Photon avalanche and the mean-field approximation

Starting from a microscopic description, we show the analogy between photon avalanche and second-order phase transition. This justifies the validity of the mean-field approximation. Then we show that the rate equations reproduce quantitatively the experimental results as soon as the Gaussian intensity profile of the input beam is taken into account. Moreover, we apply the general Landau theory to the photon avalanche: the absorption between the excited state is the control parameter of the transition whereas the ground-state absorption is an external field. By this way the impact of the residual nonresonant ground-state absorption is clarified.