Dependence of the neodymium random laser threshold on the diameter of the pumped spot

We experimentally studied the dependence of the threshold energy density E_th/S in Nd_0.5La_0.5Al₃(BO₃)₄ random laser on the diameter of the pumped spot d and found that at d≥130μm, E_th/S is proportional to 1/d+const. This functional dependence is different from the one commonly expected in the case of diffusion, ∝1/d²+const. However, the obtained experimental dependence does not mean the failure of the diffusion model. Calculating the mean photon´s residence time τ_res^p (which photons, making their diffusion-like random walks, spend inside the gain volume) as the function of d and further assuming that E_th/S∝(τ^p_res)^-1, we predicted the experimentally obtained functional dependence, ∝1/d+const. The major difference between our model and that of and was in the boundary conditions.