Abstract

Spectrophotometric measurements of reflectance vs wavelength are often used to determine the optical constants for single layers of dielectric materials coated on transparent substrates. If the thin film is inhomogeneous, each minimum of the reflectance curve is displaced from the value of R expected for a homogeneous film by an amount ΔR. It has been claimed previously¹ that, for a linear variation in the refractive index, the degree of inhomogeneity is approximated by Δn/n ≃ ΔR/ (4.4R), where n is the average refractive index of the film and Δn is the total change in index over the thickness of the film. This paper explores the range of validity of this relation by comparing it to the results obtained from two analytical models. The first model makes use of a simple computation for a single inhomogeneous layer which uses only the refractive indices at the interfaces of the film. This model ignores the details of the index variation within the layer. The second model involves a multilayer computer calculation which simulates a linear index profile using many thin layers. When Δn/n < 0.2, the approximate formula gives reasonably accurate answers for fused silica or glass substrates (with refractive indices in the 1.45–1.5 range).

© 1985 Optical Society of America