  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.

Optics