Steady State Analysis of Photon Avalanche Effect

Abstract

An analysis of the three-level model for avalanche up-conversion in a steady state case is presented. Until now, no quantitative criterion has been defined to distinguish avalanche from nonlinear processes giving rise to anti--Stokes emissions. From our model, we drive a quantitative limit for the ratio between non resonant and resonant absorption cross-section to observe an avalanche process. Application of these calculations to practical cases demonstrates the ability of our model to predict an avalanche behavior. The interest of avalanche to pump up-conversion lasers is discussed by introducing a term in the rate equations due to the stimulated emission.