Recently developed explicit analytic closed-form scalar and dyadic Green's functions, resulting from the solution of the integral equations describing scalar and electromagnetic (E.M.) wave propagation through a thin plasmonic layer, are applied here to the examination of scalar and electromagnetic wave transmission through a nano-hole in the plasmonic layer. Taking the radius of the nano-hole to be the smallest length scale of the system, exact solutions for the transmitted and reflected fields in the presence of the nano-hole are determined analytically and in closed form for both the scalar and vector (E.M.) cases. In the case of the electromagnetic wave propagation, a numerical integration technique has been used to obtain numerical solutions for the dyadic Green's function in the presence of the nano-hole, enabling the analysis of electromagnetic wave transmission through the nano-hole.
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