Local phase structure of wave dislocation lines: twist and twirl

Generic wave dislocations (phase singularities, optical vortices) in three dimensions have anisotropic local structure, which is analysed, with emphasis on the twist of surfaces of equal phase along the singular line, and the rotation of the local anisotropy ellipse (twirl). Various measures of twist and twirl are compared in specific examples, and a theorem is found relating the (quantized) topological twist and twirl for a closed dislocation loop with the anisotropy C line index threading the loop.