Focusing of a light beam of Gaussian field distribution in continuous and periodic lens-like media

The behavior of a light beam traveling in continuous or periodic lens-like media is considered. The light beam is assumed to be launched with a Hermite-Gaussian or Laguerre-Gaussian field distribution. Under suitable conditions and for most focusing media we find that the beam center follows a paraxial ray, and an independent equation determines the motion of the beam radius. The form of the field distribution does not change. In a continuous inhomogeneous focusing medium, the beam cross section varies periodically in distance with a period half of that of the oscillatory motion of the beam center. In periodic media, a particular solution is found for the case when the beam propagates with a nearly constant cross section. Discussions include an acoustic lens-guide and a lens-guide using heat diffusion in a gas.