Phase-plane analysis of rational harmonic mode-locking in an erbium-doped fiber ring laser

We investigate the system performance of rational harmonic mode-locking in an erbium-doped fiber ring laser using the phase-plane technique of the nonlinear control engineering. Contributions from harmonic distortion, a Gaussian-like modulating signal, and its duty cycle to the system behavior are studied. We also demonstrate 660× and 1230× repetition rate multiplications on a 100-MHz pulse train generated from an active harmonically mode-locked fiber ring laser, and we hence achieve 66- and 123-GHz pulse operations by using the above-mentioned technique. It has been found out that the maximum obtainable rational harmonic order is limited by the harmonic distortion of the system as well as the pulse width of the generated signal, which in turn is determined by the duty cycle of the modulating signal. Furthermore, the rational harmonic order increases the complexity of the pulse formation process and hence challenges its stability.