title: Quantum frequency translation by four-wave mixing in a fiber:                     low-conversion regime.
abstract: In this paper we consider frequency translation enabled by Bragg scattering, a                     four-wave mixing process. First we introduce the theoretical background of the                     Green function formalism and the Schmidt decomposition. Next the Green functions                     for the low-conversion regime are derived perturbatively in the frequency                     domain, using the methods developed for three-wave mixing, then transformed to                     the time domain. These results are also derived and verified using an                     alternative time-domain method, the results of which are more general. For the                     first time we include the effects of convecting pumps, a more realistic                     assumption, and show that separability and arbitrary reshaping is possible. This                     is confirmed numerically for Gaussian pumps as well as higher-order                     Hermite-Gaussian pumps.
authors.affiliation: Department of Photonics Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark. lman@fotonik.dtu.dk
authors.forename: L
authors.initials: L
authors.lastname: Mejling
authors.forename: C J
authors.initials: CJ
authors.lastname: McKinstrie
authors.forename: M G
authors.initials: MG
authors.lastname: Raymer
authors.forename: K
authors.initials: K
authors.lastname: Rottwitt