Nonparaxial Mathieu and Weber accelerating beams

TL;DR

This paper introduces nonparaxial Mathieu and Weber accelerating beams, expanding the class of nondiffracting, self-healing beams capable of large-angle bending along various trajectories, with potential applications across wave systems.

Contribution

It generalizes accelerating beams to nonparaxial regimes using Mathieu and Weber functions, broadening beam shaping capabilities beyond Airy beams.

Findings

Beams bend along circular, elliptical, or parabolic trajectories.

Beams retain nondiffracting and self-healing properties.

The concept applies to various linear wave systems.

Abstract

We demonstrate both theoretically and experimentally nonparaxial Mathieu and Weber accelerating beams, generalizing the concept of previously found accelerating beams. We show that such beams bend into large angles along circular, elliptical or parabolic trajectories but still retain nondiffracting and self-healing capabilities. The circular nonparaxial accelerating beams can be considered as a special case of the Mathieu accelerating beams, while an Airy beam is only a special case of the Weber beams at the paraxial limit. Not only generalized nonparaxial accelerating beams open up many possibilities of beam engineering for applications, but the fundamental concept developed here can be applied to other linear wave systems in nature, ranging from electromagnetic and elastic waves to matter waves.