Three-dimensional nonparaxial accelerating beams from the transverse Whittaker integral

TL;DR

This paper explores three-dimensional nonparaxial accelerating beams derived from the transverse Whittaker integral, including Mathieu, Weber, and Fresnel beams, which follow semicircular trajectories with nearly invariant shapes, expanding understanding of multidimensional wave phenomena.

Contribution

It introduces a new class of 3D nonparaxial accelerating beams based on the transverse Whittaker integral, demonstrating their shapes and trajectories using Mathieu, Weber, and Fresnel functions.

Findings

Beams accelerate along semicircular paths with invariant shapes.

Transverse patterns are determined by angular spectra from special functions.

Results enhance understanding of multidimensional nonparaxial wave phenomena.

Abstract

We investigate three-dimensional nonparaxial linear accelerating beams arising from the transverse Whittaker integral. They include different Mathieu, Weber, and Fresnel beams, among other. These beams accelerate along a semicircular trajectory, with almost invariant nondiffracting shapes. The transverse patterns of accelerating beams are determined by their angular spectra, which are constructed from the Mathieu functions, Weber functions, and Fresnel integrals. Our results not only enrich the understanding of multidimensional nonparaxial accelerating beams, but also display their real applicative potential -- owing to the usefulness of Mathieu and Weber functions, and Fresnel integrals in describing a wealth of wave phenomena in nature.