Hybrid vector beams with non-uniform orbital angular momentum density induced by designed azimuthal polarization gradient

Based on angular amplitude modulation of orthogonal base vectors in common-path interference method, we propose an interesting type of hybrid vector beams with unprecedented azimuthal polarization gradient and demonstrate in experiment. Geometrically, the configured azimuthal polarization gradient is indicated by intriguing mapping tracks of angular polarization states on Poincaré sphere, more than just conventional circles for previously reported vector beams. Moreover, via tailoring relevant parameters, more special polarization mapping tracks can be handily achieved. More noteworthily, the designed azimuthal polarization gradients are found to be able to induce azimuthally non-uniform orbital angular momentum density, while generally uniform for circle-track cases, immersing in homogenous intensity background whatever base states are. These peculiar features may open alternative routes for new optical effects and applications.

Orbital angular momentum density and spiral spectra of Lorentz–Gauss vortex beams passing through a single slit

Based on the Hermite–Gaussian expansion of the Lorentz distribution and the complex Gaussian expansion of the aperture function, an analytical expression of the Lorentz–Gauss vortex beam with one topological charge passing through a single slit is derived. By using the obtained analytical expressions, the properties of the Lorentz–Gauss vortex beam passing through a single slit are numerically demonstrated. According to the intensity distribution or the phase distribution of the Lorentz–Gauss vortex beam, one can judge whether the topological charge is positive or negative. The effects of the topological charge and three beam parameters on the orbital angular momentum density as well as the spiral spectra are systematically investigated respectively. The optimal choice for measuring the topological charge of the diffracted Lorentz–Gauss vortex beam is to make the single slit width wider than the waist of the Gaussian part.

Fractional Fourier transform of Lorentz-Gauss vortex beams

An analytical expression for a Lorentz-Gauss vortex beam passing through a fractional Fourier transform (FRFT) system is derived. The influences of the order of the FRFT and the topological charge on the normalized intensity distribution, the phase distribution, and the orbital angular momentum density of a Lorentz-Gauss vortex beam in the FRFT plane are examined. The order of the FRFT controls the beam spot size, the orientation of the beam spot, the spiral direction of the phase distribution, the spatial orientation of the two peaks in the orbital angular momentum density distribution, and the magnitude of the orbital angular momentum density. The increase of the topological charge not only results in the dark-hollow region becoming large, but also brings about detail changes in the beam profile. The spatial orientation of the two peaks in the orbital angular momentum density distribution and the phase distribution also depend on the topological charge.

Hollow vortex Gaussian beams

A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the special distribution of the optical field, which is caused by the initial vortex phase, the dark region of a hollow vortex Gaussian beam will not disappear upon propagation. The analytical expressions for the beam propagation factor, the kurtosis parameter, and the orbital angular mo- mentum density of a hollow vortex Gaussian beam passing through a paraxial ABCD optical system are also derived, respec- tively. The beam propagation factor is determined by the beam order and the topological charge. The kurtosis parameter and the orbital angular momentum density depend on beam order n, topological charge m, parameter y, and transfer matrix ele- ments A and D. As a numerical example, the propagation properties of a hollow vortex Gaussian beam in free space are demonstrated. The hollow vortex Gaussian beam has eminent propagation stability and has crucial application prospects in op- tical micromanipulation.