Enhanced propagation of photon density waves in random amplifying media

We demonstrate enhanced wavelike character of diffuse photon density waves (DPDW) in an amplifying random medium. The amplifying nature makes it necessary to choose the wave solution that grows inside the amplifying medium, and has a propagation vector pointing opposite to the growth direction. This results in negative refraction of the DPDW at an absorbing-amplifying random medium interface as well as the possibility of supporting "anti"-surface-like modes at the interface. A slab of an amplifying random medium sandwiched between two absorbing random media supports waveguide resonances that can be utilized to extend the imaging capabilities of DPDW.