Nonparaxial gaussian beams: 2. Splitting of the singularity lines and the optical magnus effect

Abstract

The Poynting vector field lines for the lowest modes of a nonparaxial Gaussian beam exhibit a number of loops and rings in the vicinity of the phase singularity lines (Airy’s fringes), with negative energy fluxes present inside these loops and rings. The positions of these fluxes are nonsymmetric with respect to rotation about the optical axis. This asymmetry leads to a local splitting of the phase singularity lines, after which the beam cross section transforms from circular to elliptic. The asymmetry of the beam cross section can be eliminated by considering a superposition of circularly polarized even and odd modes. However, this approach only uniformly redistributes the negative energy fluxes in the azimuthal direction of the cross section, rather than completely eliminates these fluxes. Any small perturbation of the resulting symmetric beam gives rise to a unique phenomenon—the optical Magnus effect in the free space, whereby the beam intensity pattern rotates upon changing the circular polarization from right to left. This effect implies the presence of a spin-orbit coupling in the nonparaxial Gaussian beam propagating in the free space.