Detailed study of the flat bands appeared in two-dimensional magnetic photonic crystals with square symmetry

By virtue of the efficiency of the Dirichlet-to-Neumann map method, the details of the band structure of a two-dimensional magnetic photonic crystal having a square array of parallel circular ferrite rods in air background influenced by an external static magnetic field applied in the rod direction has been investigated. We show that there are two sets of flat bands at the band structure of the system for TM-polarization. These flat bands are created around the magnetic surface plasmon frequency and frequency in which the magnetic permeability has singular value. For the frequency around the magnetic surface plasmon, the modes are highly localized at the interface of the cylindrical ferrite rods and air background and also by approaching the modes to the magnetic surface plasmon frequency the localization length decreases and the number of field's nodes increases considerably. Moreover, we realized that the modes with frequencies lying immediately below the singular value act similar to as resonance cavity modes created in a single metallic cylindrical waveguide.