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A semi-analytical formalism for the optical properties of a metal-insulator-metal periodic nanostructure using coupled-mode theory is presented. This structure consists in a dielectric layer in between two metallic layers with periodic one-dimensional nanoslit corrugation. The model is developed using multiple-scattering formalism, which defines transmission and reflection coefficients for each of the interface as a semi-infinite medium. Total transmission is then calculated using a summation of the multiple paths of light inside the structure. This method allows finding an exact solution for the transmission problem in every dimension regime, as long as a sufficient number of diffraction orders and guided modes are considered for the structure. The resonant modes of the structure are found to be related to the metallic slab only and to a combination of both the metallic slab and dielectric layer. This model also allows describing the resonant behavior of the system in the limit of a small dielectric layer, for which discontinuities in the dispersion curves are found. These discontinuities result from the out-of-phase interference of the different diffraction orders of the system, which account for field interaction for both inner interfaces of the structure.

Optical transmission theory for metal-insulator-metal periodic nanostructures