Extension matrix representation theory of light beams and the Beauregard effect

TL;DR

This paper introduces an extension matrix framework to represent light beams in free space, revealing the Beauregard effect as observable evidence when certain symmetry conditions are met, with potential applications in beam design.

Contribution

It develops a novel extension matrix representation for light beams, enabling the first observation of the Beauregard effect under specific symmetry conditions.

Findings

Identification of a symmetry axis in the extension matrix

Observation of the Beauregard effect when the symmetry axis is oblique to the propagation axis

Theoretical framework capable of representing various light beams

Abstract

It is shown that a light beam in free space is representable by an integral over a vectorial angular spectrum that is expressed in terms of an extension matrix, which describes the vectorial nature of the beam. A symmetry axis of the extension matrix is identified. When it is neither perpendicular nor parallel to the propagation axis, we arrive at such beams that show us for the first time the observable evidence of the Beauregard effect. The advanced representation theory may yield any kinds of light beam, and the uncovered Beauregard effect would play its unique roles in applications.