Double refraction of light by a bulk material was probably first reported by Erasmus Barfholin (1625-1698), a professor of medicine at the University of Copenhagen. In 1669, he observed that images seen through a mineral named Iceland spar (calcite) were doubled, as shown in Fig. 7.1. When the crystal was rotated, one of the two images remained fixed but the other rotated with the crystal. Observing that light passing through the crystal was split into two rays, he coined the terms ordinary and extraordinary rays to account for the stationary and the moving images, respectively. Double refraction was such a serious contradiction to Newton's corpuscular theory of light that much attention was focused on optical crystallography after the publication of Christiaan Huygens' Traite de la Lumiere in 1690 [347, Ch. 1]. Crystals were classified into cubic, hexagonal, tetragonal, trigonal, orthorhombic, monoclinic and triclinic classes [325]. Any respectable text on optics, down to the latest version of Principles of Optics by Born and Wolf [348], has a chapter or more on crystal optics. In fairness, the ubiquity of quartz in optics necessitates that attention—so does stress in translucent materials such as plastics and glasses [349]. Columnar thin films have been grown by PVD for over a century [9] and are morphologically similar to certain types of crystals [60, Ch. 10]. This becomes clear when comparing the SEMs of the minerals ulexite and trona in Fig. 7.2 with the SEM in Fig. 7.3 of an amorphous germanium CTF. Now, morphology at length-scales considerably smaller than the wavelength crucially affects the macroscopic electromagnetic properties - €”to wit, Sec. 6.5.2. Therefore, CTFs are optically similar to certain types of crystals, and many optical elements can be made of CTFs [43]. This chapter is devoted to the response of CTFs to normally as well as obliquely incident plane waves. The derivation of a 4 x— 4 matrix ordinary differential equation (MODE) for arbitrary propagation in a CTF is followed by the exact analytical solution of that equation. The derived solution is used in turn to solve the boundary value problem of the reflection and transmission of plane waves by CTFs of constant thickness. Characteristic features for incidence and propagation in the morphological significant plane are pointed out; in particular, the 4 x— 4 MODE then breaks up into two 2 x— 2 autonomous MODEs. Normal incidence on CTFs is separately considered, with application to wave plates, polarizers, and filters.