Arrays of optical vortices formed by "fork" holograms

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 used 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.Comment: 9 pages, 8 figure

Transverse rotation of the momentary field distribution and the orbital angular momentum of a light beam

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.Comment: 9 pages, 1 figure with animatio

Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows

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 paraxial 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.Comment: 17 pages, 5 figures. For resubmission, the language is improved, numerical mistakes in Fig. 4 are corrected and discussion is modified accordingl

A Simple Analytical Model of the Angular Momentum Transformation in Strongly Focused Light Beams

A ray-optics model is proposed to describe the vector beam transformation in a strongly focusing optical system. In contrast to usual approaches basing on the focused field distribution near the focal plane, we employ the transformed beam pattern formed immediately near the exit pupil. In this cross section, details of the output field distribution are of minor physical interest but proper allowance is made for transformation of the incident beam polarization state. This enables to obtain the spin and orbital angular momentum representations which are valid everywhere in the transformed beam space. Simple analytical results are available for the transversely homogeneous circularly polarized incident beam limited only by the circular aperture. Behavior of the spin and orbital angular momenta of the output beam and their dependences on the focusing strength (aperture angle) are analyzed. The obtained analytical results are in good qualitative and reasonable quantitative agreement to the calculation performed for the spatially inhomogeneous Gaussian and Laguerre-Gaussian beams. In application to Laguerre-Gaussian beams, the model provides possibility for analyzing the angular momentum transformation in beams already possessing some mixture of the spin and orbital angular momenta. The model supplies efficient and physically transparent means for qualitative analysis of the spin-to-orbital angular momentum conversion. It can be generalized to incident beams with complicated spatial and polarization structure.Comment: 18 pages, 5 figures. The paper has appeared as an attempt to clearly understand transformations of the light beam polarization in the course of strong focusing. It provides description of the optical vortex formation after focusing a circularly polarized beam and explains why the the orbital angular momentum emerges in the focused bea

Polarization-dependent transformation of a paraxial beam upon reflection and refraction: a real-space approach

We analyze the paraxial beam transformation upon reflection and refraction at a plane boundary. In contrast to the usual approach dealing with the beam angular spectrum, we apply the continuity conditions to explicit spatial representations of the electric and magnetic fields on both sides of the boundary. It is shown that the polarization-dependent distortions of the beam trajectory (in particular, the "longitudinal" Goos-H\"anchen shift and the "lateral" Imbert-Fedorov shift of the beam center of gravity) are directly connected to the incident beam longitudinal component and appear due to its transformation at the boundary.Comment: 10 pages, 1 figure. Formulae (32), (33), footnote 2 and Ref. 27 are added, some sentences are correcte