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.
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