  We present a quantum-mechanical model that describes fiber-based frequency
conversion by four-wave-mixing Bragg scattering in the presence of Raman
interactions. In the case of continuous-wave pumps we find closed-form
expressions for the conversion efficiency and photon statistics, characterized
by the second-order correlation function. For pulsed pumps, we derive a highly
general model based on Green functions, and provide a numerical solution method
using a split-step scheme. In both cases, we find that noise from spontaneous
Raman scattering can pose a serious challenge to this type of frequency
conversion if the pumps are less than 30 THz from the quantum fields. However,
this impact can be mitigated with crosspolarized pumps and on the anti-Stokes
side, through cooling of the fiber.
