Analyzing bull's eye structures by a vertical mode expansion method with rotational symmetry

A bull's eye structure is a metallic film with a circular subwavelength aperture surrounded by concentric annular grooves. It is an important structure for realizing applications of the extraordinary optical transmission phenomenon. The structure is invariant under rotations about the central axis perpendicular to the film. In this paper, an efficient numerical method is developed for analyzing bull's eye and other structures that consist of different annular regions where the material properties are one-dimensional. The method is a new variant of the recently developed vertical mode expansion method which combines field expansions in one-dimensional eigenmodes with various techniques for solving scalar two-dimensional Helmholtz equations. The method exploits the rotational symmetry by solving the different Fourier components separately. For normal incident waves, the method is particularly efficient, since it is only necessary to solve one Fourier mode. The method is used to analyze bull's eye structures with different configurations. In particular, we found that the normalized transmission coefficient can be larger than 52 for a bull's eye structure with 22 grooves.