Propagation properties of partially coherent modified Bessel-Gauss beams through the gradient-index medium

Based on the ABCD matrix method and Collins diffraction integral formula, the general analytical expression for the partially coherent modified Bessel-Gauss beam propagating in a gradient-index medium is derived. The propagation trajectory, intensity, and phase distribution of such a beam are numerically investigated. The effects of the topological charge, the coherence parameter, and the coefficient of the gradient refractive index on propagation properties are considered. Results show that the propagation trajectory of such beam focuses and diverges periodically, which is different from free-space propagation. The period of intensity distribution is consistent with that of phase distribution under different cases. As propagation distance increases, the dark core always exists and the phase singularities remain stable and do not split. The dark core can be modulated by topological charge and coherence parameter, and the periodical distance can be modulated by the coefficient of the gradient refractive index. These results will help to explore such beams and find applications in optical communication and optical trapping.