# Why is it important to measure permittivity and permeability complex of materials?

I know that in general, $$\epsilon(r,\omega)$$ and $$\mu(r,\omega)$$ are complex tensors, so now how do you resolve maxwell equations?

I don't understand why there are techniques to measure them if you could know these parameters from knowledge of the crystal structure of materials.

• This question is equally applicable to any branch of physics. The point is that theories should be guided and validated by experimental measurements. A lot of materials are not crystalline (silica etc), or non single-crystal. So crystal selection rules techniques will not help there. A lot depends material surface roughness, a lot depends on deposition method, abundance of dopands, annealing/non-annealing etc. etc. There is only one material the optical properties of which I would trust without re-measuring them - crystalline silicon in wafers, and only because it is an industry standard. – Cryo Apr 1 at 3:09
• Even then, as soon as you pattern this silicon, all trust is gone. – Cryo Apr 1 at 3:10

If a theory describing the crystal lattice predicts a certain value of $$\epsilon$$ or $$\mu$$ (complex or otherwise) conducting an experiment to measure the actual value will tell you if your model is correct. All models need to be compared to experiment.