Anisotropic and gyrotropic version of Polder and van Santen's mixing formula

Abstract

Abstract In order to account for the permittivity contrast between a host medium and inhomogeneities embedded in it the continuous rotating medium concept with a spatially random permittivity tensor ϵ0[ϵ(ω, r)δ ij +iα(ω, r)e ijl h l ) is introduced. Here ϵ(ω, r) is the dimensionless permittivity, α(ω, r)≡Ω (∂ϵ(ω, r)/∂ω), Ω (rad s−1) is the angular frequency of rotation of the random medium around the h axis and e ijl is the third rank antisymmetric tensor (the Levi-Civita tensor). Under this assumption and with the application of strong fluctuation theory and the bilocal approximation we find the effective permittivity tensor (EPT); in the low-frequency limit the quasistatic EPT represents the anisotropic and gyrotropic version of Polder and van Santen's mixing formula. In Nature there exists a large variety of rotating inhomogeneous media (millisecond pulsars, dust particles in air flowing in turbulent motion, polluted water in rotation). In order to demonstrate the gyrotropicity a simple laboratory expe...