Analysis of Gain Volume in Random Laser in a Spherical Multiple Scattering Medium

We performed numerical simulation of a random laser in a spherical multiple scattering medium in order to examine the saturation absorption in the excitation process and the resultant increasing process of the gain volume under the random laser action. The size of the gain volume increases with 1/3 power of the excitation pulse energy in the weak excitation region, and then approaches a critical value L_th when the excitation pulse energy is increased above the threshold. The dependence of L_th, as well as the dependence of the threshold excitation pulse energy on the dye concentration, transport mean free path, stimulated emission cross section and excited state lifetime were also examined. These results of the simulation well correspond to the experimental results by a two-beam spatial-correlation method.