On the Burgers vector of a wave dislocation

TL;DR

This paper proposes a new method to define and compute the Burgers vector for wave dislocations, linking it to wavefront twisting and current flow, with explicit calculations and numerical analysis.

Contribution

It introduces a regularized phase gradient approach to define the Burgers vector for wave dislocations, connecting it to physical properties like wavefront twisting and current flow.

Findings

Explicit computation of the Burgers vector for wave dislocations.

Relation of the screw component to wavefront helicity.

Numerical distribution of the edge component in random waves.

Abstract

Following Nye and Berry's analogy with crystal dislocations, an approach to the Burgers vector of a wave dislocation (phase singularity, optical vortex) is proposed. It is defined to be a regularized phase gradient evaluated at the phase singularity, and is computed explicitly. The screw component of this vector is naturally related to the helicoidal twisting of wavefronts along a vortex line, and is related to the helicity of the phase gradient. The edge component is related to the nearby current flow (defined by the phase gradient) perpendicular to the vortex, and the distribution of this component is found numerically for random two-dimensional monochromatic waves.