We have derived an analytic approach, based on the hypothesis of the effective-medium theory, to evaluate the effective dielectric magnitudes, including the effective third order nonlinear optical susceptibility , of a heterogeneous two-component medium in which one of the components (the host matrix or the embedded particle respectively) presents nonlinear behaviour. Our formulation allows us to solve the full nonlinear problem in the whole range of concentrations without treating the nonlinear effects as a small perturbation to the linear behaviour. Therefore, it can be considered as an upper limit of the commonly used low-field nonlinear approximations for heterogeneous materials. Under certain conditions, these composites can exhibit a bistable regime that the present theory properly describes in wide ranges of the concentration, shape, wavelength, dielectric contants and intrinsic nonlinear optical susceptibility of the nonlinear component as well as in terms of the intensity of the external electric field. The present approach has been used to calculate the nonlinear optical response of Cu-Al_2O_3 nanocomposites.
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