Optical vortices in brief: introduction for experimentalists

In this review, starting with the essence of phase singularities (Sect. 1 ) and continuing with the methods for the generation of singular beams of different kind (Sect. 2 ), we concentrate on optical vortices (OVs), which are the only known purely two-dimensional dark beams carrying point phase singularities. We describe some methods to determine their topological charges (Sect. 3 ) and how to convert them, e.g., in the linear process of diffraction from a hologram with an encoded OV, as well as after nonlinear processes of cascaded four-wave mixing and of the non-perturbative process of high harmonic generation (Sect. 5 ). In Sect. 6 , we describe a method based on singular optics for the generation of long-range Bessel-Gaussian beams. Particular attention is paid to the suppression of the interaction of pairs of OVs and to the generation of large arrays of hundreds of OVs on a common background beam in square-shaped and hexagonal OV lattices (Sect. 7 ). The rich possibilities for the controllable generation of ordered focal structures of bright peaks and the possible additional structuring of each peak with other singular beams are illustrated, as well as the mixing of such OV arrays. New experimental results, devoted to novel possibilities for generating rich structures composed by bright peaks in the artificial far field from OV lattices with high TCs, are also presented for the first time in this paper and discussed in detail in (Sect. 8 ). In the last section, we describe a new method for the generation of arrays of long-range Bessel–Gaussian beams (Sects. 9 ). Without any claim for completeness or comprehensiveness, we believe that this overview will present to reader at least some of the beauty of experimental singular optics in space and could serve as a valuable initial step in order to dig deeper into the field.