Abstract

Airy beams possess a number of properties that ensure their multifunction and high relevance in many applications. This fact stimulates scientists to search for new modifications and generalizations of classical Airy beams. Several generalizations of the Airy functions are known, on the basis of both the modification of the differential equation and the variations in the integral representation. In this paper we propose and investigate a new type of Airy beams—fractional Airy beams (FrAiB). They are based on the generalization of the integral representation and are close to the Olver functions, but we are considering a wider range of the power-law dependence of the argument, including non-integer (fractional) values of the power. A theoretical and numerical analysis of the FrAiBs, as well as their symmetrized variants, was performed. The properties of FrAiBs, such as being non-diffracting and autofocusing, were numerically investigated by means of the fractional Fourier transform, describing the beam transformations by paraxial optical systems. We believe that new beams can be useful for laser manipulation techniques and lensless laser patterning.

© 2017 Optical Society of America

Propagation characteristics of ring Airy beams modeled by fractional Schrödinger equation

Xianwei Huang, Zhixiang Deng, Xiaohui Shi, and Xiquan Fu
J. Opt. Soc. Am. B 34(10) 2190-2197 (2017)

Multifocus autofocusing Airy beam

Tong Li, Fei Zi, Kaikai Huang, and Xuanhui Lu
J. Opt. Soc. Am. A 34(9) 1530-1534 (2017)

Dynamics of finite energy Airy beams modeled by the fractional Schrödinger equation with a linear potential

Xianwei Huang, Zhixiang Deng, and Xiquan Fu
J. Opt. Soc. Am. B 34(5) 976-982 (2017)

Finite-energy Airy–Lorentz–Gaussian beam and its paraxial propagation

Bin Tang and Lirong Bian
J. Opt. Soc. Am. A 36(10) 1624-1630 (2019)

Potential barrier-induced dynamics of finite energy Airy beams in fractional Schrödinger equation

Xianwei Huang, Xiaohui Shi, Zhixiang Deng, Yanfeng Bai, and Xiquan Fu
Opt. Express 25(26) 32560-32569 (2017)