A method for synthesis of designs of multilayer structures with prescribed frequency dependent properties

Abstract

This synthesis method is based on an approximate reflection coefficient for plane waves. Computations show that the exact and approximate reflection coefficients differ slightly for small values. Maxima of the reflection coefficients occur at about the same wavelength, but values differ considerably. Multilayer designs were derived starting with a specification of transmission as a function of frequency. Exact calculations verified that the design does approximate specified performance. The synthesis procedure is not systematic because the number of layers is arbitrary. In practice, this number would be minimized. Also, solving the simultaneous quadratics, eq. (9) is not straightforward in general. Interpretations are provided of multilayer performance. Increasing numbers of layers or optical paths in a layer varies the number of Fourier components available. Layer thickness is related to bandwidth, and from eqs. (5), (10, and (11) when f = f m/2, each layer is a quarter wave plate. Other work has shown some of the relationship of this approximate method to the impedance theory of iterative structures [5, 6]