“Möbius” microring resonator

A new category of optical microring resonator, which is analogous to the M\"obius strip, is proposed. The "M\"obius" microring resonator allows the conversion between modes with different polarizations in the ring and light must circulate two cycles to be converted back to the original polarization status, which is similar to a M\"obius strip. This topology structure of polarization leads to the free spectral range be half of that corresponds to the cavity round trip. The eigenmodes of this microring are hybridizations of different polarizations and the breaking of the rotation invariance of the ring makes the transmission be related with the polarization of input light. Our work opens the door towards the photonic devices with nontrivial mode topology and provides a novel way to engineering photonic structures for fundamental studies.