Non-integer tangential singular beams in the near field: Collinear phase-shifting holography for topological charge determination.

The article focuses on the introduction and experimental validation of non-integer (fractional) tangential singular beams, a new class of optical vortex beams constructed by modulating the spatial phase with a piecewise tangent function. These beams allow precise control of the topological charge (TC)—a key property characterizing vortex beams—through parameters that adjust the number of phase jumps and their magnitude, enabling fractional TC values. Using numerical simulations and an experimental setup based on collinear phase-shifting digital holography (PSH) with spatial light modulators (SLMs), the study demonstrates accurate near-field phase reconstruction and TC measurement with an average error around 1%, overcoming limitations of traditional vortex detection methods. The work highlights the potential of fractional tangential beams for applications requiring enhanced control over beam singularities, while noting that far-field vortex dynamics remain a subject for future research.