Optical Rankine Vortex

Abstract

Rankine vortex charateristics of a partially coherent optical vortex are explored using classical and physical optics. Unlike a perfectly coherent vortex mode, the circulation is not quantized.Excess circulation is predicted owing to the wave nature of the composite vortex fields. Based on these findings we propose a vortex stellar interferometer.Vortices exist in all realms of physics and thus the vortex state is universal and robust. In practice the rotational motion is often characterized as a Rankine vortex [1] whereby an inner region near the vortex core rotates as a solid body, and an outer region rotates as an ideal fluid.Within a characteristic radius, R cr , the tangential velocity tends to increase linearly with radial distance from the vortex core, and outside this radius it decreases inversely. Optical (and other wavefunction) vortices are frequently described as perfectly coherent modes exhibiting the quantized circulation of an ideal fluid. This Letter describes how spatial coherence properties require an optical vortex to exhibit Rankine vortex characteristics. Not only does the circulation of the system violate the quantization rule, it may also exceed that of the composing fields. This excess circulation is attributed to the wave nature of the system. We first give a geometrical optics account of the system to identify its basic features. Next we briefly introduce a vortex density formalism. Finally we give a statistical optics account that includes numerical computations of ensemble averaged quantities.