Propagation properties of partially coherent Airy beams through the gradient-index medium

We analytically and numerically investigate the propagation properties of partially coherent Airy beams through the gradient-index medium. Based on the ABCD transfer matrix and generalized Collins diffraction integral formula, the analytical expressions for the cross-spectral density of the partially coherent Airy beams propagating in the gradient-index medium are derived in detail. The propagation of the partially coherent Airy beams through the gradient-index medium is numerically simulated and analyzed. The results show that the partially coherent Airy beams propagate periodically and have the singularities of the trajectory divergence propagating in the gradient-index medium. Due to the effect of the coherent parameter, the light intensity region and the space of the singularity of the partially coherent Airy beams are significantly bigger compared to those of the conventional Airy beams. The trajectory of the partially coherent Airy beams in the gradient-index medium and the corresponding singularities can be modulated by the coherence parameter and distribution factor. These results are of great importance in understanding the shaping of partially coherent Airy beams with a gradient-index medium and will facilitate their applications in the optical communications, particle trapping, medical imaging, remote sensing, and advanced manufacturing.