Permittivity tensor ($D_i={\sum }_j{ϵ}_{ij}{E}_j$)

The permittivity tensor is the linear material-response matrix relating electric displacement field to electric field at a specified frequency. An isotropic local medium has ${ϵ}_{ij}=ϵ{\delta }_{ij}$. A magnetically biased transparent medium can have an imaginary antisymmetric transverse contribution; its eigenmodes can have opposite circular polarizations and different refractive indices.