Model of Anti-Stokes Fluorescence Cooling in a Single-Mode Optical Fiber

We report a comprehensive model that quantifies analytically and numerically the heat that can be extracted by anti-Stokes fluorescence (ASF) from a fiber doped with a quasi-two-level laser ion. This model is used to investigate the effects on cooling of all relevant fiber and pump parameters, as well as amplified spontaneous emission. Simulations of a typical Yb-doped ZBLANP single-mode fiber show that for short enough fibers the heat extraction is relatively uniform along the fiber length. There is an optimum pump wavelength and power that maximizes the heat extracted per unit length. At this power, the coolest point is at the fiber input end. At higher powers, the coolest spot moves further down the fiber. The total heat extracted from a fiber, important for payload cooling, depends on the fiber absorptive loss, the pump wavelength, and the pump power. Simple expressions are derived to predict the optimum dopant concentration that maximizes heat extraction and the maximum tolerable absorptive fiber loss above which cooling is unobtainable. In a fiber with negligible residual absorption, the cooling efficiency is predicted to be 3.7%. In the modeled fiber, it is reduced to 1.7% in part by concentration quenching, but mainly due to the fiber absorptive loss (~15 dB/km). Since the total extracted heat increases linearly with core radius and dopant concentration (up to a limit determined by concentration quenching), highly doped multimode fibers are strong candidates for payload cooling. This model can be straightforwardly expanded to design and optimize fiber lasers and amplifiers that utilize ASF for cooling.