  The polarization-sensitive propagation in the anisotropic metamaterial (AMM)
with double-sheeted hyperboloid dispersion relation is investigated from a
purely wave propagation point of view. We show that TE and TM polarized waves
present significantly different characteristics which depend on the
polarization. The omnidirectional total reflection and oblique total
transmission can occur in the interface associated with the AMM. If appropriate
conditions are satisfied, one polarized wave exhibits the total refraction,
while the other presents the total reflection. We find that the opposite
amphoteric refractions can be realized by rotating the principle axis of AMM,
such that one polarized wave performs the negative refraction, while the other
undergoes positive refraction. The polarization-sensitive characteristics allow
us to construct two types of efficient polarizing beam splitters under certain
achievable conditions.
