Backflow in vector Gaussian beams

TL;DR

This paper investigates Poynting backflow in vector Gaussian beams, showing how small parameter effects cause reversed energy flow regions that depend on polarization and beam parameters.

Contribution

It provides explicit analytical solutions demonstrating the origin of backflow in vector Gaussian beams and characterizes its dependence on polarization, topological index, and beam parameters.

Findings

Backflow occurs due to terms proportional to the small parameter in Maxwell's equations.

Backflow regions depend on polarization and can be annular or absent.

Backflow magnitude scales with the fourth power of the small parameter.

Abstract

The phenomenon of Poynting backflow in a single vector Gaussian beam is examined. The paraxial Maxwell equations and their exact solutions containing terms proportional to the small parameter $\varepsilon=\frac{\lambda}{2\pi w_0}$, or to its square, where $w_0$ is the beam waist, are made use of. Explicit analytical calculations show that just these additional expressions are responsible for the occurrence of the reversed Poynting-vector longitudinal component for selected polarizations. Concrete results for the time-averaged vector for several Gaussian beams with $n=1$ ($n$ being the topological index of the beam) are presented. Depending on the choice of polarization, the backflow area is located around the beam's axis, has an annular character or is absent. In the case of $n=2$, backflow areas were found as well. The magnitude of the backflow proved to be proportional to $\varepsilon^4$.