Hierarchy of terms in a multipole expansion

In the classical multipole expansion the various terms (dipoles, quadrupoles, etc.) are ranked according to powers of the wavenumber k. When k→0 the dominant terms are those of lowest powers, provided the moments are k-independent. However, this situation does not always hold, and the hierarchy may be upset when the current structure markedly changes with k. The point is illustrated by the example of the confined modes of a dielectric resonator