Controlling Refraction Using Sub-Wavelength Resonators

We construct metamaterials from sub-wavelength nonmagnetic resonators and consider the refraction of incoming signals traveling from free space into the metamaterial. We show that the direction of the transmitted signal is a function of its center frequency and bandwidth. The directionality of the transmitted signal and its frequency dependence is shown to be explicitly controlled by sub-wavelength resonances that can be calculated from the geometry of the sub-wavelength scatters. We outline how to construct a medium with both positive and negative index properties across different frequency bands in the near infrared and optical regime