  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.

Computational Physics;Optics