Morse Families in Anisotropic Optics

Abstract

The main objects of study in this dissertation are Morse families, which are helpful for gaining an understanding of the propagation of light rays. Previous literature on Morse families limited discussion to isotropic media, where the speed of ray propagation is independent of the direction of propagation. We extend the discussion to anisotropic media using tools of Finsler geometry. We prove that in homogeneous media, where the speed of propagation is independent of the point in the medium, any Finsler metric F generates a Morse family. We also prove that in inhomogeneous, anisotropic media, any Finsler metric F which is a perturbation of the flat Euclidean metric is a Morse family. Additionally, Morse families can be used to determine the envelopes of a family of light rays in anisotropic media.