Journal of Electromagnetic Analysis and Applications

Volume 10, Issue 2 (February 2018)

ISSN Print: 1942-0730   ISSN Online: 1942-0749

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Kramers-Kronig Relations and the Properties of Conductivity and Permittivity in Heterogeneous Media

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DOI: 10.4236/jemaa.2018.102003    2,229 Downloads   5,375 Views  Citations

ABSTRACT

The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an analogous paradigm applies to the macroscopic electric conductivity. If the causality principle is taken into account, there exist Kramers-Kronig relations for conductivity, which are mathematically equivalent to the Hilbert transform. These relations impose strong constraints that models of heterogeneous media should satisfy to have a physically plausible frequency dependence of the conductivity and permittivity. We illustrate these relations and constraints by a few examples of known physical media. These extended relations constitute important constraints to test the consistency of past and future experimental measurements of the electric properties of heterogeneous media.

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Bédard, C. and Destexhe, A. (2018) Kramers-Kronig Relations and the Properties of Conductivity and Permittivity in Heterogeneous Media. Journal of Electromagnetic Analysis and Applications, 10, 34-51. doi: 10.4236/jemaa.2018.102003.

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