PREFACE ....................................................................... ix ACKNOWLEDGMENTS AND COPYRIGHT INFORMATION ..................................... xi 1 INTRODUCTION ................................................................. 1 1.1 JH Poynting (1909) The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light ........................................................... 3 1.2 RA Beth (1936) Mechanical detection and measurement of the angular momentum of light ................................................. 10 1.3 L Allen (2002) Introduction to the atoms and angular momentum of light special issue ....................................................... 21 2 SPIN AND ORBITAL ANGULAR MOMENTUM ........................................... 27 2.1 L Allen, MW Beijersbergen, RJC Spreeuw and JP Woerdman (1992) Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes ............................................ 31 2.2 SJ van Enk and G Nienhuis (1992) Eigenfunction description of laser beams and orbital angular momentum of light .............................. 36 2.3 G Nienhuis and L Allen (1993) Paraxial wave optics and harmonic oscillators .............................................................. 48 2.4 L Allen, J Courtial and MJ Padgett (1999) Matrix formulation for the propagation of light beams with orbital and spin angular momenta ......... 58 2.5 MV Berry (1998) Paraxial beams of spinning light ......................... 65 2.6 L Allen and MJ Padgett (2000) The Poynting vector in Laguerre-Gaussian beams and the interpretation of their angular momentum density ......................................................... 75 2.7 AT O'Neil, I MacVicar, L Allen and MJ Padgett (2002) Intrinsic and extrinsic nature of the orbital angular momentum of a light beam ......... 80 2.8 SJ van Enk and G Nienhuis (1994) Spin and orbital angular momentum of photons ............................................................... 84 2.9 SM Barnett and L Allen (1994) Orbital angular momentum and nonparaxial light beams .................................................. 89 2.10 SM Barnett (2002) Optical angular-momentum flux .......................... 98 3 LABORATORY BEAMS CARRYING ORBITAL ANGULAR MOMENTUM ......................... 109 3.1 M Padgett, J Arlt, N Simpson and L Allen (1996) An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes ................................................................... 114 3.2 JM Vaughan and DV Willets (1983) Temporal and interference fringe analysis of TEM01* laser modes ........................................... 120 3.3 C Tamm and CO Weiss (1990) Bistability and optical switching of spatial patterns in a laser ..................................................... 124 3.4 M Harris, CA Hill and JM Vaughan (1994) Optical helices and spiral interference fringes .................................................... 129 3.5 MW Beijersbergen, L Allen, HELO van der Veen and JP Woerdman (1993) Astigmatic laser mode converters and transfer of orbital angular momentum ................................................................ 135 3.6 G Molina-Terriza, J Recolons, JP Torres, L Torner and EM Wright (2001) Observation of the dynamical inversion of the topological charge of an optical vortex .......................................................... 145 3.7 MJ Padgett and L Allen (2002) Orbital angular momentum exchange in cylindrical-lens mode converters ..................................... 149 3.8 V Yu Bazhenov, MV Vasnetsov and MS Soskin (1990) Laser beams with screw dislocations in their wavefronts .................................. 152 3.9 NR Heckenberg, R McDuff, CP Smith, H Rubinsztein-Dunlop and MJ Wegener (1992) Laser beams with phase singularities .................. 155 3.10 MS Soskin, VN Gorshkov, MV Vasnetsov, JT Malos and NR Heckenberg (1997) Topological charge and angular momentum of light beams carrying optical vortices ........................................................ 167 3.11 MW Beijersbergen, RPC Coerwinkel, M Kristensen and JP Woerdman (1994) Helical-wavefront laser beams produced with a spiral phaseplate ......... 179 3.12 GA Turnbull, DA Robertson, GM Smith, L Allen and MJ Padgett (1996) The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate ............... 186 4 OPTICAL FORCES AND TORQUES ON PARTICLES .................................... 193 4.1 A Ashkin, JM Dziedzic, JE Bjorkholm and S Chu (1986) Observation of a single-beam gradient force optical trap for dielectric particles ...... 196 4.2 H He, MEJ Friese, NR Heckenberg and H Rubinsztein-Dunlop (1995) Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity .................... 199 4.3 MEJ Friese, J Enger, H Rubinsztein-Dunlop and NR Heckenberg (1996) Optical angular-momentum transfer to trapped absorbing particles ........ 203 4.4 NB Simpson, K Dholakia, L Allen and MJ Padgett (1997) Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner ................................................................. 207 5 OPTICAL FORCES AND TORQUES ON ATOMS ........................................ 211 5.1 L Allen, M Babiker, WK Lai and VE Lembessis (1996) Atom dynamics in multiple Laguerre-Gaussian beams ........................................ 215 5.2 SJ van Enk (1994) Selection rules and centre-of-mass motion of ultracold atoms ................................................................... 227 5.3 JWR Tabosa and DV Petrov (1999) Optical pumping of orbital angular momentum of light in cold cesium atoms .......................... 240 6 ROTATIONAL FREQUENCY SHIFTS ................................................ 245 6.1 BA Garetz (1981) Angular Doppler effect ................................. 247 6.2 G Nienhuis (1996) Doppler effect induced by rotating lenses ............. 250 6.3 MJ Padgett and J Courtial (1999) Poincare-sphere equivalent for light beams containing orbital angular momentum ............................... 257 6.4 I Bialynicki-Birula and Z Bialynicka-Birula (1997) Rotational frequency shift ................................................................... 260 6.5 L Allen, M Babiker and WL Power (1994) Azimuthal Doppler shift in light beams with orbital angular momentum ..................................... 264 6.6 J Courtial, DA Robertson, K Dholakia, L Allen and MJ Padgett (1998) Rotational frequency shift of a light beam .............................. 268 7 ANGULAR MOMENTUM IN NONLINEAR OPTICS ....................................... 271 7.1 J Courtial, K Dholakia, L Allen and MJ Padgett (1997) Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes ...................................... 273 7.2 WJ Firth and DV Skryabin (1997) Optical solitons carrying orbital angular momentum ........................................................ 277 7.3 M Soljacic and M Segev (2001) Integer and fractional angular momentum borne on self-trapped necklace-ring beams ............................... 281 8 ENTANGLEMENT OF ANGULAR MOMENTUM ........................................... 285 8.1 A Mair, A Vaziri, G Weihs and A Zeilinger (2001) Entanglement of the orbital angular momentum states of photons .............................. 287 8.2 S Franke-Arnold, SM Barnett, MJ Padgett and L Allen (2002) Two-photon entanglement of orbital angular momentum states ......................... 291 8.3 J Leach, MJ Padgett, SM Barnett, S Franke-Arnold and J Courtial (2002) Measuring the orbital angular momentum of a single photon ............... 297