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Very recent experiments have discovered that localized light in stronglyabsorbing media displays intriguing diffusive phenomena. Here we develop afirst-principles theory of light propagation in open media with arbitraryabsorption strength and sample length. We show analytically that photons inlocalized open absorbing media exhibit unusual Brownian motion. Specifically,wave transport follows the diffusion equation with the diffusion coefficientexhibiting spatial resolution. Most strikingly, despite that the system iscontrolled by two parameters -- the ratio of the localization (absorption)length to the sample length -- the spatially resolved diffusion coefficientdisplays novel single parameter scaling: it depends on the space via thereturning probability. Our analytic predictions for this diffusion coefficientare confirmed by numerical simulations. In the strong absorption limit theyagree well with the experimental results.

Unusual Brownian motion of photons in open absorbing media