Finite-Element Simulation of Optical Phenomena on 2D Materials
In the terahertz frequency range, the effective (complex-valued) surface conductivity of atomically thick 2D materials such as graphene has a positive imaginary part that is considerably larger than the real part. This feature allows for the propagation of slowly decaying electromagnetic waves, called surface plasmon-polaritons (SPPs), that are confined near the material interface with wavelengths much shorter than the wavelength of the free-space radiation. SPPs are promising ingredients in the design of novel optical applications promising "subwavelength optics" beyond the diffraction limit. There is a compelling need for controllable numerical schemes which, placed on firm mathematical grounds, can reliably describe SPPs in a variety of geometries. In this talk we present an adaptive, higher-order finite element approach for the simulation of SPPs on 2D materials and layered structures. Aspects of the numerical treatment such as absorbing perfectly matched layers, local refinement and a-posteriori error control are discussed. We will present a number of applications of the framework to optical device simulations. Corresponding analytical results elucidate the solution structure. We conclude by introducing a homogenization theory of layered heterostructures to design novel devices.