  It is widely believed that axions are ubiquitous in string theory and could
be the dark matter. The peculiar features of the axion dark matter are coherent
oscillations and a coupling to the electromagnetic field through the
Chern-Simons term. In this paper, we study consequences of these two features
of the axion with the mass in a range from $10^{-13}\,{\rm eV}$ to
$10^{3}\,{\rm eV}$. First, we study the parametric resonance of electromagnetic
waves induced by the coherent oscillation of the axion. As a result of the
resonance, the amplitude of the electromagnetic waves is enhanced and the
circularly polarized monochromatic waves will be generated. Second, we study
the velocity of light in the background of the axion dark matter. In the
presence of the Chern-Simons term, the dispersion relation is modified and the
speed of light will oscillate in time. It turns out that the change of speed of
light would be difficult to observe. We argue that the future radio wave
observations of the resonance can give rise to a stronger constraint on the
coupling constant and/or the density of the axion dark matter.
