Controllable beam reshaping by mixing square-shaped and hexagonal optical vortex lattices.

In the present work we show experimentally and by numerical calculations a substantial far-field beam reshaping by mixing square-shaped and hexagonal optical vortex (OV) lattices composed of vortices with alternatively changing topological charges. We show that the small-scale structure of the observed pattern results from the OV lattice with the larger array node spacing, whereas the large-scale structure stems from the OV lattice with the smaller array node spacing. In addition, we demonstrate that it is possible to host an OV, a one-dimensional, or a quasi-two-dimensional singular beam in each of the bright beams of the generated focal patterns.

Vortex algebra by multiply cascaded four-wave mixing of femtosecond optical beams.

Experiments performed with different vortex pump beams show for the first time the algebra of the vortex topological charge cascade, that evolves in the process of nonlinear wave mixing of optical vortex beams in Kerr media due to competition of four-wave mixing with self-and cross-phase modulation. This leads to the coherent generation of complex singular beams within a spectral bandwidth larger than 200nm. Our experimental results are in good agreement with frequency-domain numerical calculations that describe the newly generated spectral satellites.

Supercontinuum generation with optical vortices.

We employ an optical vortex beam for the generation of femtosecond supercontinuum in a solid state medium. We demonstrate that the continuum generation process is initiated by the filamentation of the vortex, resulting in a spatially divergent continuum. Despite the strong self-focusing and the formation of multiple hot-spots along the vortex ring, the singularity is preserved in both the near- and far-fields.