  Interface states in photonic crystals (PCs) have attracted attention for the
special properties, such as high transmission efficiency in bend waveguides,
and their generation related to the topological phase. Previous works on
interface states in PCs were mainly based on the square lattice, the honeycomb
lattice or the triangular lattice, but with different materials, shapes, or
sizes of rods resulting in the complicated structure. In this paper, an
interface is constructed by two 2D PCs with different rectangular lattices, but
the same materials, shapes, and sizes of dielectric rods, which generates
interface states. The interface states are analyzed with respect to Zak phases
and surface impedances. The retainability of the interface states in
rectangular lattice PCs is investigated by studying the relationship between
the length-width ratio of the rectangular lattice and the Zak phase. It is
found that, when the interface states are generated by changing the
length-width ratio of the rectangular lattice, the retainability of the
interface states is related to the positions of the photonic bandgaps or the
Zak phases of the bands. A more detailed examination indicates that these
conclusions are applicable to the rectangular lattice PCs with other materials,
shapes, and sizes of dielectric rods. These results can lead to new ways to
generate interface states easily, with only one kind of dielectric rod. In
addition, these outcomes may contribute to the understanding of the
relationship between the geometry and the interface state.
