Transformed multipole theory of the response fields D and H to electric octopole-magnetic quadrupole order

We consider multipole theory of linear constitutive relations for the macroscopic electromagnetic response fields D and H to electric octopole-magnetic quadrupole order. We use a recently developed transformation theory to obtain unique, physically acceptable, constitutive relations from the unphysical relations of conventional multipole theory. Explicit expressions for the transformed material constants and transformed macroscopic multipole moment densities in terms of appropriate macroscopic polarizability tensors are presented for both non-magnetic and magnetic media. The electric octopole-magnetic quadrupole contributions yield a new, physically acceptable multipole expression for the AC magnetizability; they satisfy the Post constraint; and they disagree with published results based on trial-and-error methods.