Propagation of cosine complex variable function Airy-Gaussian beams through the gradient-index medium

We introduce a new class of cosine complex variable function Airy-Gaussian (Cos-CVFAiG) beams and investigate their propagation through the gradient-index medium. Deriving the analytical expression, we show the intensity and phase distributions, the propagation trajectory and the Poynting vector. We carry out the numerical experiment to verify the rationality of the model and find that the light intensity distribution is parallel to the y axis in the transverse plane. With the distribution factor increasing, the axial intensity maximum and the number of the side lobes increase as well. Additionally, the distribution factor can change the bend extent of the ballistic trajectory and the intensity distribution region in the x-z plane. We also compare the influences of the gradient refractive index coefficient with the distribution factor on the propagation properties.