Fractal Cylindrical Fracxicon

Abstract

The paper presents the results of a numerical study of a new optical element–the fractal fracxicon. The fracxicon is an element whose phase function is a fractional power of spatial coordinates. With the power of phase function being less than two (sub-linearly chirped), a fracxicon corresponds to a fractional axicon and provides self-focusing features similar to mirror/specular Airy beams. When the power is greater than two (super-linearly chirped), a fracxicon corresponds to a generalized lens and provides self-focusing, which is faster and sharper than a lens provides. A fractal fracxicon generates beams that exhibit such properties as self-similarity and self-focusing. This type of optical elements can be used as versatile tools in the field of optical micromanipulation and data encoding.