Tailoring Accelerating Beams in Phase Space

TL;DR

This paper introduces a novel phase space method using Wigner distribution functions to design arbitrary accelerating light beams in free space, extending beyond traditional caustic approaches.

Contribution

It presents a new phase space approach for constructing accelerating beams, capable of handling 2D and 3D fields, thus broadening the design possibilities.

Findings

WDF-based method can generate initial fields and angular spectra.

Applicable to both 2D and 3D accelerating beams.

Enables highly-tailored beam design for various applications.

Abstract

An appropriate design of wavefront will enable light fields propagating along arbitrary trajectories thus forming accelerating beams in free space. Previous ways of designing such accelerating beams mainly rely on caustic methods, which start from diffraction integrals and only deal with two-dimensional fields. Here we introduce a new perspective to construct accelerating beams in phase space by designing the corresponding Wigner distribution function (WDF). We find such a WDF-based method is capable of providing both the initial field distribution and the angular spectrum in need by projecting the WDF into the real space and the Fourier space respectively. Moreover, this approach applies to the construction of both two- and three-dimensional fields, greatly generalizing previous caustic methods. It may therefore open up a new route to construct highly-tailored accelerating beams and facilitate applications ranging from particle manipulation and trapping to optical routing as well as material processing.