Er-doped fiber is a three-states system. The typical pumping wavelength is 980 and 1480 nm, and the oscillation wavelength is around 1550 nm (see here). In the case of 980 nm pumping, compared with the case of 1480 nm pumping, the efficiency of power conversion from the pumping light to the signal light is lower, as well as the the width of absorption spectrum is narrower.
The gain coefficient of Er fiber is enlarged by increasing an amount of Er3+. However, as the Er concentration increases, the pumping efficiency decreases because of the concentration quenching. Er concentration for the quenching is, for pure SiO2 host, several hundreds wtppm. The Er concentration is increased when Al, which can suppress the concentration quenching, is co-doped into SiO2 host (Al2O3-SiO2 host), but is at most up to around 1000 wtppm. The effect of increasing Er3+ concentration on improving gain coefficient is limited. This limitation is made by a cooperative up-conversion between the ions. The cooperative up-conversion is the following phenomenon; provided that a couple of Er3+, excited to a 4I13/2, are close to each other, one of two Er3+ is excited to 4I9/2, while the other is deactivated to the ground state. The increase in the density of Er3+ cause the formation of Er3+ clustering, and then makes the distance between the ions closer, which yields the cooperative up-conversion. This process is schematically shown in Fig. 1 (a).
In an Er:Yb fiber where Yb and Er are co-doped, it is possible to improve the limitation of Er3+ doping concentration, which is a reason for the concentration quenching (suppression of concentration quenching). This is because the distance of Er3+ becomes long when Er+3 is surrounded by several Yb3+, of which radius is comparable with that of Er3+, and forms a cluster. The wide absorption band of Yb3+ is utilizable for the pumping wavelength.
Energy level diagram of Er:Yb is shown in Fig. 1 (b). After excited to the 2F5/2 level by 910-980 nm light, Yb3+ interacts with Er3+, then transfers to the ground state, 2f7/2, while Er3+ is excited to the 4I11/2 level (energy transfer). Er3+, excited to the 4I11/2 level, goes through a non-radiative decay, and is relaxed to the 4I12/2 level. As a result, the inverse distribution is formed between the 4I13/2 and 4I15/2 levels. The efficiency of energy transfer from Yb3+ to Er3+ largely depends on the doping ratio of Er3+ and Yb3+ and the core composition. An Er:Yb fiber, at 980 nm pumping, has a lower conversion efficiency (~ 45 %) compared with an Er fiber because of the complex process of energy transfer, such as Er-Yb transitions and parasitic oscillation between the levels in Yb.
Fig. 2 represents cross-sections of absorption and stimulated emission of Er3+ in the Er:Yb-doped phosphate glass as a reference.
Fig. 2 Cross-section of absorption and stimulated emission of Er3+