Thermal modeling, heat mitigation, and radiative cooling for double-clad fiber amplifiers

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.