We examine how intense optical beams can penetrate deeply into highly absorbing media by a nonlinear, photobleaching process. The role of stimulated recovery to the dye ground state can be important and is delineated. This analysis of nonlinear absorption processes is applicable in general to situations where chromophores are irradiated, for instance, in biology. We examine the implications for the bending of cantilevers made of heavily dye-loaded nematic photosolids, that is nematic glasses and elastomers that have large mechanical reactions to light. In particular we describe the bending of cantilevers sufficiently absorbing that they would not bend if Beer's law were applicable. We quantify the role of optically generated heat in determining the mechanical response and conclude that in general it is minor in importance compared with optical effects.