  We extend a field theoretic approach for the investigation of the electronic
charge-current density response of crystalline systems to arbitrary applied
electromagnetic fields. The approach leads to the introduction of microscopic
polarization and magnetization fields, as well as free charge and current
densities, the dynamics of which are described by a lattice gauge theory. The
spatial averages of such quantities constitute the fields of macroscopic
electrodynamics. We implement this formalism to study the orbital electronic
response of a class of insulators to applied uniform dc electric and magnetic
fields at zero temperature. To first-order in the applied fields, the free
charge and current densities vanish; thus the response of the system is
characterized by the first-order modifications to the microscopic polarization
and magnetization fields. Associated with the dipole moment of the microscopic
polarization (magnetization) field is a macroscopic polarization
(magnetization), for which we extract various response tensors. We focus on the
orbital magnetoelectric polarizability (OMP) tensor, and find the accepted
expression as derived from the "modern theory of polarization and
magnetization." Since our results are based on the spatial averages of
microscopic fields, we can identify the distinct contributions to the OMP
tensor from the perspective of this microscopic theory, and we establish the
general framework in which extensions to finite frequency can be made.
