Dielectric Haloscopes to Search for Axion Dark Matter: Theoretical
  Foundations
  We study the underlying theory of dielectric haloscopes, a new way to detect
dark matter axions. When an interface between different dielectric media is
inside a magnetic field, the oscillating axion field acts as a source of
electromagnetic waves, which emerge in both directions perpendicular to the
surface. The emission rate can be boosted by multiple layers judiciously placed
to achieve constructive interference and by a large transverse area. Starting
from the axion-modified Maxwell equations, we calculate the efficiency of this
new dielectric haloscope approach. This technique could potentially search the
unexplored high-frequency range of 10--100 GHz (axion mass 40--400 $\mu$eV),
where traditional cavity resonators have difficulties reaching the required
volume.
