Vector Beams with Parabolic and Elliptic Cross-Sections for Laser Mate-rial Processing Applications

Beam profile engineering, where a desired optical intensity distribution can be generated by an array of phase shifting (or amplitude changing) elements is a promising approach in laser material processing. For example, a spatial light modulator (SLM) is a dynamic diffractive optical element allowing for experimental implementations of controllable beam profile. Scalar Mathieu beams have elliptical intensity distribution perceivable as "optical knives" in the transverse plane and scalar Weber beams have a parabolic distribution, which enables us to call them "optical shovels". Here, we introduce vector versions of scalar Mathieu and Weber beams and use those vector beams as a basis to construct controllable on-axis phase and amplitude distributions with polarization control. Further, we generate individual components of optical "knife" and "shovel" beams experimentally using SLMs as a toy model and report on our achievements in the control over the beam shape, dimensions and polarization along the propagation axis.