Anisotropic and gyrotropic version of Polder and van Santen's mixing formula
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 ε 0 [ε(ω, r ) ij + i α(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 experiment with a cylinder rotating around its axis is proposed. If one measures the Fresnel intensity coefficient (parallel polarization) in the plane normal to the cylinder axis then the gyrotropicity effect can be clearly seen only if Ω is sufficiently high.
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Document Type: Research Article
Affiliations: Institute of Electronics of the Bulgarian Academy of Sciences, 1784, Sofia, Bulgaria
Publication date: 01 April 1992