  Working in the crystal-momentum representation, we calculate the optical
conductivity of noncentrosymmetric insulating crystals at first order in the
wave vector of light. The time-even part of this tensor describes natural
optical activity and the time-odd part describes nonreciprocal effects such as
gyrotropic birefringence. The time-odd part can be uniquely decomposed into
magnetoelectriclike and purely quadrupolar contributions. The
magnetoelectriclike component reduces in the static limit to the traceless part
of the frozen-ion static magnetoelectric polarizability while at finite
frequencies it acquires some quadrupolar character in order to remain
translationally invariant. The expression for the orbital contribution to the
conductivity at transparent frequencies is validated by comparing numerical
tight-binding calculations for finite and periodic samples.
