Topological properties of coupled resonator array based on accurate band structure

The topological edge states of the coupled-resonator optical waveguide (CROW) system have been widely researched. Without breaking time-reversal symmetry nor needing to construct complicated optical modes as pseudospins, the CROW system offers characteristics that are effective for exploration of photonic topological effects and has potential for applications in nanodevices. We extend the previous method by using specific coupling conditions to calculate the system's actual band structure, thereby providing a new perspective of this system. Two types of topological properties, one with and the other without an artificial magnetic field, are identified based on the band diagrams. Fractal spectra including the Hofstadter butterfly spectrum are obtained, revealing the abundant physics associated with the CROW system. By connecting the band diagrams with the corresponding structural parameters, we propose a triangular lattice array with reduced losses at the corners and propose a scheme with the potential for use as a reconfigurable multipath platform.