Airy-related beams generated from a higher-order cosine-hyperbolic-Gaussian beam passing through a multiple Airy transforms optical system

The present paper investigates the propagation properties of a higher-order cosine-hyperbolic Gaussian beam passing through n-times Airy transforms optical system. The intensity distribution, centroid, beam width, and propagation factor (M2-factor) of the output beam are obtained analytically, and their features are analyzed with numerical examples. It is demonstrated that the resulting beam can be expressed as a finite superposition of Airy modes, and its spot profile is Airy–like. The numerical results show that the main m peak intensity is wider and the number of secondary lobes of the light spot decrease as the number of the Airy transforms is increased. The beam’s shift is larger when the decentered parameter b or the number of the Airy transforms increases. The beam width and M2-factor are smaller when the Airy control parameters are decreased. Furthermore, under certain parameter conditions the transverse intensity may exhibit intensity modulation bands; the structure of these bands depends strongly on the number of Airy transforms. It is also found that the non-diffracting propagation distance of the transformed beam in free space decreases as the number of Airy transforms or the Airy control parameter α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} increases. The results of this study may be beneficial for beam shaping of Airy beams.