Gain saturation study and measurement of terminal level lifetime for Yb:YAG crystal

We formulate a set of coupled rate equations describing the dynamic behaviour of a laser extraction based on the energy-level structure of a Yb:YAG crystal. A numerical computation of the energy extraction is carried out which includes the effects of the pulse width and the terminal level lifetime. According to the result of the computation, we formulated an empirical expression for the saturation fluence in Yb:YAG crystals that explicitly depends upon the ratio of the pulse width to the terminal level lifetime. The empirical saturation fluence, when substituted within the Frantz and Nodvik solution for energy extraction, can be used to accurately model the energy extracted from Yb:YAG crystal amplifiers. An experiment is performed in a Yb:YAG disc amplifier to measure the input fluence, output fluence and pulse length. We compare the experimental gain saturation data of the Yb:YAG disc amplifier with our empirical solution and determine the terminal level lifetime from a best fit to the data. The terminal level lifetime of Yb:YAG is found to be 275 ps ± 105 ps.