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Approximate formulas for the reflectance, transmittance and scattering losses of nonabsorbing multilayer systems with randomly rough boundaries

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Abstract

New formulas for calculating the coherent reflectance, coherent transmittance, and scattering losses that characterize nonabsorbing multilayer systems with randomly rough boundaries are presented. These formulas were derived within the framework of the scalar theory of diffraction. The principal attention is paid to the approximate formulas related to a multilayer system with boundaries mutually uncorrelated from the statistical point of view. The formulas for a system with identically rough boundaries and for a system equivalent to a single thin film with uncorrelated boundaries are also presented. For all the models of a multilayer system with randomly rough boundaries it is assumed that slopes on all boundaries are small. Spectral dependences of the reflectance, transmittance, and scattering losses of some multilayer systems calculated with the derived formulas are presented. Some numerical results are compared with those published elsewhere.

© 1993 Optical Society of America

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