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 (M-2) 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. (C) 2004 Elsevier B.V. All rights reserved.