Relation between the relaxation of intrinsic stimulated picosecond emission from GaAs with a characteristic charge-carrier cooling time

During the powerful picosecond optical pumping of a thin ($\sim$1 $\mu$m) GaAs layer, a stimulated intense (up to 1 GW/cm$^2$) picosecond emission appeared. As was found, for a fixed density of the pump pulse energy, with an increase of its diameter the characteristic picosecond time $\tau_r$ of the emission and carrier density $n$ relaxation increases. Due to interrelation of the density and the temperature of the carriers at high-intensity emission (in the saturation state of the emission amplification), time $\tau_r$ is associated with the characteristic temperature relaxation time $\tau_T$ of the photo-pumped carriers, which was determined earlier theoretically with the emission-caused carrier heating taken into account. The corresponding analytical expressions for $\tau_r$ as a functions of $\tau_T$ are consistent with the above experimental results.