Optical Angular Momentum Book

	Preface
	Acknowledgments and Copyright Information
1	Introduction	1
1.1	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	Mechanical detection and measurement of the angular momentum of light	10
1.3	Introduction to the atoms and angular momentum of light special issue	21
2	Spin and Orbital Angular Momentum	27
2.1	Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes	31
2.2	Eigenfunction description of laser beams and orbital angular momentum of light	36
2.3	Paraxial wave optics and harmonic oscillators	48
2.4	Matrix formulation for the propagation of light beams with orbital and spin angular momenta	58
2.5	Paraxial beams of spinning light	65
2.6	The Poynting vector in Laguerre-Gaussian beams and the interpretation of their angular momentum density	75
2.7	Intrinsic and extrinsic nature of the orbital angular momentum of a light beam	80
2.8	Spin and orbital angular momentum of photons	84
2.9	Orbital angular momentum and nonparaxial light beams	89
2.10	Optical angular-momentum flux	98
3	Laboratory Beams Carrying Orbital Angular Momentum	109
3.1	An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes	114
3.2	Temporal and interference fringe analysis of TEM[subscript 01] laser modes	120
3.3	Bistability and optical switching of spatial patterns in a laser	124
3.4	Optical helices and spiral interference fringes	129
3.5	Astigmatic laser mode converters and transfer of orbital angular momentum	135
3.6	Observation of the dynamical inversion of the topological charge of an optical vortex	145
3.7	Orbital angular momentum exchange in cylindrical-lens mode converters	149
3.8	Laser beams with screw dislocations in their wavefronts	152
3.9	Laser beams with phase singularities	155
3.10	Topological charge and angular momentum of light beams carrying optical vortices	167
3.11	Helical-wavefront laser beams produced with a spiral phaseplate	179
3.12	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	Observation of a single-beam gradient force optical trap for dielectric particles	196
4.2	Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity	199
4.3	Optical angular-momentum transfer to trapped absorbing particles	203
4.4	Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner	207
5	Optical Forces and Torques on Atoms	211
5.1	Atom dynamics in multiple laguerre-Gaussian beams	215
5.2	Selection rules and centre-of-mass motion of ultracold atoms	227
5.3	Optical pumping of orbital angular momentum of light in cold cesium atoms	240
6	Rotational Frequency Shifts	245
6.1	Angular Doppler effect	247
6.2	Doppler effect induced by rotating lenses	250
6.3	Poincare-sphere equivalent for light beams containing orbital angular momentum	257
6.4	Rotational frequency shift	260
6.5	Azimuthal Doppler shift in light beams with orbital angular momentum	264
6.6	Rotational frequency shift of a light beam	268
7	Angular Momentum in Nonlinear Optics	271
7.1	Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes	273
7.2	Optical solitons carrying orbital angular momentum	277
7.3	Integer and fractional angular momentum borne on self-trapped necklace-ring beams	281
8	Entanglement of Angular Momentum	285
8.1	Entanglement of the orbital angular momentum states of photons	287
8.2	Two-photon entanglement of orbital angular momentum states	291
8.3	Measuring the orbital angular momentum of a single photon	297