  This is a PhD dissertation. Ignited by the chiral anomaly of recently
discovered Weyl (semi-)metals, we study the chiral magnetic effect and the
natural optical activity of noncentrosymmetric metals. Both phenomena are
related to the linear-in-$\mathbf{q}$ spatial dispersion of the optical
conductivity tensor, and can be calculated within the formalism of the
semiclassical kinetic equation. Therefore, we calculate the dispersion of
optical conductivity up to the linear order of the wave vector, in the low
frequency regime, with both the semiclassical Boltzmann equation and the Kubo
formula. The two different methods of calculation provide us the same result.
In this result, the static and dynamic chiral magnetic effects are revealed to
have different origin: one comes from topology, related to Berry monopoles, and
the other has a geometric origin, which is determined by the orbital magnetic
moment. The Faraday rotation of the polarization of light transmitted through a
slab of the sample provides us the most direct way to measure the magnitude of
dynamic chiral magnetic effect. We develop an effective medium theory for
electromagnetic wave propagating through gapless nonuniform systems, to
calculate macroscopic sample inhomogeneities induced corrections to the chiral
magnetic conductivity. We show that, in metals with low carrier density, the
way in which macroscopic fluctuations of the local conductivity affect the
frequency dependent of the measured optical polarization rotation angle: by
creating a sharp feature near the plasma edge, which can be detected by
experiments. Then we narrow down our research a bit further to the current
induced magnetization.
