A geometric-optical phase space formulation for paraxial light beam propagation

It is shown that the traditional classical wave picture of light beam propagation in paraxial approximation may be conveniently equivalent to phase representative points picture of ray’s-ensemble in geometric-optical phase space. In this description, the Kogelnik’s abcd law for light beam propagation in configuration space domain is replaced by the transformation equation of the beam ellipse in phase space domain, where the beam ellipse’s area plays the role of wavelength of light beam