A strict framework for analyzing linear and nonlinear propagation in photonic and terahertz graphene waveguides

Two-dimensional (sheet) materials, with graphene being a prominent example, are recently finding their way in a variety of photonic and terahertz waveguide applications. We provide a framework for the rigorous study of three-dimensional guided-wave devices that comprise both bulk and sheet materials. Our formulation, relying on the finite element method, allows for arbitrary anisotropy in the susceptibility and surface conductivity tensors describing bulk and sheet material properties, respectively. A number of emerging graphene-comprising waveguide platforms are critically assessed, targeting both linear and in particular nonlinear (third-order) applications in the near- and far-infrared spectral region.