Extended Snell’s law based on surface current radiation

Abstract

The generalized laws of reflection and refraction have been proposed in many related reports, but they still have some imperfections. For example, the first principle lies in the Fermat principle, but the realization of surface phase gradient utilizes the scattering of superelements. The former belongs to geometric optics, and the latter is attributed to wave optics. Therefore, this paper avoids the Fermat principle and gives the generalized Snell’s law from a new perspective by controlling the conductivity or polarizability of materials. The findings indicate that the surface current can manipulate the reflected and refracted light. The key is to obtain the relationship between the different components of the spectrum and the wave vectors parallel to the surface of the reflected and refracted waves by using the Fourier transform of the polarizability. This model is applicable to the metamaterial at the nanoscale, making it possible to design flexible surface structures.