Vertical mode expansion method for transmission of light through a single circular hole in a slab.

An efficient method is developed for rigorously analyzing the scattering of light by a layered circular cylindrical object in a layered background, and it is applied to the study of the transmission of light through a subwavelength hole in a metallic film, where the hole may be filled by a dielectric material. The method relies on expanding the electromagnetic field (subtracted by one-dimensional solutions of the layered media) in one-dimensional modes, where the expansion "coefficients" are functions satisfying two-dimensional Helmholtz equations. A system of equations is established on the boundary of the circular cylinder to solve the expansion "coefficients." The method effectively reduces the original three-dimensional scattering problem to a two-dimensional problem on the boundary of the cylinder.