  We propose a three dimensional Discontinuous Petrov-Galerkin Maxwell approach
for modeling Raman gain in fiber laser amplifiers. In contrast with popular
beam propagation models, we are interested in a truly full vectorial approach.
We apply the ultraweak DPG formulation, which is known to carry desirable
properties for high-frequency wave propagation problems, to the coupled Maxwell
signal/pump system and use a nonlinear iterative scheme to account for the
Raman gain. This paper also introduces a novel and practical full-vectorial
formulation of the electric polarization term for Raman gain that emphasizes
the fact that the computer modeler is only given a measured bulk Raman gain
coefficient. Our results provide promising qualitative corroboration of the
model and methodology used.
