Photon migration in disordered media

Numerical and analytical methods are used to study a model for the multiple scattering of photons in the presence of randomly reflecting inclusions. The photons are injected into a semi-infinite medium near its surface, and are absorbed by the surface or within the medium. In the medium the photons can diffuse only through voids between the reflecting inclusions, where the void structure has been modeled as a fractal object. Our analytical approach is based on an analogy between the kinetics of a continuous-time random-walk model and the movement of random walkers on fractals. For the case of nonabsorbing media, we find the survival of photons within the medium after n steps to be S(n)nw-1+1/d and the intensity profile at a distance from the injection point to be w-d, where dw is the diffusion exponent for fractals. For the case of absorbing media, scales as exp(-w1/d), where is the absorption coefficient of the fractal medium, and are exponents related to the fractal dimensions, and is a constant. We also calculate the mean time and the average maximal depth of photons that emerge at a distance.