Propagation properties of finite Airy beams on curved surfaces

Airy beams have provided exciting inspiration in the field of optical communication, particle manipulation, and imaging. We investigate the propagation properties of the exponential truncation Airy beams (ETABs) on constant Gaussian curvature surfaces (CGCSs) in this paper. The analytical expression of the electric field of ETABs propagating on the CGCSs is derived. It shows that the equivalent periodical accelerations of the trajectories of ETABs on the curved surface are always larger than the constant one on the flat surface because the CGCSs have a strong focusing ability. For the same reason, the non-diffraction propagation of ETABs is found when the focusing ability of the CGCSs is strong enough. Moreover, we investigate the self-healing length of ETABs on CGCSs and explore that the ability of self-healing is related to the geometry of CGCSs besides the width of the block and the size of the beam. The self-healing length gets larger with the increase of radius of CGCSs and finally consists with that on the flat surface. These propagation characteristics are different from those in the flat space and are useful for the future applications of ETABs in particle manipulation on waveguides, light-sheet fluorescence microscopy, curved nanophotonics, and so on. (C) 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Automated summary

This paper investigates the propagation properties of exponential truncation Airy beams (ETABs) on constant Gaussian curvature surfaces (CGCSs). The study shows that the trajectories of ETABs on curved surfaces have larger equivalent periodical accelerations compared to those on flat surfaces, due to the strong focusing ability of CGCSs. Non-diffraction propagation of ETABs is observed when the focusing ability of CGCSs is strong enough. Additionally, the self-healing length of ETABs on CGCSs is found to be related to the geometry of the surfaces, and it increases with the radius of CGCSs, eventually reaching the same length as on flat surfaces. These findings have implications for future applications of ETABs in particle manipulation on waveguides, light-sheet fluorescence microscopy, curved nanophotonics, etc.