  We study a photonic analog of the chiral magnetic (vortical) effect. We
discuss that the vector component of magnetoelectric tensors plays a role of
"vector potential," and its rotation is understood as "magnetic field" of a
light. Using the geometrical optics approximation, we show that "magnetic
fields" cause an anomalous shift of a wave packet of a light through an
interplay with the Berry curvature of photons. The mechanism is the same as
that of the chiral magnetic (vortical) effect of a chiral fermion, so that we
term the anomalous shift "chiral magnetic effect of a light." We further study
the chiral magnetic effect of a light beyond geometric optics by directly
solving the transmission problem of a wave packet at a surface of a
magnetoelectric material. We show that the experimental signal of the chiral
magnetic effect of a light is the nonvanishing of transverse displacements for
the beam normally incident to a magnetoelectric material.
