Currently, cylindrical beams with radial or azimuthal polarization are being used successfully for the optical manipulation of micro- and nano-particles as well as in microscopy, lithography, nonlinear optics, materials processing, and telecommunication applications. The creation of these laser beams is carried out using segmented polarizing plates, subwavelength gratings, interference, or light modulators. Here, we demonstrate the conversion of cylindrically polarized laser beams from a radial to an azimuthal polarization, or vice versa, by introducing a higher-order vortex phase singularity. To simultaneously generate several vortex phase singularities of different orders, we utilized a multi-order diffractive optical element. Both the theoretical and the experimental results regarding the radiation transmitted through the diffractive optical element show that increasing the order of the phase singularity leads to more efficient conversation of the polarization from radial to azimuthal. This demonstrates a close connection between the polarization and phase states of electromagnetic beams, which has important implications in many optical experiments.

We obtain analytical expressions for the complex amplitudes of optical vortices deformed by astigmatic transforms, i.e., passed either through a cylindrical lens or through an inclined spherical lens. We also obtain similar analytical expressions describing propagation of an optical vortex generated when a Gaussian beam illuminates an inclined spiral phase plate (SPP) or when an elliptic Gaussian beam illuminates a SPP (not inclined). All these optical vortices with a topological charge (TC) $n$ are described by the $n$-th order Hermite polynomial with a complex argument. It is shown that the argument is real only on a straight line in the transverse plane of the laser beam. There are $n$ intensity nulls on this line. The treated here astigmatic transforms are used to determine the integer TC of optical vortices. We conduct a comparative experimental study of different astigmatic transforms and we show that the transform with a cylindrical lens is the best for determining the TC. Unlike other similar works, in this study we achieve transformation of $n$-degenerate intensity null of an optical vortex with the TC $n=100$ into $n$ isolated first-order intensity nulls.

Donut-shaped laser radiation, carrying orbital angular momentum, namely optical vortex, was recently shown to provide vectorial mass transfer, twisting transiently molten material and producing chiral micro-scale structures on surfaces of different bulk materials upon their resolidification. In this paper, we show that at high-NA focusing nanosecond laser vortices can produce chiral nanoneedles (nanojets) of variable size on thin films of such plasmonic materials, as silver and gold films, covering thermally insulating substrates. Main geometric parameters of the produced chiral nanojets, such as height and aspect ratio, were shown to be tunable in a wide range by varying metal film thickness, supporting substrates, and the optical size of the vortex beam. Donut-shaped vortex nanosecond laser pulses, carrying two vortices with opposite handedness, were demonstrated to produce two chiral nanojets twisted in opposite directions. These results suggest optical interference of the incident and reflected laser beams as a source of complex surface intensity distributions in metal films, possessing spiral components and driving both center-symmetric and spiral thermocapillary melt flows to yield in frozen nanoneedles with their pre-determined spiral nanocarving.

We considered a generalization of the Laguerre–Gaussian (LG) laser beam family by using a complex shift of the beam complex amplitude in Cartesian coordinates. In this case, LG-beams lose their axial symmetry. The normalized orbital angular momentum is the sum of the beam topological charge and the term which is in square dependence on the asymmetry parameter. By optical trapping and moving the polystyrene microspheres in the focus of the asymmetric LG-beam, it is proven that the velocity of the microspheres increases with increasing the asymmetry parameter and constant topological charge.