Angular Momenta and Spin-Orbit Interaction of Nonparaxial Light in Free Space

We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are presented. We apply the general theory to symmetric and asymmetric Bessel beams exhibiting spin- and orbital-dependent intensity profiles. The exact wave solutions are clearly interpreted in terms of the Berry phases, quantization of caustics, and Hall effects of light, which can be readily observed experimentally.Comment: 8 pages, 3 figure

Geometric Spin Hall Effect of Light at Polarizing Interfaces

The geometric Spin Hall Effect of Light (geometric SHEL) amounts to a polarization-dependent positional shift when a light beam is observed from a reference frame tilted with respect to its direction of propagation. Motivated by this intriguing phenomenon, the energy density of the light beam is decomposed into its Cartesian components in the tilted reference frame. This illustrates the occurrence of the characteristic shift and the significance of the effective response function of the detector. We introduce the concept of a tilted polarizing interface and provide a scheme for its experimental implementation. A light beam passing through such an interface undergoes a shift resembling the original geometric SHEL in a tilted reference frame. This displacement is generated at the polarizer and its occurrence does not depend on the properties of the detection system. We give explicit results for this novel type of geometric SHEL and show that at grazing incidence this effect amounts to a displacement of multiple wavelengths, a shift larger than the one introduced by Goos-H\"anchen and Imbert-Fedorov effects.Comment: 6 pages, 4 figure

Internal flows and energy circulation in light beams

We review optical phenomena associated with the internal energy redistribution which accompany propagation and transformations of monochromatic light fields in homogeneous media. The total energy flow (linear-momentum density, Poynting vector) can be divided into spin part associated with the polarization and orbital part associated with the spatial inhomogeneity. We give general description of the internal flows in the coordinate and momentum (angular spectrum) representations for both nonparaxial and paraxial fields. This enables one to determine local densities and integral values of the spin and orbital angular momenta of the field. We analyse patterns of the internal flows in standard beam models (Gaussian, Laguerre-Gaussian, flat-top beam, etc.), which provide an insightful picture of the energy transport. The emphasize is made to the singular points of the flow fields. We describe the spin-orbit and orbit-orbit interactions in the processes of beam focusing and symmetry breakdown. Finally, we consider how the energy flows manifest themselves in the mechanical action on probing particles and in the transformations of a propagating beam subjected to a transverse perturbation.Comment: 50 pages, 21 figures, 173 references. This is the final version of the manuscript (v1) modified in accord to the referee's remarks and with allowance for the recent development. The main changes are: additional discussion of the energy flows in Bessel beams (section 4.1), a lot of new references are added and the Conclusion is shortened and made more accurat

Goos–hänchen and imbert–fedorov beam shifts: an overview

We consider reflection and transmission of polarized paraxial light beams at a plane dielectric interface. The field transformations taking into account a finite beam width are described based on the plane-wave representation and geometric rotations. Using geometrical-optics coordinate frames accompanying the beams, we construct an effective Jones matrix characterizing spatial-dispersion properties of the interface. This results in a unified self-consistent description of the Goos-Hanchen and Imbert-Fedorov shifts (the latter being also known as the spin Hall effect of light). Our description reveals the intimate relation of the transverse Imbert-Fedorov shift to the geometric phases between constituent waves in the beam spectrum and to the angular momentum conservation for the whole beam. Both spatial and angular shifts are considered as well as their analogues for higher-order vortex beams carrying intrinsic orbital angular momentum. We also give a brief overview of various extensions and generalizations of the basic beam-shift phenomena and related effects