Wigner picture of partially coherent accelerating beams

TL;DR

This paper develops a phase-space Wigner distribution framework for analyzing partially coherent accelerating beams, providing explicit formulas and methods for constructing such beams with finite power.

Contribution

It introduces a general Wigner distribution approach for partially coherent accelerating beams, including explicit formulas and construction methods.

Findings

Derived a general expression for the Wigner distribution of accelerating beams.

Obtained a closed-form WDF for beams with Gaussian energy spectrum.

Demonstrated how to construct finite-power partially coherent accelerating beams.

Abstract

We advance a phase-space theory of partially coherent accelerating, non-diffracting beams employing the Wigner distribution function (WDF). We derive a general expression for the WDF of any accelerating, diffraction-free beam of arbitrary degree of spatial coherence and find an elegant closed-form expression for the WDF of such beam with a Gaussian energy spectrum of noise. We also show how partially coherent accelerating beams of finite power can be constructed within the Wigner picture.