Intrinsic limits of the efficiency of erbium 3-μm lasers

Mathematical modeling, based on rate equations, is used to estimate the theoretical limit of the emission efficiency of 3-μm Er:YAG laser (laser transition ⁴I₁₁2/→⁴I₁₃2/) in both continuous wave (CW) and free-generation regimes. This model exclusively uses spectroscopic data and includes upconversion from both initial and terminal laser levels as well as the cross relaxation from the "pump level" ⁴S₃2/. The recirculation of the excitation on the metastable levels of the Er³⁺ ion - produced by the energy-transfer processes, very active at high erbium concentrations - leads to supraunitary quantum efficiency and high emission efficiency in the CW regime. In the Q-switch regime, in contrast with CW (or free generation) regime, the energy-transfer processes are "frozen" during the giant pulse generation, the access to the stored energy is limited and the laser efficiency is rather low. In this paper, we find simple analytic expressions for the emission efficiency in CW, free-generation, and Q-switch regimes. The same figures of merit are used for all these regimes. The predictions of our model are then compared with available experimental results. Some suggestions to improve the overall efficiency of the 3-μm erbium lasers, working in the Q-switch regime, are given.