Dispersion equations for vacuum-deposited tilted-columnar biaxial media

Abstract

We consider the application of the Bragg-Pippard (BP) equations for form birefringence to a tilted-columnar biaxial thin film with columns of index n(c) and voids of known index n(v). In such a situation the three forward BP equations that express the principal refractive indices n1, n2, and n3 as functions of n(c), n(v), the packing fraction p(c), and the depolarization factors L1, L2, and L3 can be inverted. The procedure described for adding dispersion to the principal indices involves entry to the BP model via the inverted equations, modification of n(c) to allow for dispersion, and then exit from the model via the forward BP equations. We discuss the introduction of composite columns to the model to allow for angular dependence of n(c) and the selection of suitable dispersion functions for bulk tantalum oxide, titanium oxide, and zirconium oxide. Theory and experiment both show that the dispersion of the normal-incidence birefringence Deltan of the thin films is several times larger than the dispersion of the individual principal refractive indices.