Modeling and experimental characterization of two-wave mixing in Yb-doped fiber amplifiers

Two-wave mixing between forward- and backward-propagating signal light has recently been observed in frequency-modulated single-frequency fiber laser systems. The phenomenon is a potential limiting factor for power scaling of such frequency-tunable lasers. In this contribution, we derive a perturbative coupled-mode theory for two signals that counter-propagate in an Yb-doped fiber with a constant frequency detuning. We apply the theory to analyze experimental results dedicated to extracting the central material parameter that relates the Yb inversion to a (real) refractive-index change. The perturbative theory is derived to all orders, and argued to be convergent. The experimental results and our analysis support previous estimates of the ratio between changes in the gain coefficient and the refractive index.