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Surface impedance is an important concept in classical wave systems such asphotonic crystals (PCs). For example, the condition of an interface stateformation in the interfacial region of two different one-dimensional PCs issimply Z_SL +Z_SR=0, where Z_SL (Z_SR)is the surface impedance of thesemi-infinite PC on the left- (right-) hand side of the interface. Here, wealso show a rigorous relation between the surface impedance of aone-dimensional PC and its bulk properties through the geometrical (Zak) phasesof the bulk bands, which can be used to determine the existence ornon-existence of interface states at the interface of the two PCs in aparticular band gap. Our results hold for any PCs with inversion symmetry,independent of the frequency of the gap and the symmetry point where the gaplies in the Brillouin Zone. Our results provide new insights on therelationship between surface scattering properties, the bulk band propertiesand the formation of interface states, which in turn can enable the design ofsystems with interface states in a rational manner.

Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems