Focusing properties of Gaussian beams through a compound optical system

The focusing properties of Gaussian beams through a compound optical system consisting of a concave lens, a convex lens and a subsystem, are discussed. Based on the matrix optical method, formulae of the waist width and imaging distance of focused Gaussian beams through the system are derived. It is shown that the system is capable of achieving both smaller focused waist width and larger imaging distance. The results are illustrated and confirmed with numerical calculation examples.