Femtosecond laser direct writing fractional-order vortex beam generator with longitudinal light field evolution

Owing to the distinctive attributes of radially notched intensity profile and carrying non-integral orbital angular momentum, fractional-order vortex beams (FVBs) have stimulated tremendous research interest. Traditional methods for generating FVBs either necessitate bulky optical components or are only capable of producing a specific type of FVB. These limitations hinder their application in integrated micro-optics. Here, a design of fractional spiral zone plates (FSZPs) is presented for generating two different types of FVBs at distinct positions along the propagation direction, and the underlying mechanism is analyzed using ray optics theory and verified by numerical simulations. The FSZPs with various fractional topological charges (TCs) are fabricated by two-photon polymerization femtosecond laser direct writing (FsDLW) technique, and the experimentally generated fractional-order perfect vortex beam (PVB) on the focal plane and fractional-order Bessel-like beam at a certain distance behind the focal plane match well with theoretical analysis and numerical simulations. Furthermore, the self-healing properties of the generated fractional-order Bessel-like beams are confirmed by the experiments. We envision that this work will provide a new path for the generation of compact and cost-effective fractional-order PVBs and fractional-order Bessel-like beams, facilitating the miniaturized applications of FVBs in fields such as particle manipulation and optical communication.