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.
Bubbles defects have been always observed in sapphire
crystals. Their distribution and size are strongly dependent on the
growth conditions. We have studied the effect of the pulling rate
on the bubbles' size and their distribution in sapphire rods grown
by the micropulling down (μ-PD) technique. Using a central circular
capillary die of shape factor 0.33, the bubbles' diameter decreased
as a function of the pulling rate. The transmission decreased at a
pulling rate greater than 1 mm/min.
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