Relation between coupled-mode theory and equivalent layers for multilayer interference coatings

The method of equivalent layers is a commonly used technique for designing optical multilayer interference coatings. Herpin's theorem [C. R. Acad. Sci . 225, 182 (1947)] states that every symmetrical multilayer structure is eq uivalent, at one arbitrary wavelength, to a single homogeneous layer. The H erpin equivalent layer is described by two design parameters, the equivalen t index and the equivalent thickness. Alternatively, we recently developed an exact coupled-mode analysis for the description of multilayer interferen ce coatings composed of a symmetrical combination of layers. The design par ameters of the coupled-mode theory are the exact coupling coefficient and t he exact detuning coefficient. Recently we used this method in the design o f chirped mirrors for dispersion compensation. We prove that the two method s are equivalent and derive relations that link the design parameters of bo th formalisms. By use of these relations it is possible to translate betwee n the coupled-mode formalism and the method of equivalent layers. The simul taneous availability of both design methods gives a new perspective on the analytical design of optical interference coatings with challenging spectra l response characteristics. (C) 2000 Optical Society of America.