The propagation properties of the first-order and the second-order Airy vortex beams through strongly nonlocal nonlinear medium

•The propagation of the first-order and second-order Airy vortex beams is expressed..•The intensity, phase distribution, beam centers, and Poynting vector are discussed.•The propagation trajectory is a sinusoidal function which focuses two times in one period.•The phase, energy flow and AM density flow distribution show a reversal.•As the order is increased, the vortex is stronger.

By using the transfer matrix method, the propagation of the first-order and the second-order Airy vortex (AiV) beams through strongly nonlocal nonlinear medium is exhibited. Based on the Huygens diffraction integral formula, we derive the analytical expressions of the first-order and the second-order AiV beams propagate through the paraxial ABCD system and present corresponding characteristic parameters such as propagation path, intensity, phase distributions, beam centers, the Poynting vector and angular momentum (AM) density flow. The propagation trajectory is periodical and looks like a sine wave. The AiV beam focuses two times in one period. The phase, energy flow and AM density flow distribution show a reversal when the beam propagates near the focusing point. Additionally, as the order increased, the vortex of the second-order AiV beam is stronger.