Period-4 modulation instability in ring fiber cavities

We predict the existence of a period-4 temporal dynamics in the nonlinear stage of modulation instability of light inside a passive ring fiber Kerr cavity. We investigate analytically and numerically the stability of period-doubled continuous-wave solutions of the Ikeda map describing waves oscillating between two well-defined power levels at consecutive round trips. We prove that conditions exist for which spectral sidebands can be amplified leading to the formation of a temporal modulation pattern which repeats itself identically every four cavity round trips. We show that this dynamics exists for realistic parameters of a driven fiber cavity, which makes it potentially accessible to experimental observation.