Facilitated by the advent of photonic crystal fibers two decades ago, the moded-locked fiber lasers become the new trend of ultrafast light sources. Nevertheless, their major limitations are the output wavelength range and pulse quality. Motivated by building widely tunable ultrashort light sources, this thesis focuses on the experimental and theoretical studies of fiber optical parametric process. As one important application of this process, fiber optical parametric oscillator (FOPO), promises to address the shortcomings of fiber lasers.

From the application point of view, it is important to manage and optimize the output performance of light sources such as the pulse duration, pulse shape, spectrum width and so on. So there is a need to clearly understand the pulse evolution from a platform of applied mathematics. Under this theoretical guidance, experimental work can be better oriented to develop functional light sources which address needs for applications such as pulsed-light microscopy, multiphoton spectroscopy and so on.

We demonstrate FOPO as tunable light sources in both femtosecond and picosecond domains. For the femtosecond operation, we generate sub-50f s pulses with linear chirp. The studies on the pulse quality are carried out where the fiber length inside the oscillator is varied. In particular, our studies focus on dispersive pulse broadening and walk-off effects which influence the performance of FOPO. The optimal condition, i.e., the shortest pulse duration, arises from the minimization of these two effects. For the picosecond operation, we generate pulses with the duration of 2 ∼ 4ps. The experiment also reveals that the spectral shape and width of output pulses are determined by cross-phase modulation and cavity synchronization. More precisely, the spectrum exhibits pump power dependent broadening which can be asymmetric with a red or blue shift depending on cavity synchronization. Moreover, the average power conversion efficiency is maximized by adjusting the cavity length to the long range of its operation which leads to a blue shifted spectrum.

To capture the operational principles and precisely emulate the performance of FOPO, we also focus on the theoretical analysis of fiber optical parametric processes. We extend the previous theory of partially degenerate four-wave mixing to the ultrafast situation where waves are all ultrashort pulses with broadband spectra. Then we perform the simulation based on justified parameters and compare our calculation results with experimental data. We find both experimentally and numerically that there exhibits an interesting symmetry behavior in the frequency domain - two widely separated spectral sidebands can always behave as mirror images of one another with respect to the center frequency of the controlling pump pulse. We call this interesting physical phenomenon "Spectral Mirror Imaging". Not just limited to the numerical computation, under certain operation regime we obtain an analytic solution and clarify the physical mechanisms of this phenomenon. A simple analytical expression for the coupled governing equations of two sideband spectra is obtained, which reveals that the opposite values of group-velocity dispersion and the complex-conjugated parametric gain are the physical mechanisms responsible for this phenomenon. Furthermore, we give a comparison between spectral reversal and time reversal.