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 excited by a vertical or horizontal oriented Hertzian dipole above anisotropic and spatially dispersive two-dimensional surfaces of infinite extent embedded in planarly layered uniaxial media is investigated using the dyadic Green function approach. The spectral-domain transmission line analogy Green function formulation and iso-frequency contours equations are derived. The methods to accurately and efficently evaluate the two-dimensional Fourier integral arisen from the spatial-domain Green function computation are also developed. To resolve the numerical inefficiency due to the highly oscillatory integrand and singularities of surface plasmonic waves possessing large wavenumber, two numerical strategies, the extrapolation of the real-axis integration combined with singularity subtraction, and the deformed vertical integration path, are proposed and applicable to a wide range of observation distance. As a demonstration 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 and show that its light-matter interaction can be significantly reinforced when placed above uniaxially epsilon-near-zero substrates. The proposed formulation may provide methodology for the computational analysis of two-dimensional materials and surface plasmonic waves.