  In the presence of a background magnetic field, axion dark matter induces an
electric field and can thus excite phonon-polaritons in suitable materials. We
revisit the calculation of the axion-photon conversion power output from such
materials, accounting for finite volume effects, and material losses. Our
calculation shows how phonon-polaritons can be converted to propagating photons
at the material boundary, offering a route to detecting the signal. Using the
dielectric functions of GaAs, Al$_2$O$_3$, and SiO$_2$, a fit to our loss model
leads to a signal of lower magnitude than previous calculations. We demonstrate
how knowledge of resonances in the dielectric function can directly be used to
calculate the sensitivity of any material to axion dark matter. We argue that a
combination of low losses encountered at $\mathcal{O}(1)$ K temperatures and
near future improvements in detector dark count allow one to probe the QCD
axion in the mass range $m_a\approx 100$ meV. This provides further impetus to
examine novel materials and further develop detectors in the THz regime. We
also discuss possible tuning methods to scan the axion mass.
