EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 20 Radio OAM can be observed by phased arrays Optimal results with vector sensing antennas Thidé et al., Phys. Rev. Lett., 99, 087701, 2007 Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 21 Field vector sensing means total configurability The ultimate radio coronagraph! Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 22 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 EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 23 Observations at 94 GHz of angular momentum induced azimuthal (rotational ) Doppler shift Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 24 Rotational Doppler shift spectrum Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 25 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 EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 26 Spiral (OAM) spectrum imaging results …and its response Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 27 EM equivalent of fluid vorticity Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 28 The OAM topological degree of freedom has revolutionised wireless communications Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 29 Hyperentangled SAM and OAM photon states break the linear-optics channel capacity threshold Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 30 The conventional Shannon dimensionality of 2 can be exceeded by using OAM degrees of freedom Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 31 Recent call for funding of practical “on-the-scene” information-rich applications using OAM etc. Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 32 Thank you for your attention ....there may be more things in heaven and earth than even Maxwell had dreamt of … Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 33 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 EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 34 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 EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 35 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 EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 36 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 Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 37 LOIS has measured the photon spin current V in ionospheric radio signals since 2003 Bo Thidé EISCAT_3D Workshop, Uppsala, 19 – 21 May 2010 38