Gain dynamics in Er$^3$+:Yb$^3$+ co-doped fiber amplifiers

Understanding the gain dynamics of fiber amplifiers is essential for the implementation and active stabilization of low noise amplifiers or for coherent beam combining schemes. The gain dynamics of purely Er3+ or Yb3+ doped fiber amplifiers are well studied, whereas no analysis for co-doped systems, especially for Er3+:Yb3+ co-doped fiber amplifiers has been performed, so far. Here, we analyze for the first time the gain dynamics of Er3+:Yb3+ co-doped fiber amplifiers theoretically and experimentally. It is shown that due to the energy transfer between the Yb3+ and Er3+ ions a full analytical solution is not possible. Thus, we used numerical simulations to gain further insights. Comparison of experimental and numerical results shows good qualitative agreement. In addition, we were able to determine the Yb3+-Er3+ transfer function of the energy transfer experimentally.