Paraxial propagation of partially coherent Hermite-Gauss beams

The paraxial propagation of partially coherent beams with the Hermite-Gauss modes is investigated. A more generalized and simple expression of the mean-squared width and the beam propagation ratio (M2) of the beam with different mode order is obtained in terms of the cross-spectral density. Our results show that the higher order strengthens the variations of the mean-squared width and the beam propagation ratio for partially coherent beams, and the relation between the two parameters of partially coherent beams is independent of the coherence length.