Fundamental and applied concepts concerning the ability of light beams to carry a certain mechanical angular momentum with respect to the propagation axis are reviewed and discussed. Following issues are included: Historical reference; Angular mo
mentum of a paraxial beam and its constituents; Spin angular momentum and paradoxes associated with it; Orbital angular momentum; Circularly-spiral beams: examples and methods of generation; Orbital angular momentum and the intensity moments; Symmetry breakdown and decomposition of the orbital angular momentum; Mechanical models of the vortex light beams; Mechanical action of the beam angular momentum; Rotational Doppler effect, its manifestation in the image rotation; Spectrum of helical harmonics and associated problems; Non-collinear rotational Doppler effect; Properties of a beam forcedly rotating around its own axis. Research prospects and ways of practical utilization of optical beams with angular momentum.
Singular light beams with optical vortices (OV) are often generated by means of thin binary gratings with groove bifurcation (fork holograms) that produce a set of diffracted beams with different OV charges. Usually, only single separate beams are us
ed and investigated; here we consider the whole set of diffracted OV beams that, at certain conditions, are involved in efficient mutual interference to form a characteristic pattern where the ring-like structure of separate OV beams is replaced by series of bright and dark lines between adjacent diffraction orders. This pattern, well developed for high diffraction orders, reflects the main spatial properties of the diffracted beams as well as of the fork grating used for their generation. In particular, it confirms the theoretical model for the diffracted beams (Kummer beam model) and enables to determine the sign and the absolute value of the phase singularity embedded in the hologram.
Based on the Mie theory and on the incident beam model via superposition of two plane waves, we analyze numerically the momentum flux of the field scattered by a spherical microparticle placed within the spatially inhomogeneous circularly polarized p
araxial light beam. The asymmetry between the forward- and backward-scattered momentum fluxes in the Rayleigh scattering regime appears due to the spin part of the internal energy flow in the incident beam. The transverse ponderomotive forces exerted on dielectric and conducting particles of different sizes are calculated and special features of the mechanical actions produced by the spin and orbital parts of the internal energy flow are recognized. In particular, the transverse orbital flow exerts the transverse force that grows as a^3 for conducting and as a^6 for dielectric subwavelength particle with radius a, in compliance with the dipole mechanism of the field-particle interaction; the force associated with the spin flow behaves as a^8 in both cases, which testifies for the non-dipole mechanism. The results can be used for experimental identification and separate investigation of the spin and orbital parts of the internal energy flow in light fields.
Special features of the optical-vortex (OV) beams generated by thick holographic elements (HE) with embedded phase singularity are considered theoretically. The volume HE structure is based on the 3D pattern of interference between an OV beam and a s
tandard reference wave with regular wavefront. The incident beam diffraction is described within the framework of a linear single-scattering model in which the volume HE is represented by a set of parallel thin layers with the fork holographic structure. An explicit integral expression is derived for the complex amplitude distribution of the diffracted paraxial beam with OV. The numerical analysis demonstrates that the HE thickness may essentially influence not only selectivity and efficiency of the OV beam generation but also the amplitude and phase profile of the diffracted beam as well as regularities of its propagation. We have studied the generated OV morphology and laws of its evolution; in particular, the possibility of obtaining a circularly symmetric OV beam regardless of the diffraction angle is revealed.
It is known that internal energy flow in a light beam can be divided into the orbital flow, associated with the macroscopic energy redistribution within the beam, and the spin flow originating from instantaneous rotation of the field vectors inherent
in circular or elliptic polarization. In contrast to the orbital one, experimental observation of the spin flow constituent seemed problematic because (i) it does not manifest itself in the visible transformation of the beam profile and (ii) it converts into the orbital flow upon tight focusing of the beam, usually employed for the energy flow detection by the mechanical action on probe particles. We propose a two-beam interference technique that permits to obtain appreciable level of the spin flow in moderately focused beams and to detect the orbital motion of probe particles within a field where the transverse energy circulation is associated exclusively with the spin flow. This result can be treated as the first demonstration of mechanical action of the spin flow of a light field.
Spatial characteristics of diffracted beams produced by a fork hologram from an incident circular Laguerre-Gaussian beam whose axis differ from the hologram optical axis are studied theoretically. General analytical representations for the complex am
plitude distribution of a diffracted beam are derived in terms of superposition of Kummer beams or hypergeometric-Gaussian beams. The diffracted beam structure is determined by combination of the proper topological charge m of the incident vortex beam and the topological charge l of the singularity imparted by the hologram. Evolution of the diffracted beam structure is studied in detail for several combinations of m and l and for various incident beam displacements with respect to the optical axis of the hologram. Variations of the intensity and phase distribution due to the incident beam misalignment are investigated and possible applications for the purposeful optical-vortex beam generation and optical measurements are discussed.
The transverse beam pattern, usually observed in experiment, is a result of averaging the optical-frequency oscillations of the electromagnetic field distributed over the beam cross section. An analytical criterion is derived that these oscillations
are coupled with a sort of rotation around the beam axis. This criterion appears to be in direct relation with the usual definition of the beam orbital angular momentum.
