We have observed the fluidlike rotation of a pair of identical optical vortices (OV's) as they propagate through free space. Similar to vortex filaments in a fluid, the initial rotation rate is found to be inversely proportional to the squared distance of separation. Owing to unusually small vortex cores, we obtained rotation rates that were 2 orders of magnitude larger than expected for "conventional" large core OV's.[S0031-9007(97)04388-3] 42.40.Jv, 47.15.Ki, 47.32.Cc It is well known that two identical vortex filaments in an incompressible inviscid fluid orbit each other at a rate inversely proportional to the orbital area [1] owing to an effective interaction manifested in the flow field. On the other hand, it has been shown analytically [2] and experimentally [3] that optical vortices (OV's) in a propagating beam having a Gaussian intensity profile exhibit rotation rates that are independent of the separation distance. This contrast seems to suggest that fluidlike effective interactions between OV's do not occur. However, both fluid flow and the diffraction of light may be described using potential theory, and one may expect similar phenomena to occur in both systems. Here we report the first experimental evidence of an effective interaction between identical OV filaments, showing that over short propagation distances (i.e., before the vortices diffract and overlap), the rotation rate indeed varies inversely with the squared distance of separation.A topological vortex [4] in optics is characterized by a helical wave front and a dark circular core whose wave function vanishes at the central point owing to destructive interference. The electric field of a beam containing a single vortex may be expressed as E͑r, f, z͒ E BG ͑r, z͒A͑r, z͒ exp͓iF͑r, z͔͒ 3 exp͑2ikz͒ exp͑imf͒ ,where E is the normalized scalar electric field, the background field is typically a Gaussian envelope E BG ͑r, z 0͒ exp͑2r 2 ͞w 2 0 ͒ of size w 0 , and where ͑r, f͒ are the polar coordinates in the transverse plane of the beam, F represents the wave front curvature of the propagating beam, z is the optical axis, k 2p͞l is the wave number, l is the wavelength of light, and m is the topological charge. (Note that in quantum mechanics, m is an orbital angular momentum quantum number.) Finally, A͑r, z͒ is the core function describing the amplitude of the vortex core which vanishes at r 0. We are primarily interested in so-called vortex filaments (or quasi-point vortices) which are characterized by a vanishing core size in the initial plane. A model function which has a well-defined core size w V arises in various physical systems (such as nonlinear refractive media [5][6][7] and Bose-Einstein quantum fluids [8]) and is given byA point vortex exists in the theoretical limit as w V ! 0, although it is not physical because the beam would contain infinite transverse momentum. The paraxial approximation will be assumed through this report so that, in practice, w 0
