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We present a numerical study on the coherent sideband generation from an incoherently pumped fiber optical parametric oscillator (FOPO). We revisit the fiber dispersion condition in a parametric process that fulfills the convection-induced phase-locking mechanism when pumping incoherently. Particularly, there exist analytical solutions for phase-matching frequencies in a convection-induced phase-locking process when using a parametric gain fiber with two zero dispersion wavelengths. With the optical feedback, we manage to circulate and amplify the convection sideband in a singly resonant FOPO. The autocorrelation shows that the coherence of the oscillating convection sideband can be strongly influenced by the cavity feedback fraction.

The recent development of fiber mode-locked lasers with fiber parametric gain has opened up an intriguing field of ultrafast pulse generation. Thanks to the tunability of the parametric gain in optical fibers, the gain media of mode-locked lasers are no longer limited to the choice of rare-earth-doped fibers. In our previous study, optical time-stretch was introduced into the cavity of a fiber optical parametric oscillator as a temporal diffracting distance to overcome localization of the parametric gain. The implementation of the diffracting distance for pulse stretching and compression relied on two dispersive elements with opposite sign dispersion. In this context, we propose a new design of passively mode-locked fiber optical parametric oscillators with only a single mono-dispersive element. We utilize the parametric process as a time lens at which the spectral components of the two oscillating parametric sidebands are phase-conjugated in the temporal domain. This allows both mode-locked sidebands to oscillate and switch periodically inside the fiber cavity with only a single dispersive element. We numerically simulate the pulse generation of this switching mode-locked fiber parametric oscillator.