UNIVERSAL CONSTITUTIVE RELATIONS FOR OPTICAL EFFECTS IN TRANSMISSION AND REFLECTION IN MAGNETIC CRYSTALS

For long wavelength radiation the (D) under tilde and (H) under tilde fields in Maxwell's equations may be expressed as multipole expansions which contain the multipole moment densities: electric dipole !:, mag netic dipole (M) under tilde,..., that are induced in matter by the ra diation. Quantum-mechanical perturbation theory yields expansions for the multipole moment densities, which show that these are induced by t he (E) under tilde and (B) under tilde fields of the radiation, by the ir successive space gradients, and also by the first time-derivative o f each. These forms are shown to have a simple phenomenological basis. When used in Maxwell's equations these constitutive relations are abl e to explain successfully optical effects which occur in transmission. However, such success is not achieved for reflection phenomena, for w hich it is found that the usual Maxwell boundary conditions on (D) und er tilde and (H) under tilde impose additional constraints. The multip ole forms of (D) under tilde and (H) under tilde which satisfy these c onstraints are shown to be covariant.