Symmetry constraints for electromagnetic constitutive relations

We consider linear constitutive relations for the macroscopic electromagnetic fields D and H in terms of the fields E and B and of their space and time derivatives. For E and B fields in the form of harmonic plane waves, symmetry conditions are deduced for the tensors representing material constants in the constitutive relations. Some examples are discussed of how these symmetries, as well as origin independence of physical quantities, are achieved in a multipole theory of constitutive relations. These examples show that neither the symmetry of the material constants nor their origin independence are sufficient to specify completely the material constants in such a theory. A further symmetry condition is suggested for this purpose, namely that the Fresnel reflection matrix must satisfy reciprocity. This leads to agreement with published experimental data.