Fresnel Refraction and Diffraction of Surface Plasmon Polaritons in Two-Dimensional Conducting Sheets

The propagation of surface plasmon polaritons (SPPs) along two-dimensional (2D) materials, such as graphene, is a complex phenomenon linking the microscale electronic properties to macroscale optical properties. Complex geometries increase the complexity of understanding the nature and performance of optoelectronic devices based on surface wave propagation. Here, we demonstrate that under a proper design of macroscopic conductivity profile, the propagation characteristics of SPPs in 2D materials can be made analogous to the propagation of plane waves in homogeneous layers with minimal out-of-plane scattering. Such a direct resemblance enables prediction, design, and calculation of SPP propagation through advanced geometries using fundamental laws of optics. We demonstrate that the propagation of surface waves can be manipulated in-plane using reflection, refraction, diffraction, and also generalized refraction laws analogous to plane waves. We present simple mathematical models to calculate the scattered electromagnetic fields of SPP waves based on Fresnel equations. The presented formulation could facilitate the transfer of many existing plane wave based optical phenomenon to a surface wave based integrated optoelectronic devices.