  We present a systematic investigation on the dynamics of a hollow Gaussian
beam (HGB) in metamaterials. We predict self-trapped propagation of HGBs and
evolution of the beam is highly influenced by dimensionless dispersion
coefficient (k), which determines the strength of dispersion over diffraction.
The evolutions of HGBs such as disappearance of single ringed intensity pattern
and appearance of patterns with a central bright spot are achievable with less
propagation distance in metamaterials with higher values of k. On the other
hand, metamaterials with low values of k can preserve single ring intensity
distribution over a long propagation distance without focusing. When the
strength of dispersion over diffraction increases, it significantly influences
the evolution of the beam and may lead to the formation of tightly focussed
beam with high peak intensity at the center. The phenomenon of tight focussing
is found to have some applications in trapping of nanosized particles.
