Topological resonances in a Möbius ring resonator

A Möbius strip, fascinating for its unique topological property of being a one-side nonorientable surface, has inspired mathematicians, physicists, engineers, and artists for many centuries. In a coherent system, coherent waves on the nonorientable surfaces reveal rich topological dynamics due to the interplay of coherence and topology. Here we experimentally observe topological resonances in a Möbius ring resonator formed in a twisted optical fiber loop. The twisted polarization-maintaining fiber ring encourages the hybridization of two polarization states, giving rise to the crucial Berry phase. This geometrical phase leads to the frequency shifts of fiber resonant modes with a non-trivial fractional mode number. Moreover, the resonant modes are topological, only resonating with certain polarized modes with circular chirality. These topological features introduce geometrical factors into coherent wave resonances, paving the way for topological information processing for quantum information, and coherent wave dynamics.