Optical Vortex Filaments

This chapter examines the vortex core size and how it affects the propagation dynamics of neighboring optical vortices in the same beam. When the core is small compared to the distance between neighboring vortices, the vortices may be called vortex filaments. Such vortices have been found to exhibit unusual propagation dynamics such as rapid fluid-like vortex-vortex “effective interactions” [1,2]. In linear media this effect occurs over short propagation distances (compared to the diffraction length of the beam), whereas in nonlinear refractive (self-defocusing) media, the phenomenon may be sustained over longer distances [3] owing to the formation of optical vortex solitons [4]. Filament motion in the transverse plane depends on the distance from nearby vortices. In contrast large-core optical vortices move independently and relatively slowly (i.e., over length scales on the order of the diffraction length of the beam) [5]. Both large-core vortices and optical vortex solitons propagate as self-similar waves; hence, this greatly simplifies the mathematical analysis. However, vortex filaments in a linear material radiate diffraction rings and are significantly more difficult to treat. Here we present both ray-optics and physical optics descriptions for the latter case, i.e., for small-core vortices (within the paraxial approximation).