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Graphene is a sheet of carbon,just one atom thick.They possess the strongest mechanical strength and can achieve the highest carrier mobility,several times higher than that of the best semiconductor structures.It is a promising new material for the next generation of electronic devices and for many non-electronics applications.Understanding the optical properties of graphene and graphene nanostructures is of importance in the development of graphene-based optoelectronic devices.We have carried out a theoretical and computation study of optical response of graphene over a wide frequency range,from terahertz to ultraviolet.It is found that the optical response is highly anisotropic at high frequencies.This property can be useful for developing polarization devices.