  The Chiral Magnetic Effect (CME) has been investigated as a new transport
phenomenon in condensed matter. Such an effect appears in systems with chiral
fermions and involves an electric current generated by a magnetic field by
means of an "exotic" magnetic conductivity. This effect can also be connected
with extensions of the usual Ohm's law either in magnetohydrodynamics or in
Lorentz-violating scenarios. In this work, we study the classical propagation
of electromagnetic waves in isotropic dispersive matter subject to a
generalized Ohm's law. The latter involves currents linear in the magnetic
field and implies scenarios inducing parity violation. We pay special attention
to the case of a vanishing electric conductivity. For a diagonal magnetic
conductivity, which includes the CME, the refractive index is modified such
that it implies birefringence. For a nondiagonal magnetic conductivity,
modified refractive indices exhibiting imaginary parts occur ascribing a
conducting behavior to a usual dielectric medium. Our findings provide new
insight into typical material properties associated with a magnetic
conductivity.
