  We present both modeling and computational advancements to a unique
three-dimensional discontinuous Petrov-Galerkin finite element model for the
simulation of laser amplification in a fiber amplifier. Our model is based on
the time-harmonic Maxwell equations, and it incorporates both amplification via
an active dopant and thermal effects via coupling with the heat equation. As a
full vectorial finite element simulation, this model distinguishes itself from
other fiber amplifier models that are typically posed as an initial value
problem and make significantly more approximations. Our model supports co-,
counter-, and bi-directional pumping configurations, as well as inhomogeneous
and anisotropic material properties. The longer-term goal of this modeling
effort is to study nonlinear phenomena that prohibit achieving unprecedented
power levels in fiber amplifiers, along with validating typical approximations
used in lower-fidelity models. The high-fidelity simulation comes at the cost
of a high-order finite element discretization with many degrees of freedom per
wavelength. This is necessary to counter the effect of numerical pollution due
to the high-frequency nature of the wave simulation. To make the computation
more feasible, we have developed a novel longitudinal model rescaling, using
artificial material parameters with the goal of preserving certain quantities
of interest. Our numerical tests demonstrate the applicability and utility of
this scaled model in the simulation of an ytterbium-doped, step-index fiber
amplifier that experiences laser amplification and heating. We present
numerical results for the nonlinear coupled Maxwell/heat model with up to 240
wavelengths.
