Unconventional diffusion of light in strongly localized open absorbing media

Very recent experiments have discovered that localized light in strongly absorbing media displays intriguing diffusive phenomena. Here we develop a first-principles theory of light propagation in open media with arbitrary absorption strength and sample length. We show analytically that waves in localized open absorbing media exhibit highly unconventional diffusion. Specifically, wave energy transport follows the diffusion equation with the diffusion coefficient exhibiting spatial resolution. Most strikingly, despite that the system is controlled by two parameters - the ratio of the localization (absorption) length to the sample length - the spatially resolved diffusion coefficient displays novel single parameter scaling: It depends on the position in the sample via the returning probability. Our analytic predictions for this diffusion coefficient are confirmed by numerical simulations. In the strong absorption limit they agree well with the experimental results.