Illumination intensities that are used to induce scattering and fluorescence in aerosols can be large enough to cause variations in the refractive index. Methods used to calculate the scattering from homogeneous particles may not be valid for these systems. We use the finite-difference time-domain method and an iterative technique to model scattering by microspheres that contain a saturable absorber. We illustrate this technique by calculating the scattering from spheres that contain tryptophan. We show the Mueller scattering matrices along with the internal intensity distributions for different incident intensities. The backscattering increases as the illumination intensity becomes large enough to saturate the absorption in regions of the sphere.