Optical dislocation networks in highly random media

Networks of optical dislocations in gaussian speckle patterns are studied both theoretically and experimentally. A simple product wavefunction is suggested to describe an arbitrary dislocation network. Phase maps predicted by this wavefunction are tested against measured interferograms for a variety of different dislocations and good agreement is found between theory and experiment. Simple arguments based upon the sampling theorem are presented which suggest that in the gaussian limit the dislocation network contains all the information needed to reconstruct the total wavefield, and alternatively, that the wavefield may also be reconstructed from a small fragment of the phase map using the method of zero crossings. It is also argued that there must exist some degree of correlation between neighboring dislocations.