How to describe the scattered ultrashort laser pulse profiles measured inside and at the surface of a random medium using the diffusion theory

The temporal profiles of ultrashort laser pulses propagating in random scattering media were measured inside and outside the media and analyzed using the diffusion theory. The scattered pulse profiles measured inside the random media were found to be described by the photon density instead of the photon flux. In contrast, the scattered pulse profiles emitted from the surface of the media were found to be described by either the photon density or the photon flux. These results can be consistently explained by the diffuse intensity of transport theory.