Rational harmonic mode-locking pulse quality of the dark-optical-comb injected semiconductor optical amplifier fiber ring laser

We study the rational harmonic mode-locking (RHML) order dependent pulse shortening force and dynamic chirp characteristics of a gain-saturated semiconductor optical amplifier fiber laser (SOAFL) under dark-optical-comb injection, and discuss the competition between mode-locking mechanisms in the SOAFL at high-gain and strong optical injection condition at higher RHML orders. The evolutions of spectra, mode-locking and continuous lasing powers by measuring the ratio of DC/pulse amplitude and the pulse shortening force (I(pulse)/P(avg)(2) ) are performed to determine the RHML capability of SOAFL. As the rational harmonic order increases up to 20, the spectral linewidth shrinks from 12 to 3 nm, the ratio of DC/pulse amplitude enlarges from 0.025 to 2.4, and the pulse-shortening force reduces from 0.9 to 0.05. At fundamental and highest RHML condition, we characterize the frequency detuning range to realize the mode-locking quality, and measure the dynamic frequency chirp of the RHML-SOAFL to distinguish the linear and nonlinear chirp after dispersion compensation. With increasing RHML order, the pulsewidth is broadened from 4.2 to 26.4 ps with corresponding chirp reducing from 0.7 to 0.2 GHz and linear/nonlinear chirp ratio changes from 4.3 to 1.3, which interprets the high-order chirp becomes dominates at higher RHML orders.