A simple, single-mode, coherent Gaussian laser beam with wavefronts that are spherical as they pass through a reference plane is assumed, and then by using only the Huygen’s principle and scalar diffraction theory, the propagation characteristics are found, and the formulas for the beam at a distance from the reference plane are derived. The action of a lens on a wavefront is discussed, and the lens formula is derived.
C. S. Williams, "Gaussian Beam Formulas From Diffraction Theory," Appl. Opt. 12, 872-876 (1973)