Effects of the cosine complex variable function on the Airy-Gaussian and Airy-Gaussian-vortex beams in a chiral medium

We introduce new kinds of beams, cos-Airy-Gaussian and the cos-Airy-Gaussian-vortex beams, which in theory can be achieved by adding a cosine complex variable function onto normal beams. The analytical expressions for these beams propagating in a chiral medium are deduced, and we focus on exploring the effects of the cosine factor on them. It is shown that the cosine factor can eliminate the central lobe and the x-direction side lobe of the origin intensity distribution when the Airy-Gaussian beams tend to be Airy beams. During propagation, the intensity of the cos-Airy-Gaussian beams transfers from the side lobe in the y-direction to a certain lobe and finally flows to the side lobe in the x-direction. Moreover, the cos-Airy-Gaussian beams have a special transverse displacement along the z-axis when the distribution factor χ0 is small, which is unpredictable in analytical expressions unlike the normal Airy-Gaussian beams. In addition, we have developed several new formulae about the ultimate transverse displacements and the overlap position of the beams and the optical vortex, which have not been used before, and we find that there are always ultimate transverse displacements of the Airy-Gaussian beams and vortex because of the existence of the distribution factor χ0.