Non-linear dynamics of absorption and photo-bleaching of dyes
  The celebrated Lambert-Beer law of light absorption in photochromic media is only valid at low intensities of incident light and low concentration of chromophore. Here we address the generic problem of photo-absorption dynamics, experimentally studying the case of azobenzene isomerization. We show that the non-linear regime is very common and easy to achieve in many practical situations, especially in thick samples where the light depletes the chromophore in the first layers and can propagate through the medium with a sub-exponential law. Importantly, the crossover into the non-linear absorption regime only weakly depends on the dye concentration and solution viscosity. We experimentally quantify the characteristics of this peculiar optical response and determine the key transition rate constants. 
Francesca Serra and Eugene M. Terentjev