Modelling of distribution of circular beams of Airy in parabolic fiber

Abstract

Recently, the attention of researchers has been turned to various beams possessing the property of autofocusing, among which are circular beams of Airy, beams of Pierce, hypergeometric and other beams. The sharp autofocusing property inherent in the above beams is very useful in optical manipulation, useful for multiphoton polymerization, is used for nonlinear effects and for polarization transformations. A classic focusing element is a lens that has a quadratic dependence on the radius. The diffractive version of the parabolic lens has radial lines, condensing to the edge of the optical element as a linear chirp. This structure can be obtained by "twirling" the Airy function along the circumference with displacement and scaling. The study of the behavior of various types of self-focusing laser beams in parabolic environments extends the spectrum of optical signals used for telecommunications. In particular, a fractional Fourier transform is used to describe fibers with a parabolic refractive index. In this paper we consider circular Airy beams, which have a radial dependence. Modelling of the passage of these beams through an optical fiber with a parabolic change in the refractive index was performed on the basis of the use of a fractional Fourier transform.