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Controlling the angular spectrum content of light fields is a basic beam shaping strategy implying the control of the wavevector distribution. Here we propose a novel class of refractive optical elements generated by folding the conical surface of a usual (conical) axicon. In particular, we explore folding processes where the continuous deformation of the circular cross-section of an axicon lead to the appearance of geometrical singularities (cusps). This is illustrated considering two prototypical families derived from hypocycloidal and epicycloidal geometries. Such topological axicons have been fabricated at the micron scale by using photopolymerization technique and characterized both experimentally and theoretically.
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Artur Aleksanyan, Albertas Žukauskas, Benjamin Sanchez-Padilla, Mangirdas Malinauskas, Etienne Brasselet, "Beam shaping using topological axicons (Conference Presentation)," Proc. SPIE 9950, Laser Beam Shaping XVII, 99500N (7 November 2016); https://doi.org/10.1117/12.2237131