Paraxial propagation of the first-order chirped Airy vortex beams propagating in a quadratic index media

We investigate the propagation of the first-order chirped Airy vortex (FCAiV) beams in a quadratic index media analytically by applying the Huygen-Fresnel integral. The intensity, the phase, the energy flow density, and the angular momentum density are investigated for different chirped parameters, decay factors and parameters related to the gradient refractive index. There is an inversion of the self-acceleration of the FCAiV beams during the propagation. The FCAiV beams propagating in the quadratic index media hold a periodic evolution. The focusing intensity, the intensity distribution, the centre of mass of the FCAiV beams can be controlled by choosing different parameters.