When is the permittivity tensor not Hermitian?

Question

I understand that a permittivity tensor is symmetric if there is no absorption. On the other hand is it always Hermitian? Under what cases would that not be the case?

Answer 1

According to this text, the energy dissipated by a dielectric is given by

$$ Q = \frac{i \omega}{16 \pi} \left\{ \left( \varepsilon_{i k}^{*} - \varepsilon_{k i } \right) E_{i} E_{k}^{*} + \left( \mu_{i k}^{*} - \mu_{k i } \right) H_{i} H_{k}^{*} \right\} \tag{1} \label{1} $$

That means that if the matrix is non hermitian, it absorbs energy.

I'm not aware of what conditions would make it real in addition, which would be a symmetric matrix.