Abstract
We consider semi-classical macroscopic electrodynamics that is translationally invariant (independent of the choice of an arbitrary, implicit set of coordinate origins for molecule-fixed axes) for linear, homogeneous, anisotropic media interacting with harmonic, plane electromagnetic waves. We extend a previous formulation at electric octopole-magnetic quadrupole order to include media comprising magnetic molecules (those possessing both time-even and time-odd properties). This requires two additional invariant, time-odd molecular polarizabilities. Overall, the electrodynamics depends on 10 invariant polarizabilities—5 time even (one each of electric dipole and electric quadrupole–magnetic dipole order, and three of electric octopole-magnetic quadrupole order) and 5 time odd (one, two, and two, respectively)—that are required for the description of linear transmission and reflection phenomena, and material constants. The two additional time-odd polarizabilities account for certain predicted effects, and one of them contributes to the inverse ac permeability of magnetic media. The results are presented in a form that is suitable for numerical computation.
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