  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.
