Periodic properties of partially coherent generalized Hermite cosh-Gaussian beams through a gradient-index medium

In this paper, we conducted a detailed investigation on the evolution of a partially coherent generalized Hermite cosh-Gaussian beam (PCGHchGB) through a gradient-index medium. Analytical formula for a PCGHchGB propagating in the gradient-index medium is obtained based on ABCD transfer matrix and generalized diffraction integral formula. We discuss the periodic changes of the corresponding beam through the gradient-index medium by performing numerical examples. Our obtained results demonstrate that the gradient-index parameter of media and the initial beam parameters, such as the coherence width, beam waist width, decentered beam parameter, and beam orders, affect the evolution characteristics on the intensity distribution of the PCGHchGB in the gradient-index medium. The results of this work could be beneficial for applications in optical communication and nonlinear optics.