Interface states of simple rectangular photonic crystals with dislocated and non-dislocated photonic bandgaps

In this paper, the interface with two 2D photonic crystals (PCs) is constructed with different rectangular lattices but the same material, shape and size of dielectric rods and interface states are realized. The existence of interface states is analyzed with Zak phase and surface impedance. When the length-width ratio of rectangular lattices is changed, the retainabilities of the interface states with dislocated and non-dislocated photonic bandgaps (PBGs) are studied by the relationship between length-width ratio of rectangular lattice and Zak phase. It is found that, when the interface states are realized by changing the length-width ratio of rectangular lattices, the retainability of the interface states with dislocated PBGs is mainly influenced by the positions of PBGs, while the retainability of the interface states with non-dislocated PBGs is mainly influenced by Zak phases of the bands. At the selected ky in this paper, the retainability of the interface states with dislocated PBGs is better than that with non-dislocated PBGs, and it is adjustable. Further study shows that these conclusions are universal applicable to rectangular PCs with different materials, shapes and sizes of dielectric rods. These results provide a new way to realize interface states with only one kind of dielectric rod easily and construct optical waveguide with strong retainability.