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

We propose a generalization of the Fourier modal method aimed at calculating localized eigenmodes of integrated optical resonators. The method is based on constructing an analytical 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 used the proposed method to calculate modes of a rectangular dielectric block located on a metal surface. We show that the excitation of these modes by the surface lasmon-polariton (SPP) results in resonant features in the SPP transmission spectrum. In a magnetized structure, the mode excitation results in resonant magneto-optical effects. The proposed method can be used to design and investigate optical properties of integrated and plasmonic optical devices.