Evolution of vortex density in a non-diffracting speckle field with its continuous phase removed

We break down the equilibrium state and the diraction invariant property of a non-diracting speckle “eld byremoving its continuous part of the phase while leaving all vortices behind. During the propagation of such aphase corrected non-diracting speckle “eld, the vortex density drops down to a minimum value and then comesback to an equilibrium value which is even higher than the initial one. Before the phase corrected “eld returnsback to its new equilibrium state, another least-squares phase removal will be applied, at the position wherethere is a minimum vortex density, to further remove vort ices from the speckle “eld. Such a process of removingleast-squares phase and propagating the phase corrected “eld over a distance can be repeated to eliminate mostof optical vortices. Statistical results show that most of optical vortices can be removed from a non-diract ingspeckle “eld. Finally, a semi-plane wave without optical vortices can be obtained from an initial non-diractingspeckle “eld with multiple steps of least-square phase correction.Keywords: Non-diracting speckle “eld, Optical v ortices, Least-squares phase removal