Propagation of hollow vortex Gaussian beams in a strongly nonlocal nonlinear media

An analytical expression of a hollow vortex Gaussian beam is derived in a strongly nonlocal nonlinear media. The analytical expressions of the beam width, the curvature radius, the kurtosis parameter, and the orbital angular momentum density for the hollow vortex Gaussian beam have been also derived. The normalized intensity, the beam width, the curvature radius, the kurtosis parameter, and the orbital angular momentum density versus the axial propagation distance are all periodic, and the period is the same. Their periodic behaviors are also demonstrated. When the parameter η is used to describe the strength of the nonlocality, the periodic behaviors of the normalized intensity distribution, the beam width, the curvature radius in the strongly nonlocal nonlinear media of η  =  0.5 are opposite to those in the strongly nonlocal nonlinear media of η  =  1.0, respectively. When η reaches a critical value, the normalized intensity distribution, the beam width, and the curvature radius keep unvaried upon propagation. The periodic evolution of the kurtosis parameter is independent of the parameter η. The magnitude of the orbital angular momentum density is inversely proportional to the beam width, while the corresponding distribution area is proportional to the beam width. The periodic evolutions of the hollow vortex Gaussian beam in the strongly nonlocal nonlinear media are well exhibited, and have promising application in optical switch and optical micromanipulation. (paper)