Fiber optical parametric amplifiers (OPAs) and Raman amplifiers (RAs) are both based on the third-order nonlinear susceptibility of glass fibers. Recently, there have been some efforts to combine these two nonlinear phenomena in order to extend the amplification and wavelength conversion windows to the S-band, or to lower the required parametric pump power in order to achieve the same signal gain. We propose a new technique utilizing these two amplication principles in a single piece of highly-nonlinear dispersion-shifted fiber (HNL-DSF). We call this Raman-mediated fiber OPA (RM-OPA),
which is different from the previous Raman-assisted OPA (RA-OPA) work. The previously investigated RA-OPA required an extra Raman pump with power around 1 W, on top of the erbium-doped fiber amplifier (EDFA) required to amplify the OPA pump. Therefore, Raman amplification was simply employed as a power booster for the OPA pump, i.e. RA "assists" OPA. On the other hand, our new approach does not require an extra EDFA as pre-amplifier, and the single piece of HNL-DSF provides both RA and OPA effects. In other words, there is essentially no parametric amplification without the presence of the Raman pump. While combining RA and OPA have been investigated both analytically and experimentally before, it involved only introducing some extra Raman terms in the nonlinear Schrödinger equations (NLSE) additively, which is sufficient for the case when one pump is used to amplify the signal (and idler) through both RA and OPA. However, the situation is significantly different here, where the parametric pump is amplified by the RA, while the OPA gain varies along the gain medium as the parametric pump power itself is a function of the distance along the HNL-DSF. In this paper, we will present an approximate analytical model for this RM-OPA, in a co-propagating configuration. Through certain simplifying assumptions, we produce closed-form equations allowing intuitive insights into the RM-OPA operation, given the coupling amongst the parametric pump, Raman pump, signal and idler. These equations provide a framework for optimizing such kind of fiber amplifiers. Important RM-OPA design guidelines are also discussed.