Evolution of on-axis intensity of anomalous hollow Gaussian beams in highly nonlocal nonlinear media

In this paper, we focus on the on-axis intensity evolutions of anomalous hollow Gaussian beams in highly nonlocal nonlinear media. It is found that the evolution of on-axis intensity is always periodic and the incident power of the beams plays a key role. By selecting the different amplitude of the incident power, the on-axis intensity evolutions exhibit themselves as three different shapes in each evolution period, i.e. the protrusion situation, the platform situation and the indentation situation. We analyze the three situations in detail, and the extreme values of on-axis intensity and their positions are all given analytically. The influences of the beam ellipticity and the off-waist departure distance on the on-axis intensity evolutions are also discussed. It is found that the evolution of on-axis intensity becomes more complicated, and the on-axis intensity evolution in each period splits into two intensity peaks.