It is demonstrated that the microscopic mechanism of the photorefractive (PR) effect in organic composites with; low glass transition temperatures involves the formation of refractive index gratings through a,space-charge held-modulated Kerr effect. A tensorial formulation of the macroscopic aspects of the PR Kerr effect and its microscopic interpretation is presented. The second-order dipole orientation term containing the anisotropy of the first-order optical polarizability alpha(-omega;omega) is shown to yield the dominant contribution to the Kerr susceptibility chi((3))(-omega;omega,0,0). a class of special chromophores having negligible second-order polarizabilities : beta(-omega;omega,0) and large dipole moments mu has been identified in order to optimize this term. These chromophores are not subject to the efficiency-transparency tradeoff typically encountered with second-order nonlinear optical (NLO) chromophores, providing highly transparent materials with large PR Kerr response. Contrary to previous approaches in this field, the best-performing PR polymers are then expected to employ chromophores that would be-useless for second-order applications (negligible beta). We report PR of the material 30% 2,6-di-n-propyl-4H-pyran-4-ylidenemalononitrile (DPDCP) : 15% N,N’-bis(3-methylphenyl)-N,N’-bis(phenyl)benzidine (TPD):55% poly(methyl methacrylate) (PMMA):0.3% C-60 as an illustration of this principle. A 100 mu m thick film of this material exhibits a steady-state diffraction efficiency of eta=25% and net two-beam coupling of Gamma=50 cm(-1) at a bias field of 100 V/mu m and a wavelength of 676 nm. The macroscopic Kerr susceptibility of the material is related to molecular electronic properties of the chromophore DPDCP which were independently determined by experiments in solution and by quantum chemical calculations.