  This work is focussed on the role of the angle of incidence of an incoming
electromagnetic wave in its transmission through a subwavelength nano-hole in a
thin semiconductor plasmonic layer. Fully detailed calculations and results are
exhibited for $ p$- and $s$-polarizations of the incident wave for a variety of
incident angles in the near, middle and far zones of the transmitted radiation.
Our dyadic Green's function formulation includes both (1) the electromagnetic
field transmitted directly through the $ 2D $ plasmonic layer superposed with
(2) the radiation emanating from the nano-hole. Interference fringes due to
this superposition are explicitly exhibited. Based on an integral equation
formulation, this dyadic Green's function approach does not involve any appeal
to metallic boundary conditions. It does incorporate the role of the $ 2D $
plasmon of the semiconductor layer, which is smeared due to its lateral wave
number dependence. We find that the interference fringes, which are clustered
near the nano-hole, flatten to a uniform level of transmission directly through
the sheet alone at large distances from the nano-hole. Furthermore, as the
incident angle increases, the axis of the relatively large central transmission
maximum through the nano-hole follows it, accompanied by a spatial compression
of interference fringe maxima forward of the large central transmission
maximum, and a spatial thinning of the fringe maxima behind it.
