  Recent angle resolved photoemission spectroscopy measurements have identified
an inversion symmetry breaking Weyl semimetal phase in TaAs and NbAs. In an
inversion symmetry breaking Weyl semimetal the left and the right handed Weyl
points can occur at different energies and the energy mismatch between the Weyl
points of opposite chirality is known as the chiral chemical potential. In the
presence of the chiral chemical potential, the nontrivial Berry curvature of
the Weyl fermions gives rise to the \emph{dynamic} chiral magnetic effect. This
describes how a time dependent magnetic field leads to an electrical current
along the applied field direction, which is also proportional to the field
strength. We derive a general formula for the dynamic chiral magnetic
conductivity of the inversion symmetry breaking Weyl semimetal. We show that
the measurement of the natural optical activity or rotary power provides a
direct confirmation of the existence of the dynamic chiral magnetic effect in
inversion symmetry breaking Weyl semimetals.
