Modulational instability in a passive fiber cavity, revisited

Modulation instability in a passive fiber cavity is revisited. We address the problem in the statement with a continuous-time Ikeda map, rather than in the mean-field limit. It is found that plane wave solutions are unstable for both normal and anomalous dispersion regimes of an optical fiber. The origin of the instability in the continuous-time Ikeda map is in the mode mixing introduced by the beam splitter. The obtained conditions for the instability were compared with ones known for the discrete-time Ikeda map, showing appreciable difference, which, however reduces in the mean-field limit.