Dislocations in waves and in crystals were compared, in tutorial style, with particular emphasis on signs and senses. Reconnection of dislocations and the disappearance of a closed loop were treated as examples. There was a fundamental difference between the regularized phase gradient of a wave dislocation or wave vortex, as defined in a recent paper, and the Burgers vector of a dislocation in a crystal; the latter, as was well known, was not strictly a vector at all, because, to define it, a sense of direction for the dislocation line had to be chosen arbitrarily. The Burgers vector in a crystal was more analogous to the phase circulation of ±2π around a wave dislocation. The new vector now associated with a wave dislocation could be called, not the Burgers vector, but simply 'the phase gradient vector'. A new result was to see that, by an isotropic scaling, two parallel straight dislocation lines of opposite sign had identical phase patterns in the plane normal to them, regardless of whether they were of pure edge, or mixed edge/screw type.

Sense and Sign in Wave and Crystal Dislocations. J.F.Nye: Journal of Optics, 2011, 13[6], 064007