Editing Permittivity (section)

=== Tensorial permittivity ===

According to the [[Drude model]] of magnetized plasma, a more general expression which takes into account the interaction of the carriers with an alternating electric field at millimeter and microwave frequencies in an axially magnetized semiconductor requires the expression of the permittivity as a non-diagonal tensor:<ref>{{cite journal |last1=Prati |first1=E. |year=2003 |title=Propagation in gyroelectromagnetic guiding systems |journal=Journal of Electromagnetic Waves and Applications |volume=17 |issue=8 |pages=1177–1196 |bibcode=2003JEWA...17.1177P |doi=10.1163/156939303322519810 |s2cid=121509049 }}</ref>

<math display="block">\mathbf{D}(\omega) = \begin{vmatrix}
    \varepsilon_1 & -i \varepsilon_2 & 0 \\
  i \varepsilon_2 &    \varepsilon_1 & 0 \\
    0             &    0             & \varepsilon_z \\
\end{vmatrix} \; \operatorname{\mathbf{E}}(\omega)</math>

If {{mvar|ε}}{{sub|2}} vanishes, then the tensor is diagonal but not proportional to the identity and the medium is said to be a uniaxial medium, which has similar properties to a [[uniaxial crystal]].