Dielectric tensor in an isotropic media

[QuantumDuality]

In the lecture notes http://top.electricalandcomputerengineering.dal.ca/PDFs/Web Page PDFs/ECED6400 Lecture Notes.pdf at page 15 eq. (2.46) it says that the dielectric tensor in an isotropic media can be represented by:

δ_{i j} A(k,ω) + k_i k_j B(k,ω)

I understood that in the case of I. M. the a dielectric tensor was just ε_r δ_{i j}
because it was constant. Where did the other term come from?

 

[DrDu]

Spatial dispersion. If you allow for the polarisation to depend nonlocally on the field, and do a Taylor expansion, you get these k dependent terms. In an isotropic and optically active medium, also terms of first order in k appear.