Analysis of solid-state saturable absorbers with temperature dependent absorption cross-sections

We describe a comprehensive model which can be used in the continuous-wave (cw) analysis of solid-state transition metal-doped saturable absorbers, which, in addition to the commonly observed temperature dependence of the refractive index and fluorescence lifetime, also exhibit a temperature dependent absorption cross-section. By using a rate equation analysis, two coupled differential equations are derived for the beam power and the q-parameter of the pump beam. To test the validity of the model, we analyzed the cw and pulsed saturation data taken with Cr4+:forsterite crystals which are subject to these three thermal effects at 1064 nm. Data for electric field parallel to the crystal b-axis (E‖b) and c-axis (E‖c) were analyzed. Results indicate that when thermal loading effects are taken into account, better agreement is obtained between the cross-section results of the cw and pulsed saturation data. In particular, inclusion of thermal effects reduced the fractional deviation between the average cw and pulsed cross-section values from 23% to 2% and from 34% to 29% for the E‖c and E‖b cases, respectively. In the E‖b case, the average absorption cross-section and the normalized strength of excited-state absorption were further determined to be 5.98 × 10−19 cm2 and 0.45, respectively. The presented model can be readily extended to analyze other thermal effects or other media with different energy-level schemes.