Basic prerequisites for limit-cycle oscillations within a synchronously pumped passive optical nonlinear fiber-ring resonator

By taking into account Kerr nonlinearity and negative second-order dispersion, we show by numerical investigations that in a passive optical nonlinear fiber ring resonator synchronously pumped with femtosecond pulses a temporal delay via a resonator length detuning or via third-order dispersion leads to limit cycle behavior, which is represented by an oscillatory evolution of the temporal as well as the spectral pulse shape. By introducing a two-dimensional iterative map, we show that limit cycles arise due to the mutual coupling of different spectral pulse components. The resulting system behavior can be used to introduce additional adjustable frequency components into frequency combs.