  We theoretically investigate the terahertz dielectric response of a
semiconductor slab hosting an infrared photoinduced grating. The periodic
structure is due to the charge carries photo-excited by the interference of two
tilted infrared plane waves so that the grating depth and period can be tuned
by modifying the beam intensities and incidence angles, respectively. In the
case where the grating period is much smaller than the terahertz wavelength, we
numerically evaluate the ordinary and extraordinary component of the effective
permittivity tensor by resorting to electromagnetic full-wave simulation
coupled to the dynamics of charge carries excited by infrared radiation. We
show that the photoinduced metamaterial optical response can be tailored by
varying the grating and it ranges from birefringent to hyperbolic to
anisotropic negative dielectric without resorting to microfabrication.
