Supersymmetric field theory of local light diffusion in semi-infinite media

A supersymmetric field theory of light diffusion in semi-infinite disordered media is presented. With the help of this technique we justify-at the perturbative level-the local light diffusion proposed by Tiggelen, Lagendijk, and Wiersma [Phys. Rev. Lett. 84, 4333 (2000)], and show that the coherent backscattering line shape of medium bar displays a crossover from two-dimensional weak to quasi-one-dimensional strong localization.