Using numerical simulations, we demonstrate the feasibility of tunable gradient refractive index optics at terahertz frequencies based on two-dimensional graded plasmonic crystals (GPCs). They consist of semiconductor rods with spatially dependent radii. In the effective medium approximation, the GPCs can be considered as effective media with a graded effective dielectric permittivity. The semiconductor rods have the Drude-type dispersion. By varying free charge carrier concentration in the rods, it is possible to tune their permittivity. In accordance to effective medium theory, the effective permittivity of the whole GPC is changed at the same time. This property is used for the demonstration of a GPC-based lens with a tunable focus, beam deflector with tunable angle of the beam deflection, and the half Maxwell-fisheye and the Luneburg lens as antennas with tunable radiation patterns. In particular, these GPCs can be made invisible to the incoming radiation by equaling the real part of the rods permittivity to the permittivity of air background.
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