Abstract
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 …nk−1,nk having quarterwave thicknesses at the monitoring wavelength λ0. The expression thus derived is of the form , where PN and QN are functions of refractive indices and their interdependence is expressed by the relation (QN − PN)/(4ns) = (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 λ < λ0 such that within limits of acceptable variations (Δ λ) 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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