Eikonal equation, alternative expression of Fresnel's equation and Mohr's construction in optical anisotropic media

摘要

A new approach to the study of propagation of plane light waves in anisotropic media, based on the local properties of second order symmetric tensors is described. First, the eikonal equation for anisotropic media is obtained following an alternative procedure based on the propagation of field discontinuities. It is emphasized that eikonal equation is an exact derivation from Maxwell equations. Also, an alternative expression for Fresnel's equation is introduced. The main part of this paper deals with the use of Mohr's plane graphical construction in optics of anisotropic media. This construction, borrowed from mechanics, is proposed and justified in order to analyze (in the environment of a generic point) the propagation of plane light waves in both uniaxial and biaxial media. Mohr's construction is plotted on a plane and allows qualitative and quantitative analysis, in contrast with three-dimensional representations. This graphical method presents many advantages especially when dealing with uniaxial media or when one component of the unit wave vector vanishes in biaxial media. Likewise, the inverse problem of Fresnel's equation is also regarded: if phase velocity is known, the directions of propagation to which this velocity belongs can also be found.