Stationary states and instabilities of a Möbius fiber resonator

We examine the steady state and dynamic behavior of an optical resonator comprised of two interlinked fiber loops sharing a common pump. A coupled Ikeda map models with great accuracy the field evolution within and exchange between both fibers over a single round trip. We find this supports a range of rich multidimensional bistability in the continuous wave regime, as well as previously unseen cavity soliton states. Floquet analysis reveals that modulation and parametric instabilities occur over wider domains than in single-fiber resonators, which can be tailored by controlling the relative dispersion and resonance frequencies of the two fiber loops. Parametric instability gives birth to a train of pulses with a peculiar period-doubling behavior.