Effects of Raman scattering and attenuation in silica fiber-based parametric frequency conversion

Four-wave mixing in the form of Bragg scattering (BS) has been predicted to enable quantum noise-less frequency conversion by analytic quantum approaches. Using a semi-classical description of quantum noise that accounts for loss and stimulated and spontaneous Raman scattering, which are not currently described in existing quantum approaches, we quantify the impacts of these effects on the conversion efficiency and on the quantum noise properties of BS in terms of an induced noise figure (NF). We give an approximate closed-form expression for the BS conversion efficiency that includes loss and stimulated Raman scattering, and we derive explicit expressions for the Raman-induced NF from the semi-classical approach used here. We find that Raman scattering induces a NF in the BS process that is comparable to the 3-dB NF associated with linear amplifiers.