Wigner picture of 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.

Figures (3)

• Figure 1: Evolution of the WDF of an accelerating wave packet with propagation distance $z$ produced by a fairly coherent source with $\xi_c = 4$. The cut-off parameter of a Gaussian cut-off is $a = 0.1$.
• Figure 2: Evolution of the WDF of an accelerating wave packet with propagation distance $z$ engendered by a relatively incoherent source with $\xi_c = 1$. We employ a Gaussian cut-off with the cut-off parameter $a = 0.1$.
• Figure 3: Intensity profiles of accelerating wave packets generated by highly coherent $\xi_c = 10$ (left) and moderately incoherent $\xi_c = 2$ (right) sources as functions of X for three propagation distances: $z = 0$ (solid curve), $z = 2$ (dashed curve), and $z = 4$ (dotted curve). The cut-off parameter of a Gaussian cut-off is $a = 0.1$.