  An integral equation formulation is presented for describing the scalar wave
propagation through a nano-hole on a plasmonic layer in terms of scalar Green's
function for the associated Helmholtz problem. Taking the radius of the
nano-hole to be the smallest length parameter of the system, we obtain an exact
closed-form analytic solution of the integral equation for the scalar Green's
function for scalar wave propagation through the nano-hole and the dispersion
relations for such a plasmonic layer.
