Polarization and longitudinal modes of Möbius fiber ring lasers

Möbius optical cavity has attracted great interest for unique topological property. Here, polarization and longitudinal modes of two types of Möbius fiber ring lasers are investigated. A theoretical model is established with Jones matrix to solve the polarization eigenmodes and longitudinal modes of a twisted polarization-maintaining-fiber ring cavity. It is found that the twisting of the fiber axis causes polarization hybridization and a geometry-dependent phase, which induces a frequency shift to the longitudinal modes. The Möbius cases (180° and 90° splicing) are analyzed in detail, in which the 90° case leads to peculiar polarization and longitudinal mode properties. We believe the presented fiber ring laser provides a convenient platform to study lasers with a Möbius structure, also opens a new venue for fiber laser and its applications.