Amphoteric refraction at the isotropic–anisotropic biaxial media interface: an alternative treatment

Abstract

Amphoteric refraction of light (refraction that can be positive or negative depending on the angle of incidence) at the interface between isotropic and anisotropic biaxial media is analysed by means of an alternative method previously developed by the authors. Unlike left-handed materials (LHMs), negative (or abnormal) refraction involving anisotropic media is only due to the intrinsic properties of the media and is only exhibited by non-collinear rays (rays that do not follow an isotropic behaviour). Moreover, the axes of wavevector ellipsoids must be rotated with respect to the normal to the incidence plane. In this paper, only planes of incidence lying normal to a principal axis of the dielectric tensor are considered, and consequently comparison between traditional and alternative methods is possible because both geometrical constructions are plane. First, a very simple procedure that allows us to find the direction of wavevector k from the knowledge of non-collinear (n.c.) ray direction is outlined together with the solution of the dual problem: to find the n.c. ray direction from the k one. Then, the abnormal refraction phenomenon is studied and the equivalence between traditional and alternative methods is clearly stated. Finally, two graphical constructions to find the critical angle of incidence and the maximum angle of negative refraction are also proposed.