  We employ both the effective medium approximation (EMA) and Bloch theory to
compare the dispersion properties of semiconductor hyperbolic metamaterials
(SHMs) at mid-infrared frequencies and metallic hyperbolic metamaterials (MHMs)
at visible frequencies. This analysis reveals the conditions under which the
EMA can be safely applied for both MHMs and SHMs. We find that the combination
of precise nanoscale layering and the longer infrared operating wavelengths
puts the SHMs well within the effective medium limit and, in contrast to MHMs,
allows the attainment of very high photon momentum states. In addition, SHMs
allow for new phenomena such as ultrafast creation of the hyperbolic manifold
through optical pumping. In particular, we examine the possibility of achieving
ultrafast topological transitions through optical pumping which can photo-dope
appropriately designed quantum wells on the femtosecond time scale.
