Surprises in the multipole description of macroscopic electrodynamics

Abstract

The theory of macroscopic electrodynamics (in its multipole form) for harmonic plane-wave electric and magnetic fields in linear anisotropic media yields constitutive relations and expressions for the material constants and other macroscopic observables. It is shown that the calculated dynamic material constants are unphysical: of the 36 elements of the constitutive tensor, 27 (comprising the inverse permeability and two magnetoelectric tensors) depend on the choice of coordinate origin, while the remaining 9 (the permittivity tensor) are physical at electric dipole order, but not beyond. Thus quantities such as the time average of the instantaneous Poynting vector have origin-dependent values. We use properties of the macroscopic Maxwell equations and the equation of wave propagation to show how physically acceptable results can be obtained in a relatively simple manner for both nonmagnetic and magnetic dissipative media. In doing so, it is essential to adhere to a certain hierarchy for the pairing of electric and magnetic multipoles∕polarizabilities. We also comment on the Post constraint in relation to this theory, and use the Buckingham effect to illustrate origin-dependent and origin-independent properties.