Geometric propagation of an axially symmetric optical wavefront in a homogeneous medium

摘要

We obtain a Taylor series neighbor expansion that allows the geometric propagation of an axially symmetric wavefront in such a way that the change in shape of the wavefront is determined as an explicit function of coordinates. We then apply the expansion to the propagation of conicoids in particular. The theory is applied to Jhe propagation of a general conicoidal, a spherical, and a paraboloidal wavefront. Application of the theory to the general conicoid leads to a proof of the invariance of the product of radius of curvature and conic constant for short propagation distances in homogeneous media. For the case of the spherical wavefront, the intuitive result is obtained (i.e.the wavefront remains spherical).