Unique Berry phase in one-dimensional topological photonic systems

A new concept, to the best of our knowledge, of the unique Berry phase (UBP) for identifying the topological nature of one-dimensional (1D) topological photonic systems is presented. The advantage of this concept compared to the typical Zak phase (TZP) is that the origin position can be chosen arbitrarily. Traditionally, there are always two inversion centers for a 1D binary photonic system with inversion symmetry. The TZP is quantized at either 0 or π if one of the inversion centers is selected as the origin. Its value depends on the choice of origin location of the unit cell. However, the dependence of the TZP on the choice of the inversion center leads to ambiguities in the distinguished topology. Moreover, when the origin position is not chosen to be in the center of inversion symmetry, the TZP cannot be quantized by integer multiples. A UBP is proposed to avoid this issue in advance. The quantitative value of the UBP is the same, regardless of which inversion center is selected as the origin. It can efficiently predict a topological phase change in a 1D photonic system called the unique Berry phase.