Curvature of wave streamlines

Wave streamlines are integral curves of the local wavevector (phase gradient). An exact formula is derived, giving the curvature of streamlines as the component transverse to the local wavevector of the gradient of the logarithm of the local wavenumber. The formula is applied to quantum particles moving in a potential and classical light in the presence of a refractive-index gradient. Three limiting regimes are encompassed. The first is geometrical, in which the bending of streamlines arises solely from the classical force or optical index gradient. The second and third limits concern singularities in the pattern of wave streamlines, of two types: optical vortices, near which the streamlines are asymptotically circular, and phase saddles, near which the streamlines are asymptotically hyperbolic. (paper)