A new class of highly efficient Optical Parametric Amplifiers (OPA) is explored in this dissertation, which have the potential to reduce the power requirement on the pump and enable new functionalities. This originates from the simple notion that figure of merit (FoM) of an OPA is proportional to the product of the pump power and amplifier's length and nonlinearity. Silica fibers have been developed for over five decades and offer unparalleled transparency. By merely extending the fiber, i.e. the amplifier's length, a high FoM amplifier can be formed while keeping the pump at a moderate, sub-Watt power level. Unfortunately, optical fibers are inherently non-uniform. Their core size fluctuates along the fiber on a nanometer scale which is on the order of the fiber's molecular constituents. It is currently established that the performance of a fiber-based OPA (FOPA) is dictated by its stochastic nature. In fact, given a moderate pump power level, the highly efficient OPA will be required to maintain a strict phase matching condition across hundreds of meters. Facing this challenge, this dissertation focuses on a locally-controlled, high FoM FOPA. A high FoM FOPA operates in the deeply saturated regime in which a weak signal saturates the amplifier and depletes the pump power, effectively generating an inverse response of the pump output power to the signal input power. Given FOPAs' inhomogeneous nature, the performance limit of deeply saturated FOPAs is studied. So far, FOPAs have been commonly treated as a uniform entity; however, this study discovers unique features of the system which originate from and are strongly influenced by the fiber's inhomogeneous nature. One major example is the non- reciprocal response of deeply saturated FOPAs. It was found that deeply saturated FOPAs perform very highly, as the pump can respond to a rapidly varying (sub-THz) weak (sub-μW) signal. This is a novel method which obtained orders of magnitude improvement over current alternative technologies and relies on spectrally uninhibited construction in an open architecture. Successful ways to harness local dispersion are bound to benefit both science and engineering by enabling access to highly efficient FOPAs' full potential and creating viable technology