  We report a detailed formalism aimed at the thermal modeling and heat
mitigation in high-power double-clad fiber amplifiers. Closed form analytical
formulas are developed that take into account the spatial profile of the
amplified signal and pump in the double-clad geometry, the presence of the
amplified spontaneous emission, and the possibility of radiative cooling due to
anti-Stokes fluorescence emission. The formalism is applied to a high-power
Yb-doped silica fiber amplifier. The contributions to the heat-load from the
pump-signal quantum defect, as well as the pump and signal parasitic
absorptions are compared to the radiative cooling. It is shown that for
realistic cases, the local heat generation in kiloWatt-class fiber amplifiers
is either dominated by the quantum defect or the parasitic absorption depending
on the pump wavelength. In conventional designs, radiative cooling can be
substantial only in properly designed amplifiers, when the pump power is tens
of watts or lower, unless the parasitic absorption is reduced compared to the
commonly reported values in the literature. We also explore the impact of the
non-ideal quantum efficiency of the gain material. The developed formalism can
be used to design fiber amplifiers and lasers for optimal heat mitigation,
especially due to radiative cooling.
