LAUSR

Abstract The topology of different dimensions in photonic systems has attracted enormous interests, e.g. the Zak phase in one dimensional(1D) systems, the Chern number in two dimensional(2D) systems and the Weyl points or nodal lines in the systems of higher dimensions. It would be fantastic to find the relationship among the topology in different dimensions from one simple model and reveal the deep physical picture behind them. In this work, we propose a specially designed synthetic photonic crystal to investigate the topology in different dimensions. From this model, we find that the topology of 2D band gaps can be predicted by the parity of the edge states at the two symmetric points in our synthetic parameter space. An explicit expression of the connection between 1D Zak phase and 2D Chern number is given and the chiral edge state is confirmed by the winding number of the reflection phase in the topological nontrivial gap. Further more, two different types of topological phases in higher dimensions are found, which two bands are degenerated as Weyl points or nodal lines. Surprisingly, the existence of the Weyl points can be explained by the behavior of the singularities in our synthetic parameter space, which manifest as phase vortex points in the reflection phase spectra. The bulk edge correspondence in our synthetic system is investigated, based on which a topological protected perfect absorber is proposed. Our work paves a new way to construct topological nontrivial synthetic systems and manipulate the topology in different dimensions.