On the Surface Plasmonic Waves Excited by a Dipole Above Anisotropic and Spatially Dispersive Two-Dimensional Surfaces of Infinite Extent in Planarly Layered Media

The surface plasmonic waves (SPWs) excited by a vertical- or horizontal-oriented Hertzian dipole above anisotropic and spatially dispersive 2-D surfaces of infinite extent embedded in planarly layered uniaxial media are investigated using the dyadic Green function approach. The spectral-domain transmission line analogy Green function formulation and isofrequency-contour equations are derived. The methods to accurately and efficiently evaluate the 2-D Fourier integral arising from the spatial-domain Green function computation are also developed. To resolve the numerical inefficiency due to the highly oscillatory integrand and singularities of SPWs that possess large wavenumber, the methods of extrapolating the real-axis integration combined with singularity subtraction are proposed and found to be applicable to a wide range of observation distances. As an application example of the proposed formulation, we compute the scattered fields of a vertical dipole above the graphene biased by drift current, which exhibits significant spatial dispersion. It is shown that the light–matter interaction of graphene plasmons can be significantly reinforced when placed above uniaxially anisotropic epsilon-near-zero substrates. The proposed formulation may provide the methodology for the computational analysis of 2-D materials and SPWs.