  We apply a microscopic theory of polarization and magnetization to
crystalline insulators at zero temperature and consider the orbital electronic
contribution of the linear response to spatially varying, time-dependent
electromagnetic fields. The charge and current density expectation values
generally depend on both the microscopic polarization and magnetization fields,
and on the microscopic free charge and current densities. But contributions
from the latter vanish in linear response for the class of insulators we
consider. Thus we need only consider the former, which can be decomposed into
"site" polarization and magnetization fields, from which "site multipole
moments" can be constructed. Macroscopic polarization and magnetization fields
follow, and we identify the relevant contributions to them; for electromagnetic
fields varying little over a lattice constant these are the electric and
magnetic dipole moments per unit volume, and the electric quadrupole moment per
unit volume. A description of optical activity and related magneto-optical
phenomena follows from the response of these macroscopic quantities to the
electromagnetic field and, while in this paper we work within the independent
particle and frozen-ion approximations, both optical rotary dispersion and
circular dichroism can be described with this strategy. Earlier expressions
describing the magnetoelectric effect are recovered as the zero frequency limit
of our more general equations. Since our site quantities are introduced with
the use of Wannier functions, the site multipole moments and their macroscopic
analogs are generally gauge dependent. However, the resulting macroscopic
charge and current densities, together with the optical effects to which they
lead, are gauge invariant, as would be physically expected.
