Localized defect modes in finite magnetic two-dimensional photonic crystals

We present a detailed study of localized defect modes in finite two-dimensional magnetic photonic crystal consisting of cylindrical ferrite material in air background by using the scattering matrix method. It is shown that due to having positive and negative value of the effective magnetic permeability in interested photonic band gap, the defect modes present different behavior. Our results show that the modes appeared in positive permeability region have features similar to the modes supported by the dielectric photonic crystal while those created in the negative permeability region are strongly localized at the interface of defect ferrite rod with air background. Moreover, results indicate that defect modes occurred in the negative region are sharper than those appeared in the positive one which means the quality factor of former case is extremely high.