Abstract

A topological defect of a complex field is a point where the intensity of the field vanishes and the circulation of the phase gradient around it has a value that is an integer (called topological charge) multiple of 2tt. In optics, defects have been theoretically predicted [1,2] and experimentally observed both in linear [3] and in nonlinear [4] systems. Linear experiments consist in scattering coherent light from random diffusers, resulting in a speckle field. We compare the experimental statistical distributions of defects for the linear and the nonlinear case at large F. The nonlinear experiment [4] consists of a ring cavity in which a photorefractive BSO crystal, pumped by an Ar⁺ laser, acts as a light amplifier via a two-wave mixing mechanism. At small F, where only one mode per time is present in a periodic or chaotic alternation [5], the defects are a trivial signature of the symmetry of that specific mode. On the contrary at high F, where many modes coexist, the defect dynamics reflects the mode competition and have a role in mediating turbulence [6]. For a fixed high Fresnel number we study the fluctuations of the total number of defects in the nonlinear field. We repeat the same measurement in the linear case where the fluctuations are trivially due to a translational motion of the random diffuser. The histograms relative to the nonlinear and linear case are plotted in Fig.1a and 1b together with a Poissonian best fit. In Fig. la we report also the result of a theoretical prediction by Gil et al. [7]. The hypothesis of their work is that defects can only be created and annihilated by pairs, with rates of creation Γ = α and annihilation Γ = βn² where n is the number of pairs present. This lead to a distribution which is a square Poissonian in the number n of pairs.

© 1992 Optical Society of America