Propagation expressions for apertured Hermite-cosine-Gaussian beams

Starting from the Collins formula,a recurrence equation of Hermite-cosine-Gaussian (HCG) beams propagating through a paraxial ABCD system with a hard-edge aperture is derived,from which the propagation expressions for apertured HCG beams of any order can be derived by means of the recursive algorithm.The validity and advantage of our results are confirmed and illustrated by numerical calculations.