The vortex lattice method in the spectral problem of a rectangular waveguide with a lamellar grating

Interest in research and use of slowing-down electromagnetic systems in waveguides with rectangular grooves has recently been revived. In the present work, a rigorous solution to the spectral problem of an infinite rectangular waveguide for the longitudinal electrical waves with periodic slowing-down systems, with any number of arbitrary size resonators in the period, is considered. This work is a generalization of previous results, where we considered a lamellar grating with one resonator in the period by using the discrete singularities (currents) method, also known as the vortex lattice method.