The motion and structure of dislocations in wavefronts

Abstract

Scattered scalar wavefields contain line singularities where the phase of the wave is indeterminate and the amplitude is zero. Unless the wave is monochromatic, these dislocation lines, which are analogous to crystal dislocations, move along trajectory surfaces, changing their positions relative to the wave by glide and climb. The edge–screw character of a given dislocation varies along its length and as it moves. When it has no close neighbours its glide and screwness, and the way they change, are completely determined by the distribution over the trajectory surface of two scalar quantities: the phase of the dislocation and its time of arrival. It is shown how even the most general type of dislocation may be con­sidered to be carried, locally, by a plane wave, whose orientation relative to the trajectory determines the climb of the dislocation. Around a general isolated dislocation the equiphase surfaces form a helicoid; they are equally spaced along any radial line, but with a discontinuity of π across the dislocation line itself. The paper provides a theoretical framework for understanding the local phase structure and the motion of any dislocation in a scalar wave.