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An integral equation is formulated to describe electromagnetic wavetransmission through a sub-wavelength nano-hole in a thin plasmonic sheet interms of the dyadic Green's function for the associated Helmholtz problem.Taking the subwavelength radius of the nano-hole to be the smallest length ofthe system, we have obtained an exact solution of the integral equation for thedyadic Green's function analytically and in closed form. This dyadic Green'sfunction is then employed in the numerical analysis of electromagnetic wavetransmission through the nano-hole for normal incidence of the incoming wavetrain. The electromagnetic transmission involves two distinct contributions,one emanating from the nano-hole and the other is directly transmitted throughthe thin plasmonic layer itself (which would not occur in the case of a perfectmetal screen). The transmitted radiation exhibits interference fringes in thevicinity of the nano-hole, and they tend to flatten as a function of increasinglateral separation from the hole, reaching the uniform value of transmissionthrough the sheet alone at large separations.

Electromagnetic Wave Transmission Through a Subwavelength Nano-hole in a Two-dimensional Plasmonic Layer