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We derive a non-linear sigma-model for the transport of light (classicalwaves) through a disordered medium. We compare this extension of the model withthe well-established non-linear sigma-model for the transport of electrons(Schroedinger waves) and display similarities of and differences between bothcases. Motivated by experimental work (M. van Albada et al., Phys. Rev. Lett.66 (1991) 3132), we then generalize the non-linear sigma-model further toinclude resonance scattering. We find that the form of the effective action isunchanged but that a parameter of the effective action, the mean level density,is modified in a manner which correctly accounts for the data.Comment: 4 pages, 1 Figure, to be published in Europhysics Letter

Non-linear supersymmetric σ-model for diffusive scattering of classical waves with resonance enhancement