  We develop a systematic theory for optimising single-photon frequency
conversion using optical Bragg scattering. The efficiency and phase-matching
conditions for the desired Bragg scattering conversion as well as spurious
scattering and modulation instability are identified. We find that third-order
dispersion can suppress unwanted processes, while dispersion above the fourth
order limits the maximum conversion efficiency. We apply the optimisation
conditions to frequency conversion in highly nonlinear fiber, silicon nitride
waveguides and silicon nanowires. Efficient conversion is confirmed using full
numerical simulations. These design rules will assist the development of
efficient quantum frequency conversion between multicolour single photon
sources for integration in complex quantum networks.
