In case of an anistropic medium, the complex permittivity matrix is symmetric, hermitian or none of the two?

21 April 2013 1 3K Report

I am a bit confused. From thermostatics reasons, I can derive that at a small wave frequency the matrix must be symmetric. On the other side, I read for example in Chen, L. F. et al. 'Microwave Electronics - Measurement and Materials Characterization', p. 323, that the matrix is hermitian. How could such a matrix be hermitian? If it were so, in a lossy medium for example, there would be a part of energy that is simultaneously dissipated and stored in the medium. Where is the truth?

Luca Dimiccoli

< El-Batanouny, M. and Wooten, F. 'Symmetry and condensed matter physics : a computational approach', p.484: The electric susceptibility is a symmetric tensor >.

The given reasoning, based on perfect differentiability of the electrical potential energy, can work at small wave frequencies, but in general this perfect differentiability cannot be assured.

< Dyer, Stephen A. 'Survey of instrumentation and measurement', p.449: The electric permittivity is the sum of a symmetric and anti-symmetric tensors >.

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