On the use of the Fourier modal method for calculation of localized eigenmodes of integrated optical resonators

We propose the generalization of the Fourier modal method aimed at calculating localized eigenmodes of integrated optical resonators. The method is based on constructing the analytic continuation of the structure's scattering matrix and calculating its poles. The method allows one to calculate the complex frequency of the localized mode and the corresponding field distribution. We use the proposed method to calculate the eigenmodes of rectangular dielectric block located on metal surface. We show that excitation of these modes by surface plasmon-polariton (SPP) results in resonant features in the SPP transmission spectrum. The proposed method can be used to design and investigate optical properties of integrated and plasmonic optical devices.