We perform a comprehensive study on the implementation of active harmonic and rational harmonic mode-locking of a fiber optical parametric oscillator (FOPO). In particular, the effect of pump parameters and cavity designs on the characteristics of the generated pulses are analyzed. Two methods of frequency μltiplication in FOPOs are discussed and compared and we show that we can generate optical pulses with very high-repetition-rate (up to 240 GHz) using rational harmonic mode-locking. We find that optical pulses with short duration can be obtained using pump pulses with small duty cycle, large pump power, and an intra-cavity optical filter with proper bandwidth. In addition, optical pulses with low root-mean-square timing jitter are achievable when no pump phase modulation is applied and hybrid gain of erbium-doped fiber amplifier and parametric amplifier is used. High supermode noise suppression ratio is achieved by taking advantage of the fast parametric gain and the combined effect of self-phase modulation and spectral filtering. We conclude that synchronous-pumping of an actively mode-locked FOPO offers many advantages in terms of reducing the cavity loss, increasing the modulation frequency, enabling rational harmonic mode-locking, and applications to all-optical clock recovery.
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