  We theoretically consider infrared-driven hyperbolic metamaterials able to
spatially filtering terahertz radiation. The metamaterial is a slab made of
alternating semiconductor and dielectric layers whose homogenized uniaxial
response, at terahertz frequencies, shows principal permittivities of different
signs. The gap provided by metamaterial hyperbolic dispersion allows the slab
to stop spatial frequencies within a bandwidth tunable by changing the infrared
radiation intensity. We numerically prove the device functionality by resorting
to full wave simulation coupled to the dynamics of charge carries photoexcited
by infrared radiation in semiconductor layers.
