Wideband pulse propagation: a detailed calculation including Raman processes

I present a detailed derivation of wideband optical pulses interacting with a Raman transition in the kind of scheme currently used to generate the ultra broadband light fields needed to create ultrashort pulses. In contrast to the usual approach using separate field envelopes for the pump, Stokes, and anti-Stokes spectral lines, I use a single field envelope. This requires the inclusion of few-cycle corrections to the pulse propagation. The single-field model makes fewer approximations and is mathematically (and hence computationally) simpler, although it does require greater computational resources to implement. The single-field theory reduces to the traditional multi-field one using appropriate approximations