We investigate the dynamic behavior of optical vortices, or phase
singularities, in random wavefields and demonstrate the direct experimental
observation of the anomalous diffusion of optical vortices. The observed
subdiffusion of optical vortices show excellent agreement with the fractional
Brownian motion, a Gaussian process. Paradoxically, the vortex displacements
are observed exhibiting a non-Gaussian heavy-tailed distribution. We also tune
the extent of subdiffusion and non-Gaussianity of optical vortex by varying the
viscoelasticity of light scattering media. This complex motion of optical
vortices is reminiscent of particles in viscoelastic environments suggesting a
vortex tracking based microrheology approach. The fractional Brownian yet
non-Gaussian subdiffusion of optical vortices may not only offer insights into
the dynamics of phase singularities, but also contribute to the understanding
certain general physics, including vortex diffusion in fluids and the
decoupling between Brownian and Gaussian