Dispersion equations for vacuum-deposited tilted-columnar biaxial media

We consider the application of the Bragg-Pippard (BP) equations for form bi refringence to a tilted-columnar biaxial thin film with columns of index n( c) and voids of known index n(nu). In such a situation the three forward BP equations that express the principal refractive indices n(1), n(2), and n( 3) as functions of n(c), n(nu), the packing fraction p(c), and the depolari zation factors L-1, L-2, and L-3 can be inverted. The procedure described f or adding dispersion to the principal indices involves entry to the BP mode l via the inverted equations, modification of n(c) to allow for dispersion, and then exit hom the model via the forward BP equations. We discuss the i ntroduction of composite columns to the model to allow for angular dependen ce of ra, and the selection of suitable dispersion functions for bulk tanta lum oxide, titanium oxide, and zirconium oxide. Theory and experiment both show that the dispersion of the normal-incidence birefringence Deltan of th e thin films is several times larger than the dispersion of the individual principal refractive indices. (C) 2001 Optical Society of America.