Singularity displacement in random speckle patterns of diffusive and localized waves: universality lost and regained

All random wave fields possess a network of phase singularities. We show that while the phase statistics within speckle patterns is generic, the statistics of the motion of phase singularities differs substantially for diffusive and localized waves. This reflects the changing wave interaction with the underlying modes of multiply-scattering systems. Universality is regained when the motion of phase singularities is charted against the phase excursion which reflects the variation of phase change across the speckle pattern. The evolution of speckle patterns can therefore be used to monitor internal motion in complex systems and to characterize the nature of wave propagation.