Universal constitutive relations for optical effects in transmission and reflection in magnetic crystals

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Abstract
For long wavelength radiation the D and H fields in Maxwell's equations may be expressed as multipole expansions which contain the multipole moment densities: electric dipole P, magnetic dipole M, …, that are induced in matter by the radiation. Quantum-mechanical perturbation theory yields expansions for the multipole moment densities, which show that these are induced by the E and B fields of the radiation, by their successive space gradients, and also by the first time-derivative of each. These forms are shown to have a simple phenomenological basis. When used in Maxwell's equations these constitutive relations are able to explain successfully optical effects which occur in transmission. However, such success is not achieved for reflection phenomena, for which it is found that the usual Maxwell boundary conditions on D and H impose additional constraints. The multipole forms of D and H which satisfy these constraints are shown to be covariant.

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