A converted characteristic matrix method has been used to derive a generalized expression for reflectance R (for wavelength λ at normal incidence) of an all-dielectric multilayer stack consisting of K layers of refractive indices n₁,n₂,n₃… n_k-1,n_k having quarterwave thicknesses at the monitoring wavelength λ₀. The expression thus derived is of the form R = Σ^K_N=0(P_N tan^2Nϕ)/(Q_Ntan^2Nϕ), where P_N and Q_N are functions of refractive indices and their interdependence is expressed by the relation (Q_N - P_N)/(4n_S) = (K!)/N!(K - N)!]. This expression shows that R is a function of (i) the refractive indices of the various layers in the multilayer structure and (ii) the parameter ϕ = {(Π/2) [(λ - λ₀)/λ]} which assumes positive or negative values depending on whether λ < λ₀ or A > λ₀ such that within limits of acceptable variations (Δλ) in λ₀, R remains unaffected at ±ϕ. An outcome of this analysis is that it can be used in identifying, to a limited extent, the structure of an unknown optical coating once the experimentally observed parameters R and T are known.

© 1988 Optical Society of America

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