  Toroidal multipoles are a topic of increasing interest in the nanophotonics
and metamaterials communities. In this paper, we separate out the toroidal
multipole components of multipole expansions in polar coordinates (two- and
three-dimensional) by expanding the Bessel or spherical Bessel functions. We
discuss the formation of the lowest order of magnetic anapoles from the
interaction between the magnetic toroidal dipole and the magnetic dipole. Our
method also reveals that there are higher order current configurations other
than the electric toroidal multipole that have the same radiation
characteristics as the pure electric dipole. Furthermore, we find that the
anapole condition requires that there is a perfect cancellation of all higher
order current configurations.
