Ambiguity in the definition of effective dielectric permittivity of layered heterogeneous medium

Abstract

The problem of ambiguity in defining effective dielectric permittivity is studied theoretically in application to a plane layered heterogeneous medium, compounded by two and more alternating homogeneous layers with different dielectric permittivities (water and glass), for the range of wavelengths from 1 to 10 cm. The effective permittivity for such a heterogeneous medium is usually determined by the phenomenological semi-empirical Braggeman’s power rule, and the aim of the given investigation is validation of this rule by means of rigorous model of plane wave transmission and reflection. It is shown that the complex values of effective dielectric permittivity for a layered dielectric, determined by measuring its transmission and reflection coefficients, differ noticeably from one to another. It is also shown that in a wide frequency range, the Braggeman’s formula gets as a close approximation only for such an effective dielectric permittivity, which is determined by a transmission coefficient.